SyncVals · Trajectory

neonatal-drug-exposure-nlme

claude-code claude-opus-4-8 ✓ resolved GOOD_SUCCESS ↑ View task

Solved from the instruction alone, tests/ and solution/ were withheld from the agent's workspace and restored only for grading.

Reward = tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it.

Classification , post-hoc; cannot change the reward

GOOD_SUCCESSLegitimate solve, implements the asked-for behavior; tests verify real functionality.

SubtypeLegitimate Solution

EvidenceAgent trajectory shows complete implementation of NLME model from scratch. Test results show all 10 required outputs present and verified: AIC strictly decreasing (1020→971→891), LRT p-values (8e-13, ~0) both < 1e-6, correlation metrics (0.81 > 0.55, 0.97 > 0.75) all passing. All counts (n_subjects=59, n_obs=150) derived at runtime from CSV. Runtime 52 seconds well under 600s limit. Test output shows PASS (reward=1.0).

Root causeAgent properly understood a hard pharmacometrics task requiring NLME modeling from instruction.md + manifest, implemented a complete Laplace-approximation based one-compartment PK model in Julia with proper numerical optimization, and generated correct statistical outputs and diagnostic visualizations that pass all verification checks.

RecommendationN/A - task is fine

Trajectory

Tool-by-tool agent trajectory

102 tool calls · 3 tool types · 102 steps

Work only in `/app/analysis.jl`. The bundled inputs are: - `/app/Phenobarb.csv` - `/app/dataset_manifest.json` Do not read from `/tests` or `/solution`. ## Background `Phenobarb.csv` is a real neonatal pharmacokinetics study of preterm infants given intravenous phenobarbital. Each baby contributes a small number of serum concentration measurements interleaved with dose events. A neonatology analytics team wants a population PK fit that estimates clearance and volume of distribution at the population level and per subject, tests whether birth weight and Apgar category shift those parameters, and produces diagnostic plots for the clinical report. Your `analysis.jl` will be executed on a held-out perturbation of `Phenobarb.csv` with a different number of subjects and rows. Derive all counts from the CSV at runtime , do not hardcode subject or row counts. ## Input semantics `Phenobarb.csv` has exactly these columns: - `Subject` , integer subject identifier - `Wt` , birth weight in kg - `Apgar` , Apgar score at 5 minutes, integer 1 through 10 - `ApgarInd` , two-level factor, either `< 5` (asphyxiated) or `>= 5` (normal) - `time` , time in hours since first event for that subject - `dose` , dose in mg at this event row, missing for sample rows - `conc` , serum concentration in mg/L at this event row, missing for dose rows A row is a dose event when `dose` is non-missing; a sample event when `conc` is non-missing. Do not drop dose rows. Use `dataset_manifest.json` as the contract source for required output filenames and exact column order for every output CSV. ## Required modelling Fit a one-compartment open PK model with first-order elimination at the population level. Model clearance and volume on the log scale (`lCl`, `lV`). Each subject has random intercepts on `lCl` and `lV` with a diagonal (no correlation) random-effect covariance structure. Do the covariate build-up in this exact sequence: 1. **Base model** (`base`): `lCl ~ 1`, `lV ~ 1` 2. **cl_wt model** (`cl_wt`): add birth weight as fixed effect on `lCl` 3. **Full model** (`full`): keep weight on `lCl`, add `ApgarInd` on `lCl`, add weight on `lV` Each step must yield a strictly lower AIC than the step before it. The likelihood-ratio p-value for both step 1→2 and step 2→3 must be below 1e-6. ## Required output files All files go into `/app/output/`. Use exact filenames from `dataset_manifest.json`. ### Tables 1. **`model_summary.json`** , JSON for the final (full) model with exactly: - `n_obs` , integer, count of non-missing `conc` rows - `n_subjects` , integer, count of distinct Subject values - `fixed_effects` , array of objects with fields `term`, `estimate`, `std_error`, `t_value`, `df`. Terms in this exact order: `lCl.(Intercept)`, `lCl.Wt`, `lCl.ApgarInd>= 5`, `lV.(Intercept)`, `lV.Wt` - `random_effects_sd` , object with positive numeric fields `lCl`, `lV`, `Residual` - `logLik`, `aic`, `bic` , numeric scalars for the final model 2. **`lrt_chain.csv`** , columns (in order): `step, model_name, n_params, logLik, AIC, BIC, LR_stat, LR_pvalue` - `step`: 1, 2, 3; `model_name`: `base`, `cl_wt`, `full` - `LR_stat` and `LR_pvalue` are empty/missing for step 1 3. **`per_subject_params.csv`** , columns: `Subject, Cl, V` - Empirical-Bayes estimates in native units (not log scale), all positive - Sorted by integer `Subject` ascending 4. **`obs_vs_pred.csv`** , columns: `Subject, time, conc_obs, pred_pop, pred_ind` - One row per non-missing concentration observation - `pred_pop`: population prediction (zero random effects) - `pred_ind`: individual prediction (subject empirical-Bayes estimates) - `cor(conc_obs, pred_ind)` must exceed 0.75; `cor(conc_obs, pred_pop)` must exceed 0.55 - Sorted by Subject then time 5. **`residual_diagnostics.csv`** , columns: `Subject, time, fitted_ind, resid, std_resid` - `resid = conc_obs - fitted_ind` - `std_resid = resid / σ` where `σ` is the estimated residual SD …[truncated]

Let me start by exploring the data and understanding what's needed.

bash

ls /app && head -20 /app/Phenobarb.csv && cat /app/dataset_manifest.json

output

Phenobarb.csv
analysis.jl
dataset_manifest.json
output
"Subject","Wt","Apgar","ApgarInd","time","dose","conc"
1,1.4,7,">= 5",0,25,
1,1.4,7,">= 5",2,,17.3
1,1.4,7,">= 5",12.5,3.5,
1,1.4,7,">= 5",24.5,3.5,
1,1.4,7,">= 5",37,3.5,
1,1.4,7,">= 5",48,3.5,
1,1.4,7,">= 5",60.5,3.5,
1,1.4,7,">= 5",72.5,3.5,
1,1.4,7,">= 5",85.3,3.5,
1,1.4,7,">= 5",96.5,3.5,
1,1.4,7,">= 5",108.5,3.5,
1,1.4,7,">= 5",112.5,,31
2,1.5,9,">= 5",0,15,
2,1.5,9,">= 5",2,,9.7
2,1.5,9,">= 5",4,3.8,
2,1.5,9,">= 5",16,3.8,
2,1.5,9,">= 5",27.8,3.8,
2,1.5,9,">= 5",40,3.8,
2,1.5,9,">= 5",52,3.8,
{
  "dataset_name": "Phenobarb",
  "source": "nlme::Phenobarb (Pinheiro & Bates 2000, Mixed-Effects Models in S and S-PLUS, section 6.4)",
  "columns": {
    "Subject": "integer subject identifier",
    "Wt": "birth weight in kg",
    "Apgar": "Apgar score at 5 minutes, 1 through 10",
    "ApgarInd": "Apgar category factor, '< 5' or '>= 5'",
    "time": "hours since first event",
    "dose": "dose in mg, present on dose rows only",
    "conc": "serum concentration in mg/L, present on sample rows only"
  },
  "required_outputs": {
    "model_summary": "model_summary.json",
    "lrt_chain": "lrt_chain.csv",
    "per_subject_params": "per_subject_params.csv",
    "obs_vs_pred": "obs_vs_pred.csv",
    "residual_diagnostics": "residual_diagnostics.csv",
    "plot_conc_profile": "plot_conc_profile.png",
    "plot_per_subject_fit": "plot_per_subject_fit.png",
    "plot_covariate_effect": "plot_covariate_effect.png",
    "plot_obs_vs_pred": "plot_obs_vs_pred.png",
    "plot_residuals": "plot_residuals.png"
  },
  "column_order": {
    "lrt_chain": ["step", "model_name", "n_params", "logLik", "AIC", "BIC", "LR_stat", "LR_pvalue"],
    "per_subject_params": ["Subject", "Cl", "V"],
    "obs_vs_pred": ["Subject", "time", "conc_obs", "pred_pop", "pred_ind"],
    "residual_diagnostics": ["Subject", "time", "fitted_ind", "resid", "std_resid"]
  },
  "model_chain": {
    "step_1": "base: lCl + lV ~ 1",
    "step_2": "cl_wt: lCl ~ Wt, lV ~ 1",
    "step_3": "full: lCl ~ Wt + ApgarInd, lV ~ Wt"
  }
}

bash

wc -l /app/Phenobarb.csv && awk -F, 'NR>1 {print $1}' /app/Phenobarb.csv | sort -u | wc -l

output

745 /app/Phenobarb.csv
59

bash

julia -e 'using Pkg; Pkg.status()'

output

Status `/usr/local/share/julia/environments/v1.10/Project.toml`
  [336ed68f] CSV v0.10.16
  [13f3f980] CairoMakie v0.15.10
  [a93c6f00] DataFrames v1.8.2
  [31c24e10] Distributions v0.25.125
  [0f8b85d8] JSON3 v1.14.3
  [429524aa] Optim v2.1.0
  [2913bbd2] StatsBase v0.34.11
  [10745b16] Statistics v1.10.0

Now I understand the task. Let me think through the modeling approach: 1. **One-compartment PK model with first-order elimination:** - Dose events add to the amount in compartment: A(t+) = A(t-) + dose - Between events: A(t) = A(t0) * exp(-k*(t-t0)) where k = Cl/V - Concentration: C(t) = A(t) / V - For each subject i: Cl_i = exp(lCl_pop + η_Cl_i), V_i = exp(lV_pop + η_V_i) - η_Cl_i ~ N(0, σ_Cl²), η_V_i ~ N(0, σ_V²), independent - Observation: y_ij = C(t_ij; Cl_i, V_i) + ε_ij, ε_ij ~ N(0, σ²) 2. **Estimation:** Use Laplace approximation or Gaussian-Hermite quadrature, or a simpler approach: Since there are only 2 random effects per subject, I can use Laplace approximation by maximizing the conditional joint log-likelihood over η, then approximating the marginal with Laplace. Given time constraints, let me go with Laplace approximation. Actually, since we need: - AIC strictly decreasing through the chain - LRT p-value < 1e-6 for both steps The Phenobarb dataset is well-known; the model `full` is known to be much better. Let me implement carefully. Let me write a Laplace-approximation based NLME fitter. Approach: - For each subject with random effects η = (η_Cl, η_V): - Cl_i = exp(β_Cl · x_Cl + η_Cl) - V_i = exp(β_V · x_V + η_V) - Given dose/sample times, simulate the amount trajectory at each observation: - A is the amount in the compartment - k = Cl/V - Between events: A decays exponentially - At dose event: add dose - At sample event: conc_pred = A / V - Conditional log-lik: sum over obs of log N(y - pred; 0, σ²), plus log N(η; 0, diag(σ_Cl², σ_V²)) - For each subject, find η̂ = argmax of conditional log-lik, compute Hessian H at η̂ - Laplace approx: log p(y_i | θ) ≈ conditional log-lik at η̂ - 0.5 * log det(H / (2π)) Actually, the Laplace formula is: ∫ exp(f(η)) dη ≈ exp(f(η̂)) * (2π)^(d/2) / sqrt(det(-f''(η̂))) So log p(y_i | θ) = log ∫ p(y_i | η, θ) p(η | θ) dη ≈ f(η̂) + (d/2) log(2π) - 0.5 log det(-f''(η̂)) where f(η) = log p(y_i | η, θ) + log p(η | θ). Since the random effects are diagonal, we have 2 random effects per subject, so d=2. The total marginal log-likelihood is the sum over subjects. Parameters θ: - β_Cl (intercept + weight + apgar) - β_V (intercept + weight) - σ_Cl, σ_V, σ (on log scale for positivity) Optimisation over θ using Optim. Inner optimisation over η using Newton-type or BFGS. Let me write this. I need this to work fast enough (< 300 sec total). Let me code this up carefully. Actually, given the time constraints, I'll use analytical gradient where possible. Let's just use Optim with BFGS. Key steps: 1. Parse CSV 2. For each subject, set up events (dose and sample lists) 3. Define conditional log-lik as a function of η and θ 4. Inner optim: find η̂ for each subject 5. Outer optim: find θ that maximizes sum of Laplace-approximated marginal log-liks 6. Final: compute per-subject η̂, predictions, etc. Let me think about stability. For the simulation: Between events, amount decays: A(t_new) = A(t_old) * exp(-k*(t_new - t_old)) At dose event at time t: A(t+) = A(t-) + dose At sample event: predicted conc = A(t) / V I need to iterate through events in time order for each subject. Let me code this carefully. For AIC calculations: - base: 2 fixed + 2 RE SDs + 1 residual SD = 5 params - cl_wt: 3 fixed + 2 RE SDs + 1 residual SD = 6 params - full: 5 fixed + 2 RE SDs + 1 residual SD = 8 params For fixed effects table, the term `lCl.ApgarInd>= 5` means ApgarInd being ">= 5" relative to reference "< 5". So I need to ensure my factor coding makes "< 5" the reference level. For degrees of freedom, use a large-sample approximation: df ~ n_obs - n_params? Or use some other. Let me use df = n_obs - n_fixed. Actually, in nlme::nlme output, df for fixed effects is N - p, where N is the number of observations and p is the number of fixed effects (or similar). Let me use df = n_obs - n_fixed_effects. OK let me start writing. Actually I should keep th …[truncated]

bash

head -50 /app/Phenobarb.csv | awk -F, 'NR>1 && $6!="" {print "dose:",$0} NR>1 && $7!="" {print "samp:",$0}'

output

dose: 1,1.4,7,">= 5",0,25,
samp: 1,1.4,7,">= 5",2,,17.3
dose: 1,1.4,7,">= 5",12.5,3.5,
dose: 1,1.4,7,">= 5",24.5,3.5,
dose: 1,1.4,7,">= 5",37,3.5,
dose: 1,1.4,7,">= 5",48,3.5,
dose: 1,1.4,7,">= 5",60.5,3.5,
dose: 1,1.4,7,">= 5",72.5,3.5,
dose: 1,1.4,7,">= 5",85.3,3.5,
dose: 1,1.4,7,">= 5",96.5,3.5,
dose: 1,1.4,7,">= 5",108.5,3.5,
samp: 1,1.4,7,">= 5",112.5,,31
dose: 2,1.5,9,">= 5",0,15,
samp: 2,1.5,9,">= 5",2,,9.7
dose: 2,1.5,9,">= 5",4,3.8,
dose: 2,1.5,9,">= 5",16,3.8,
dose: 2,1.5,9,">= 5",27.8,3.8,
dose: 2,1.5,9,">= 5",40,3.8,
dose: 2,1.5,9,">= 5",52,3.8,
samp: 2,1.5,9,">= 5",63.5,,24.6
dose: 2,1.5,9,">= 5",64,3.8,
dose: 2,1.5,9,">= 5",76,3.8,
dose: 2,1.5,9,">= 5",88,3.8,
dose: 2,1.5,9,">= 5",100,3.8,
dose: 2,1.5,9,">= 5",112,3.8,
dose: 2,1.5,9,">= 5",124,3.8,
samp: 2,1.5,9,">= 5",135.5,,33
dose: 3,1.5,6,">= 5",0,30,
samp: 3,1.5,6,">= 5",1.5,,18
dose: 3,1.5,6,">= 5",11.5,3.7,
dose: 3,1.5,6,">= 5",23.5,3.7,
dose: 3,1.5,6,">= 5",35.5,3.7,
dose: 3,1.5,6,">= 5",47.5,3.7,
dose: 3,1.5,6,">= 5",59.3,3.7,
dose: 3,1.5,6,">= 5",73,3.7,
samp: 3,1.5,6,">= 5",83.5,,23.8
dose: 3,1.5,6,">= 5",84,3.7,
dose: 3,1.5,6,">= 5",96.5,3.7,
dose: 3,1.5,6,">= 5",108.5,3.7,
dose: 3,1.5,6,">= 5",120,3.7,
dose: 3,1.5,6,">= 5",132,3.7,
samp: 3,1.5,6,">= 5",134.3,,24.3
dose: 4,0.9,6,">= 5",0,18.6,
samp: 4,0.9,6,">= 5",1.8,,20.8
dose: 4,0.9,6,">= 5",12,2.3,
dose: 4,0.9,6,">= 5",24.3,2.3,
dose: 4,0.9,6,">= 5",35.8,2.3,
dose: 4,0.9,6,">= 5",48.1,2.3,
samp: 4,0.9,6,">= 5",59.3,,23.9

Now I have a clear picture. Let me write the analysis script.

str_replace_based_edit_tool

command: create
path: /app/analysis.jl
file_text: using DataFrames
using CSV
using JSON3
using CairoMakie
using Distributions
using Optim
using Statistics
using LinearAlgebra

# -------------------------------------------------------------------
# Load data
# -------------------------------------------------------------------
const APP_DIR = "/app"
const OUT_DIR = joinpath(APP_DIR, "output")
isdir(OUT_DIR) || mkpath(OUT_DIR)

df = CSV.read(joinpath(APP_DIR, "Phenobarb.csv"), DataFrame)
sort!(df, [:Subject, :time])

subjects_all = sort(unique(df.Subject))
n_subjects = length(subjects_all)
n_obs_total = sum(.!ismissing.(df.conc))

# -------------------------------------------------------------------
# Per-subject event extraction
# -------------------------------------------------------------------
struct SubjEvents
    subject::Int
    wt::Float64
    apgar_ge5::Int           # 1 if ">= 5", 0 if "< 5"
    times::Vector{Float64}
    doses::Vector{Float64}    # 0.0 if sample
    is_sample::Vector{Bool}
    conc::Vector{Float64}     # raw (NaN if dose-only row)
    sample_idx::Vector{Int}   # indices of sample events in the event vectors
    obs_conc::Vector{Float64} # observed concentrations (length == count(is_sample))
    obs_time::Vector{Float64} # times for those samples
end

function build_subject_events(sdf)
    sdf = sort(sdf, :time)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(Float64, n)
    is_sample = falses(n)
    cvec = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose)
            doses[i] = row.dose
        end
        if !ismissing(row.conc)
            is_sample[i] = true
            cvec[i] = row.conc
        end
    end
    sidx = findall(is_sample)
    obs_c = cvec[sidx]
    obs_t = times[sidx]
    apgar = String(sdf.ApgarInd[1])
    apgar_ge5 = apgar == ">= 5" ? 1 : 0
    return SubjEvents(sdf.Subject[1], sdf.Wt[1], apgar_ge5,
                      times, doses, is_sample, cvec, sidx, obs_c, obs_t)
end

subj_data = [build_subject_events(df[df.Subject .== s, :]) for s in subjects_all]

# -------------------------------------------------------------------
# One-compartment simulation: amounts at each event, conc at samples
# -------------------------------------------------------------------
function simulate(s::SubjEvents, Cl::Float64, V::Float64)
    k = Cl / V
    amt = 0.0
    t_prev = 0.0
    n = length(s.times)
    preds = Vector{Float64}(undef, length(s.sample_idx))
    j = 0
    for i in 1:n
        dt = s.times[i] - t_prev
        if dt > 0
            amt *= exp(-k * dt)
        end
        if s.doses[i] > 0
            amt += s.doses[i]
        end
        if s.is_sample[i]
            j += 1
            preds[j] = amt / V
        end
        t_prev = s.times[i]
    end
    return preds
end

# -------------------------------------------------------------------
# Model structure: describe design for lCl and lV
# A "model spec" holds the covariate vectors per subject for Cl and V
# plus which covariates are included.
# -------------------------------------------------------------------
struct ModelSpec
    name::String
    # column labels for the fixed effects, in order
    cl_terms::Vector{String}
    v_terms::Vector{String}
    # For each subject, the design vector for lCl and lV
    cl_x::Vector{Vector{Float64}}
    v_x::Vector{Vector{Float64}}
end

function make_spec(name, cl_terms, v_terms, subj_data)
    function vec_for(terms, s::SubjEvents)
        v = Float64[]
        for t in terms
            if t == "(Intercept)"
                push!(v, 1.0)
            elseif t == "Wt"
                push!(v, s.wt)
            elseif t == "ApgarInd>= 5"
                push!(v, Float64(s.apgar_ge5))
            else
                error("unknown term $t")
            end
        end
        return v
    end
    cl_x = [vec_for(cl_terms, s) for s in subj_data]
    v_x  = [vec_for(v_terms, s) for s in subj_dat
…[truncated]

output

Existing file was successfully overwritten at /app/analysis.jl

bash

cd /app && timeout 280 julia analysis.jl 2>&1 | tail -60

output

[stderr]
Terminated

Takes too long. Need to speed up the fit. Let me see where time is spent. The inner subject_laplace uses BFGS finite-diff + 2×2 numerical Hessian computed separately. The outer uses NelderMead + BFGS on an 8-parameter space. That's a lot of function evaluations. Let me think about optimizations: 1. The NelderMead step is expensive. Each outer eval calls Laplace for each subject. 2. Reduce iteration counts 3. Speed up inner optimization Let me think - the biggest speedup is: - Use NelderMead only briefly then switch to BFGS - Inner: use just BFGS without separate Hessian step Actually a better structure: for the inner η optimization, I can use a simple Newton-Raphson with 2D gradient and Hessian computed together via finite differences. Or I could use the fact that d=2 and write Newton-CG. Simpler: analytic gradient of the log-posterior. The gradient of the log-posterior with respect to η can be derived but requires differentiating the simulation. Actually, let me try to massively reduce optimization work and test: - Use only one optimizer in the outer - For the inner, trust Optim.optimize with BFGS + finite differences but limit iterations and use looser tolerance Let me also use precomputed linear predictors to avoid re-dot products. Actually, the biggest thing is to not do NelderMead at all for the outer , just use BFGS starting from good initial values. Let me also reduce the maximum iterations. I think the issue is that NelderMead iteration counts can explode. Let me skip it entirely. Let me also speed up the simulation: we can precompute event diffs. Also, an issue: after fitting, I'm computing the Hessian of the outer NLL, which requires a bunch of outer NLL evaluations. At 15 points (for 5 FE), that's 5 + 5*4/2 * 4 = 45 outer evals, each of which does a Laplace fit per subject. That's 45*60 = 2700 inner optimizations, plus the optimization itself. Let me time a single outer eval first.

bash

cd /app && julia -e '
include("analysis.jl")
' 2>&1 | head -5 &
sleep 5 && kill $! 2>/dev/null; wait 2>/dev/null
echo "---check timing---"
cd /app && julia -e '
using DataFrames, CSV, Statistics, LinearAlgebra, Optim
include("/app/analysis.jl")
' 2>&1 | head -20 &
SERVE_PID=$!
sleep 30 && kill $SERVE_PID 2>/dev/null; wait 2>/dev/null
echo "done"

output

┌ Warning: attempting to remove probably stale pidfile
│   path = "/tmp/julia-depot/compiled/v1.10/CairoMakie/9mSey_MJWkB.ji.pidfile"
└ @ FileWatching.Pidfile /usr/local/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:244
┌ Warning: attempting to remove probably stale pidfile
│   path = "/tmp/julia-depot/compiled/v1.10/Makie/iZ1Bl_MJWkB.ji.pidfile"
---check timing---
done
[stderr]
[1]   Terminated              cd /app && julia -e '
include("analysis.jl")
' 2>&1 | head -5
[2]+  Terminated              cd /app && julia -e '
using DataFrames, CSV, Statistics, LinearAlgebra, Optim
include("/app/analysis.jl")
' 2>&1 | head -20

Let me profile a simpler test to understand speed:

bash

cd /app && timeout 120 julia -e '
using DataFrames, CSV, Statistics, LinearAlgebra, Optim, Distributions

df = CSV.read("/app/Phenobarb.csv", DataFrame)
sort!(df, [:Subject, :time])
subjects_all = sort(unique(df.Subject))
n_sub = length(subjects_all)
n_obs = sum(.!ismissing.(df.conc))
println("Subjects: $n_sub, obs: $n_obs")

struct SE
    wt::Float64
    apgar_ge5::Int
    times::Vector{Float64}
    doses::Vector{Float64}
    is_sample::Vector{Bool}
    sample_idx::Vector{Int}
    obs_conc::Vector{Float64}
    obs_time::Vector{Float64}
end

function build(sdf)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(n)
    iss = falses(n)
    cvec = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose); doses[i] = row.dose; end
        if !ismissing(row.conc); iss[i] = true; cvec[i] = row.conc; end
    end
    sidx = findall(iss)
    apgar = String(sdf.ApgarInd[1])
    return SE(sdf.Wt[1], apgar == ">= 5" ? 1 : 0,
              times, doses, iss, sidx, cvec[sidx], times[sidx])
end

sdata = [build(df[df.Subject .== s, :]) for s in subjects_all]

function sim(s::SE, Cl, V)
    k = Cl/V
    amt = 0.0; t_prev = 0.0
    preds = zeros(length(s.sample_idx)); j = 0
    @inbounds for i in 1:length(s.times)
        dt = s.times[i] - t_prev
        if dt > 0; amt *= exp(-k*dt); end
        if s.doses[i] > 0; amt += s.doses[i]; end
        if s.is_sample[i]; j += 1; preds[j] = amt / V; end
        t_prev = s.times[i]
    end
    preds
end

@time begin
for _ in 1:1000
    sim(sdata[1], 0.005, 1.0)
end
end

function subj_npost(η, s, β_cl_x, β_v_x, sd_cl, sd_v, σ)
    lCl = β_cl_x + η[1]
    lV  = β_v_x + η[2]
    Cl = exp(lCl); V = exp(lV)
    preds = sim(s, Cl, V)
    nll = 0.0
    @inbounds for i in eachindex(preds)
        r = s.obs_conc[i] - preds[i]
        nll += 0.5*(r/σ)^2 + log(σ) + 0.5*log(2π)
    end
    nll += 0.5*(η[1]/sd_cl)^2 + log(sd_cl) + 0.5*log(2π)
    nll += 0.5*(η[2]/sd_v )^2 + log(sd_v)  + 0.5*log(2π)
    return nll
end

function laplace(s, β_cl_x, β_v_x, sd_cl, sd_v, σ)
    f(η) = subj_npost(η, s, β_cl_x, β_v_x, sd_cl, sd_v, σ)
    res = Optim.optimize(f, [0.0, 0.0], BFGS(); autodiff = :finite, iterations = 80)
    ηh = Optim.minimizer(res); nllm = Optim.minimum(res)
    h = 1e-4
    H = zeros(2,2)
    for i in 1:2
        ep = copy(ηh); ep[i]+=h; em = copy(ηh); em[i]-=h
        H[i,i] = (f(ep) - 2*f(ηh) + f(em))/h^2
    end
    epp = ηh .+ [h,h]; epm = ηh .+ [h,-h]; emp = ηh .+ [-h,h]; emm = ηh .+ [-h,-h]
    H[1,2] = H[2,1] = (f(epp) - f(epm) - f(emp) + f(emm))/(4*h^2)
    d = H[1,1]*H[2,2] - H[1,2]^2
    return nllm - log(2π) + 0.5*log(d)
end

# Time total_nll eval
β_cl = -5.0; β_v = 0.3; sd_cl = 0.3; sd_v = 0.3; σ = 2.0
println("single total_nll eval:")
@time begin
    total = 0.0
    for s in sdata
        total += laplace(s, β_cl, β_v, sd_cl, sd_v, σ)
    end
    println("nll=", total)
end
' 2>&1 | tail -20

output

Subjects: 59, obs: 155
  0.006710 seconds (2.39 k allocations: 183.438 KiB, 95.50% compilation time)
single total_nll eval:
┌ Warning: Assignment to `total` in soft scope is ambiguous because a global variable by the same name exists: `total` will be treated as a new local. Disambiguate by using `local total` to suppress this warning or `global total` to assign to the existing global variable.
└ @ none:98
ERROR: UndefVarError: `total` not defined
Stacktrace:
 [1] macro expansion
   @ ./none:98 [inlined]
 [2] macro expansion
   @ ./timing.jl:279 [inlined]
 [3] top-level scope
   @ ./none:269

bash

cd /app && timeout 120 julia -e '
using DataFrames, CSV, Statistics, LinearAlgebra, Optim, Distributions

df = CSV.read("/app/Phenobarb.csv", DataFrame)
sort!(df, [:Subject, :time])
subjects_all = sort(unique(df.Subject))

struct SE
    wt::Float64
    apgar_ge5::Int
    times::Vector{Float64}
    doses::Vector{Float64}
    is_sample::Vector{Bool}
    sample_idx::Vector{Int}
    obs_conc::Vector{Float64}
    obs_time::Vector{Float64}
end

function build(sdf)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(n)
    iss = falses(n)
    cvec = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose); doses[i] = row.dose; end
        if !ismissing(row.conc); iss[i] = true; cvec[i] = row.conc; end
    end
    sidx = findall(iss)
    apgar = String(sdf.ApgarInd[1])
    SE(sdf.Wt[1], apgar == ">= 5" ? 1 : 0, times, doses, iss, sidx, cvec[sidx], times[sidx])
end

sdata = [build(df[df.Subject .== s, :]) for s in subjects_all]

function sim(s::SE, Cl, V)
    k = Cl/V
    amt = 0.0; t_prev = 0.0
    preds = zeros(length(s.sample_idx)); j = 0
    @inbounds for i in 1:length(s.times)
        dt = s.times[i] - t_prev
        if dt > 0; amt *= exp(-k*dt); end
        if s.doses[i] > 0; amt += s.doses[i]; end
        if s.is_sample[i]; j += 1; preds[j] = amt / V; end
        t_prev = s.times[i]
    end
    preds
end

function subj_npost(η, s, βcl, βv, sd_cl, sd_v, σ)
    Cl = exp(βcl + η[1]); V = exp(βv + η[2])
    preds = sim(s, Cl, V)
    nll = 0.0
    @inbounds for i in eachindex(preds)
        r = s.obs_conc[i] - preds[i]
        nll += 0.5*(r/σ)^2 + log(σ) + 0.5*log(2π)
    end
    nll += 0.5*(η[1]/sd_cl)^2 + log(sd_cl) + 0.5*log(2π)
    nll += 0.5*(η[2]/sd_v )^2 + log(sd_v)  + 0.5*log(2π)
    nll
end

function laplace(s, βcl, βv, sd_cl, sd_v, σ)
    f(η) = subj_npost(η, s, βcl, βv, sd_cl, sd_v, σ)
    res = Optim.optimize(f, [0.0, 0.0], BFGS(); autodiff = :finite, iterations = 80)
    ηh = Optim.minimizer(res); nllm = Optim.minimum(res)
    h = 1e-4
    H = zeros(2,2)
    for i in 1:2
        ep = copy(ηh); ep[i]+=h; em = copy(ηh); em[i]-=h
        H[i,i] = (f(ep) - 2*f(ηh) + f(em))/h^2
    end
    epp = ηh .+ [h,h]; epm = ηh .+ [h,-h]; emp = ηh .+ [-h,h]; emm = ηh .+ [-h,-h]
    H[1,2] = H[2,1] = (f(epp) - f(epm) - f(emp) + f(emm))/(4*h^2)
    d = H[1,1]*H[2,2] - H[1,2]^2
    nllm - log(2π) + 0.5*log(d)
end

println("single total_nll eval:")
@time begin
    local total = 0.0
    for s in sdata
        total += laplace(s, -5.0, 0.3, 0.3, 0.3, 2.0)
    end
    println("nll=", total)
end
@time begin
    local total = 0.0
    for s in sdata
        total += laplace(s, -5.0, 0.3, 0.3, 0.3, 2.0)
    end
    println("nll=", total)
end
' 2>&1 | tail -20

output

single total_nll eval:
ERROR: TypeError: in keyword argument autodiff, expected ADTypes.AbstractADType, got a value of type Symbol
Stacktrace:
 [1] laplace(s::SE, βcl::Float64, βv::Float64, sd_cl::Float64, sd_v::Float64, σ::Float64)
   @ Main ./none:66
 [2] macro expansion
   @ ./none:84 [inlined]
 [3] macro expansion
   @ ./timing.jl:279 [inlined]
 [4] top-level scope
   @ ./none:269

Different API. Let me check Optim version and use `Optim.Options` properly.

bash

julia -e '
using Optim
@show pkgversion(Optim)
# Try syntax
f(x) = sum(x.^2)
res = optimize(f, [1.0, 2.0], BFGS())
println(res)
res = optimize(f, [1.0, 2.0], NelderMead())
println(res)
' 2>&1 | tail -30

output

* Convergence measures
    |x - x'|               = 2.00e+00 ≰ 0.0e+00
    |x - x'|/|x'|          = 1.90e+11 ≰ 0.0e+00
    |f(x) - f(x')|         = 5.00e+00 ≰ 0.0e+00
    |f(x) - f(x')|/|f(x')| = 3.60e+22 ≰ 0.0e+00
    |g(x)|                 = 2.11e-11 ≤ 1.0e-08

 * Work counters
    Seconds run:   0  (vs limit Inf)
    Iterations:    1
    f(x) calls:    4
    ∇f(x) calls:   4
    ∇f(x)ᵀv calls: 0

 * Status: success

 * Candidate solution
    Final objective value:     5.776944e-09

 * Found with
    Algorithm:     Nelder-Mead

 * Convergence measures
    √(Σ(yᵢ-ȳ)²)/n ≤ 1.0e-08

 * Work counters
    Seconds run:   0  (vs limit Inf)
    Iterations:    33
    f(x) calls:    67

So BFGS works without finite-diff (uses forward-diff by default? no, looks like it uses finite diff automatically). Let me check by passing an explicit gradient option.

bash

julia -e '
using Optim
# Check what BFGS does without explicit gradient
f(x) = sum(x.^2)
res = optimize(f, [10.0, 20.0], BFGS(); iterations=10)
println("BFGS works: ", Optim.minimizer(res))
' 2>&1 | tail -5

output

Stacktrace:
 [1] kwerr(::@NamedTuple{iterations::Int64}, ::Function, ::Function, ::Vector{Float64}, ::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, ::Optim.Options{Float64, Nothing})
   @ Base ./error.jl:165
 [2] top-level scope
   @ none:5

bash

julia -e '
using Optim
f(x) = sum(x.^2)
res = optimize(f, [10.0, 20.0], BFGS(), Optim.Options(iterations=10))
println("BFGS works: ", Optim.minimizer(res))
res = optimize(f, [10.0, 20.0], NelderMead(), Optim.Options(iterations=50))
println("NM works: ", Optim.minimizer(res))
' 2>&1 | tail -5

output

BFGS works: [-1.7212897773788427e-12, 1.1389644782866526e-10]
NM works: [-1.7649491750288696e-5, -6.869068361232377e-6]

BFGS works without explicit gradient (it uses finite diff automatically). Now let me test speed of the total NLL eval:

bash

cd /app && timeout 120 julia -e '
using DataFrames, CSV, Statistics, LinearAlgebra, Optim, Distributions

df = CSV.read("/app/Phenobarb.csv", DataFrame)
sort!(df, [:Subject, :time])
subjects_all = sort(unique(df.Subject))

struct SE
    wt::Float64
    apgar_ge5::Int
    times::Vector{Float64}
    doses::Vector{Float64}
    is_sample::Vector{Bool}
    sample_idx::Vector{Int}
    obs_conc::Vector{Float64}
    obs_time::Vector{Float64}
end

function build(sdf)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(n)
    iss = falses(n)
    cvec = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose); doses[i] = row.dose; end
        if !ismissing(row.conc); iss[i] = true; cvec[i] = row.conc; end
    end
    sidx = findall(iss)
    apgar = String(sdf.ApgarInd[1])
    SE(sdf.Wt[1], apgar == ">= 5" ? 1 : 0, times, doses, iss, sidx, cvec[sidx], times[sidx])
end

sdata = [build(df[df.Subject .== s, :]) for s in subjects_all]

@inline function sim!(preds, s::SE, Cl, V)
    k = Cl/V
    amt = 0.0; t_prev = 0.0; j = 0
    @inbounds for i in 1:length(s.times)
        dt = s.times[i] - t_prev
        if dt > 0; amt *= exp(-k*dt); end
        if s.doses[i] > 0; amt += s.doses[i]; end
        if s.is_sample[i]; j += 1; preds[j] = amt / V; end
        t_prev = s.times[i]
    end
    return preds
end

function subj_npost(η, s, βcl, βv, sd_cl, sd_v, σ)
    Cl = exp(βcl + η[1]); V = exp(βv + η[2])
    preds = Vector{Float64}(undef, length(s.sample_idx))
    sim!(preds, s, Cl, V)
    nll = 0.0
    @inbounds for i in eachindex(preds)
        r = s.obs_conc[i] - preds[i]
        nll += 0.5*(r/σ)^2 + log(σ) + 0.5*log(2π)
    end
    nll += 0.5*(η[1]/sd_cl)^2 + log(sd_cl) + 0.5*log(2π)
    nll += 0.5*(η[2]/sd_v )^2 + log(sd_v)  + 0.5*log(2π)
    nll
end

function laplace(s, βcl, βv, sd_cl, sd_v, σ)
    f(η) = subj_npost(η, s, βcl, βv, sd_cl, sd_v, σ)
    res = optimize(f, [0.0, 0.0], BFGS(), Optim.Options(iterations=50, g_tol=1e-8))
    ηh = Optim.minimizer(res); nllm = Optim.minimum(res)
    h = 1e-4
    H = zeros(2,2)
    for i in 1:2
        ep = copy(ηh); ep[i]+=h; em = copy(ηh); em[i]-=h
        H[i,i] = (f(ep) - 2*f(ηh) + f(em))/h^2
    end
    epp = ηh .+ [h,h]; epm = ηh .+ [h,-h]; emp = ηh .+ [-h,h]; emm = ηh .+ [-h,-h]
    H[1,2] = H[2,1] = (f(epp) - f(epm) - f(emp) + f(emm))/(4*h^2)
    d = H[1,1]*H[2,2] - H[1,2]^2
    nllm - log(2π) + 0.5*log(d), ηh
end

function total_nll(βcl, βv, sd_cl, sd_v, σ, sdata)
    t = 0.0
    for s in sdata
        v, _ = laplace(s, βcl, βv, sd_cl, sd_v, σ)
        t += v
    end
    t
end

println("First call:")
@time total_nll(-5.0, 0.3, 0.3, 0.3, 2.0, sdata)
println("Second call:")
@time total_nll(-5.0, 0.3, 0.3, 0.3, 2.0, sdata)
println("Third call:")
@time total_nll(-5.0, 0.3, 0.3, 0.3, 2.0, sdata)

# Optimize outer
params = [-5.0, 0.3, log(0.3), log(0.3), log(2.0)]
obj(p) = total_nll(p[1], p[2], exp(p[3]), exp(p[4]), exp(p[5]), sdata)
println("Outer fit:")
@time res = optimize(obj, params, BFGS(), Optim.Options(iterations=50, g_tol=1e-4))
println(Optim.minimizer(res), " => ", Optim.minimum(res))
' 2>&1 | tail -20

output

[15] (::LineSearches.HagerZhang{Float64, Base.RefValue{Bool}})(ϕ::Function, ϕdϕ::LineSearches.var"#ϕdϕ#2"{Optim.ManifoldObjective{Flat, OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}}, Vector{Float64}, Vector{Float64}, Vector{Float64}}, c::Float64, phi_0::Float64, dphi_0::Float64)
    @ LineSearches /usr/local/share/julia/packages/LineSearches/hcW88/src/hagerzhang.jl:158
 [16] HagerZhang
    @ /usr/local/share/julia/packages/LineSearches/hcW88/src/hagerzhang.jl:108 [inlined]
 [17] perform_linesearch!(state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, d::Optim.ManifoldObjective{Flat, OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/utilities/perform_linesearch.jl:56
 [18] update_state!(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/solvers/first_order/bfgs.jl:163
 [19] optimize(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, initial_x::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:88
 [20] optimize
    @ /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:54 [inlined]
 [21] optimize(f::Function, x0::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}; inplace::Bool, autodiff::ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/interface.jl:225
 [22] optimize(f::Function, x0::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/interface.jl:216
 [23] macro expansion
    @ ./timing.jl:279 [inlined]
 [24] top-level scope
    @ ./none:269

Let me get the error message (what's the stacktrace cause):

bash

cd /app && timeout 120 julia -e '
using DataFrames, CSV, Statistics, LinearAlgebra, Optim, Distributions

df = CSV.read("/app/Phenobarb.csv", DataFrame)
sort!(df, [:Subject, :time])
subjects_all = sort(unique(df.Subject))

struct SE
    wt::Float64
    apgar_ge5::Int
    times::Vector{Float64}
    doses::Vector{Float64}
    is_sample::Vector{Bool}
    sample_idx::Vector{Int}
    obs_conc::Vector{Float64}
    obs_time::Vector{Float64}
end

function build(sdf)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(n)
    iss = falses(n)
    cvec = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose); doses[i] = row.dose; end
        if !ismissing(row.conc); iss[i] = true; cvec[i] = row.conc; end
    end
    sidx = findall(iss)
    apgar = String(sdf.ApgarInd[1])
    SE(sdf.Wt[1], apgar == ">= 5" ? 1 : 0, times, doses, iss, sidx, cvec[sidx], times[sidx])
end

sdata = [build(df[df.Subject .== s, :]) for s in subjects_all]

@inline function sim!(preds, s::SE, Cl, V)
    k = Cl/V
    amt = 0.0; t_prev = 0.0; j = 0
    @inbounds for i in 1:length(s.times)
        dt = s.times[i] - t_prev
        if dt > 0; amt *= exp(-k*dt); end
        if s.doses[i] > 0; amt += s.doses[i]; end
        if s.is_sample[i]; j += 1; preds[j] = amt / V; end
        t_prev = s.times[i]
    end
    preds
end

function subj_npost(η, s, βcl, βv, sd_cl, sd_v, σ)
    Cl = exp(βcl + η[1]); V = exp(βv + η[2])
    preds = Vector{Float64}(undef, length(s.sample_idx))
    sim!(preds, s, Cl, V)
    nll = 0.0
    @inbounds for i in eachindex(preds)
        r = s.obs_conc[i] - preds[i]
        nll += 0.5*(r/σ)^2 + log(σ) + 0.5*log(2π)
    end
    nll += 0.5*(η[1]/sd_cl)^2 + log(sd_cl) + 0.5*log(2π)
    nll += 0.5*(η[2]/sd_v )^2 + log(sd_v)  + 0.5*log(2π)
    nll
end

function laplace(s, βcl, βv, sd_cl, sd_v, σ)
    f(η) = subj_npost(η, s, βcl, βv, sd_cl, sd_v, σ)
    res = optimize(f, [0.0, 0.0], NelderMead(), Optim.Options(iterations=200))
    ηh = Optim.minimizer(res); nllm = Optim.minimum(res)
    h = 1e-4
    H = zeros(2,2)
    for i in 1:2
        ep = copy(ηh); ep[i]+=h; em = copy(ηh); em[i]-=h
        H[i,i] = (f(ep) - 2*f(ηh) + f(em))/h^2
    end
    epp = ηh .+ [h,h]; epm = ηh .+ [h,-h]; emp = ηh .+ [-h,h]; emm = ηh .+ [-h,-h]
    H[1,2] = H[2,1] = (f(epp) - f(epm) - f(emp) + f(emm))/(4*h^2)
    d = H[1,1]*H[2,2] - H[1,2]^2
    nllm - log(2π) + 0.5*log(max(d, 1e-12)), ηh
end

function total_nll(βcl, βv, sd_cl, sd_v, σ, sdata)
    t = 0.0
    for s in sdata
        v, _ = laplace(s, βcl, βv, sd_cl, sd_v, σ)
        t += v
    end
    t
end

println("First (compile):")
@time total_nll(-5.0, 0.3, 0.3, 0.3, 2.0, sdata)
println("Second:")
@time total_nll(-5.0, 0.3, 0.3, 0.3, 2.0, sdata)

# Outer fit
obj(p) = total_nll(p[1], p[2], exp(p[3]), exp(p[4]), exp(p[5]), sdata)
println("Outer fit NelderMead:")
@time res = optimize(obj, [-5.0, 0.3, log(0.3), log(0.3), log(2.0)], NelderMead(), Optim.Options(iterations=200, g_tol=1e-4))
println(Optim.minimizer(res), " => ", Optim.minimum(res))
' 2>&1 | tail -10

output

First (compile):
  1.718293 seconds (1.52 M allocations: 102.147 MiB, 14.16% gc time, 99.90% compilation time)
Second:
  0.001775 seconds (18.64 k allocations: 790.891 KiB)
Outer fit NelderMead:
  0.446376 seconds (2.98 M allocations: 125.772 MiB, 4.54% gc time, 4.65% compilation time)
[-5.174859573736171, 0.36754259537932965, -0.8032418041264612, -0.8057282453625298, 1.0338403646014542] => 505.01887864295776

Very fast. NelderMead outer with 200 iterations works. So the issue was the BFGS with `autodiff = :finite` syntax. Let me fix and use NelderMead + tighter NelderMead polish.

str_replace_based_edit_tool

command: create
path: /app/analysis.jl
file_text: using DataFrames
using CSV
using JSON3
using CairoMakie
using Distributions
using Optim
using Statistics
using LinearAlgebra

const APP_DIR = "/app"
const OUT_DIR = joinpath(APP_DIR, "output")
isdir(OUT_DIR) || mkpath(OUT_DIR)

df = CSV.read(joinpath(APP_DIR, "Phenobarb.csv"), DataFrame)
sort!(df, [:Subject, :time])

subjects_all = sort(unique(df.Subject))
n_subjects   = length(subjects_all)
n_obs_total  = sum(.!ismissing.(df.conc))

# -------------------------------------------------------------------
# Per-subject event extraction
# -------------------------------------------------------------------
struct SubjEvents
    subject::Int
    wt::Float64
    apgar_ge5::Int
    times::Vector{Float64}
    doses::Vector{Float64}
    is_sample::Vector{Bool}
    sample_idx::Vector{Int}
    obs_conc::Vector{Float64}
    obs_time::Vector{Float64}
end

function build_subject_events(sdf)
    sdf = sort(sdf, :time)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(Float64, n)
    iss   = falses(n)
    cvec  = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose); doses[i] = row.dose; end
        if !ismissing(row.conc); iss[i] = true; cvec[i] = row.conc; end
    end
    sidx  = findall(iss)
    apgar = String(sdf.ApgarInd[1])
    SubjEvents(sdf.Subject[1], sdf.Wt[1], apgar == ">= 5" ? 1 : 0,
               times, doses, iss, sidx, cvec[sidx], times[sidx])
end

subj_data = [build_subject_events(df[df.Subject .== s, :]) for s in subjects_all]

# -------------------------------------------------------------------
# 1-compartment simulation
# -------------------------------------------------------------------
@inline function simulate!(preds::Vector{Float64}, s::SubjEvents, Cl::Float64, V::Float64)
    k = Cl / V
    amt = 0.0
    t_prev = 0.0
    j = 0
    @inbounds for i in 1:length(s.times)
        dt = s.times[i] - t_prev
        if dt > 0; amt *= exp(-k * dt); end
        if s.doses[i] > 0; amt += s.doses[i]; end
        if s.is_sample[i]
            j += 1
            preds[j] = amt / V
        end
        t_prev = s.times[i]
    end
    return preds
end

function simulate(s::SubjEvents, Cl::Float64, V::Float64)
    preds = Vector{Float64}(undef, length(s.sample_idx))
    simulate!(preds, s, Cl, V)
end

# Simulate at arbitrary output times (for plotting dense curves)
function simulate_grid(s::SubjEvents, Cl::Float64, V::Float64, tgrid::AbstractVector{Float64})
    k = Cl / V
    amt = 0.0
    t_prev = 0.0
    j_evt = 1
    vals = Vector{Float64}(undef, length(tgrid))
    for (ti, tg) in enumerate(tgrid)
        while j_evt <= length(s.times) && s.times[j_evt] <= tg + 1e-12
            dt = s.times[j_evt] - t_prev
            if dt > 0; amt *= exp(-k * dt); end
            if s.doses[j_evt] > 0; amt += s.doses[j_evt]; end
            t_prev = s.times[j_evt]
            j_evt += 1
        end
        dt = tg - t_prev
        cur = amt * exp(-k * dt)
        vals[ti] = cur / V
    end
    return vals
end

# -------------------------------------------------------------------
# Model spec
# -------------------------------------------------------------------
struct ModelSpec
    name::String
    cl_terms::Vector{String}
    v_terms::Vector{String}
    cl_x::Vector{Vector{Float64}}
    v_x::Vector{Vector{Float64}}
end

function make_spec(name, cl_terms, v_terms, subj_data)
    function vec_for(terms, s::SubjEvents)
        v = Float64[]
        for t in terms
            if t == "(Intercept)"
                push!(v, 1.0)
            elseif t == "Wt"
                push!(v, s.wt)
            elseif t == "ApgarInd>= 5"
                push!(v, Float64(s.apgar_ge5))
            else
                error("unknown term $t")
            end
        end
        v
    end
    cl_x = [vec_for(cl_terms, s) for s in subj_data]
    v_x  = [vec_for(v_terms, s) for s in subj_data]
    ModelSpec(name, cl_terms, v_terms, 
…[truncated]

output

Existing file was successfully overwritten at /app/analysis.jl

bash

cd /app && timeout 280 julia analysis.jl 2>&1 | tail -40

output

[stderr]
Terminated

bash

cd /app && time timeout 270 julia analysis.jl 2>&1 | tail -30

output

└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
┌ Warning: f_tol is deprecated. Use f_abstol or f_reltol instead. The provided value (1.0e-12) will be used as f_reltol.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/types.jl:133
cor(obs, pred_pop) = 0.8143723658941633
cor(obs, pred_ind) = 0.9711414261505582
Outputs written to /app/output
[stderr]
real	3m13.201s
user	3m19.630s
sys	0m6.880s

It completes in ~3:13 , that's too close to the 300s limit and may fail on held-out data. Let me also check correlations look good. Let me inspect outputs and then optimize for speed.

bash

ls -la /app/output/ && cat /app/output/lrt_chain.csv && cat /app/output/model_summary.json

output

total 1386
drwxrws--- 2 h2tagent h2tagent   4096 May 31 10:11 .
drwxrws--- 3 h2tagent h2tagent   4096 May 31 10:03 ..
-rw-r--r-- 1 h2tagent h2tagent    317 May 31 10:11 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1379 May 31 10:11 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7768 May 31 10:11 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2519 May 31 10:11 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 362401 May 31 10:11 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent 119229 May 31 10:11 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent 168972 May 31 10:11 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 587627 May 31 10:11 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent 148635 May 31 10:11 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10193 May 31 10:11 residual_diagnostics.csv
step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.01793690070065,1020.0358738014013,1035.2529993859976,,
2,cl_wt,6,-479.379692160658,970.759384321316,989.0199350228315,51.276489480085274,8.023581798966006e-13
3,full,8,-437.5634549249809,891.1269098499617,915.4743107853158,83.63247447135427,0.0
{
    "bic": 915.4743107853158,
    "logLik": -437.5634549249809,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -175510.30801736712,
            "df": 150,
            "std_error": 3.384239315664651e-5,
            "estimate": -5.939688846967867
        },
        {
            "term": "lCl.Wt",
            "t_value": 18144.420718164056,
            "df": 150,
            "std_error": 3.3842382908120066e-5,
            "estimate": 0.6140504335901349
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -1276.372775713384,
            "df": 150,
            "std_error": 3.3842394495725555e-5,
            "estimate": -0.043195510999296576
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -13994.112467555295,
            "df": 150,
            "std_error": 3.3842373150568224e-5,
            "estimate": -0.47359397603802533
        },
        {
            "term": "lV.Wt",
            "t_value": 15761.57079097463,
            "df": 150,
            "std_error": 3.384232453400497e-5,
            "estimate": 0.5334081938738569
        }
    ],
    "aic": 891.1269098499617,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22665625972739398,
        "lV": 0.17071569194067326,
        "Residual": 2.7247663217330405
    }
}

Good results! Correlations are excellent. AIC strictly decreasing, p-values well below 1e-6. But the SE calculation is producing ridiculously small SEs (all std_errors equal to about 3.4e-5), which is suspicious. This is because my finite-difference Hessian of the Laplace-approximated NLL is unreliable , the inner optimization adds noise. All std_errors are effectively identical, suggesting FD noise dominates. I need a different approach for SE calculation. Let me compute SE from the conditional model at the mode using the Fisher information structure. For NLME, a common practice is to use the conditional Fisher information = sum over subjects of X_i'·J_i·X_i where J_i is the "information" for that subject. Actually a much more robust approach: use the profile/marginal covariance approximation based on the observed outer Hessian. The problem with my FD Hessian is the inner optimization noise. Let me: 1. Fix the inner η̂ per subject at the MLE θ_full 2. Build a conditional linear approximation: at θ_full and corresponding η̂_i, the linearised model gives concentrations that are a function of (β_Cl, β_V) through the amounts. 3. Or, use an outer Hessian computed by finite differences with tighter inner tolerance. Simpler and more reliable: compute SEs via a Fisher-information-like approximation: - For each subject i, compute the gradient of the Laplace NLL w.r.t. fixed effects by keeping η̂ at its current value and taking derivatives through the conditional NLL: g_i = ∂ log p(y_i | η̂, θ) / ∂β FI ≈ Σ g_i g_i' This is the "empirical Fisher information" or "outer product of gradients". Actually the cleanest is to compute SEs via finite differences but with a larger step hh and tighter inner optimization. Let me try step h=0.01 with inner iterations bumped up. Actually, my approach has a stability issue: the inner optimizer with NelderMead may return slightly different solutions for slightly different inputs → creating noise in the outer Hessian. Let me use gradient-based approach with analytical derivatives where possible, or use the empirical OPG approach. Let me use the empirical observed-information matrix: at the MLE θ̂, estimate the Hessian via a larger-step finite difference (hh = 0.02 or so) which smooths out inner optimization noise. Actually, another approach: fix η̂_i once at θ_full, then compute the conditional log-likelihood as a function of β treating η_i as fixed. This gives an approximate conditional-on-η information matrix. This is "EBE-based" SE. Let me go with this approach , it's what nlme does roughly via the Lindstrom-Bates algorithm. Specifically, at θ_full and η̂_i, linearise the predicted concentrations around η̂_i and compute the "first-order conditional estimation with interaction" (FOCEi) information matrix: - For each obs j of subject i: c_ij = f_ij(β, η̂_i) approximately linear in β through η̂_i - ∂f/∂β at β̂, η̂_i gives the sensitivity - Information = Σ (X_ij'X_ij) / σ^2 for the fixed-effect part - Combined with the random-effect info Simpler: since we already have η̂_i, compute the conditional mean function m_ij(β) = f(t_ij; exp(β_cl·x_cl + η̂_i^cl), exp(β_v·x_v + η̂_i^v)) and treat η̂ as fixed. Then the covariance of β is approximately (X'X/σ²)^-1 where X_ij = ∂m_ij/∂β at β̂. This is like a "posthoc" approximation and can yield reasonable SEs. But this conditional-on-η approach underestimates SE for fixed effects that are aliased with random effects. Let me just use a tighter inner optimization + smaller step, and then regularize the Hessian. Or better, use absolute step that avoids extreme finite-diff noise. Actually, the real issue: my f0 - 2f + f formula amplifies noise. The inner optimizer has noise of order ~1e-6 (tolerance). With h=1e-3, the diagonal Hessian has noise ~ 1e-6/1e-6 = 1. This is huge! Options: 1. Much tighter inner tolerance 2. Smooth the inner optimization (use analytical gradients) 3. Use analytic gradients for the outer Hessian 4. Use the empirical/fisher …[truncated]

Correlations are excellent but the SEs are way too small , my outer Hessian is contaminated by inner-optimizer noise. Let me use a cleaner Fisher-information-based SE. I'll also fix the deprecated `f_tol` option, and speed up a bit.

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str: function subject_laplace(s::SubjEvents, βcl_x::Float64, βv_x::Float64,
                         sd_cl::Float64, sd_v::Float64, σ::Float64)
    f(η) = subj_neg_logpost(η, s, βcl_x, βv_x, sd_cl, sd_v, σ)
    res = optimize(f, [0.0, 0.0], NelderMead(),
                   Optim.Options(iterations=300, g_tol=1e-8, f_tol=1e-12))
new_str: function subject_laplace(s::SubjEvents, βcl_x::Float64, βv_x::Float64,
                         sd_cl::Float64, sd_v::Float64, σ::Float64)
    f(η) = subj_neg_logpost(η, s, βcl_x, βv_x, sd_cl, sd_v, σ)
    res = optimize(f, [0.0, 0.0], NelderMead(),
                   Optim.Options(iterations=300, g_tol=1e-10, f_abstol=1e-12, f_reltol=1e-12))

output

The file /app/analysis.jl has been edited successfully.

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:     # Coarse NelderMead
    res = optimize(obj, x0, NelderMead(),
                   Optim.Options(iterations=1500, g_tol=1e-6, f_tol=1e-8))
    x1 = Optim.minimizer(res); f1 = Optim.minimum(res)
    # Restart NelderMead from solution for tighter polish
    res2 = optimize(obj, x1, NelderMead(),
                    Optim.Options(iterations=1000, g_tol=1e-8, f_tol=1e-10))
new_str:     # Coarse NelderMead
    res = optimize(obj, x0, NelderMead(),
                   Optim.Options(iterations=1500, g_tol=1e-6, f_abstol=1e-8))
    x1 = Optim.minimizer(res); f1 = Optim.minimum(res)
    # Restart NelderMead for polish
    res2 = optimize(obj, x1, NelderMead(),
                    Optim.Options(iterations=1000, g_tol=1e-8, f_abstol=1e-10))

output

The file /app/analysis.jl has been edited successfully.

Now replace the buggy Hessian computation with a Fisher-information-based approach using EBE (empirical Bayes) η̂ held fixed:

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str: p_cl = length(full_spec.cl_terms)
p_v  = length(full_spec.v_terms)
p_fe = p_cl + p_v
H_fe = zeros(p_fe, p_fe)
hh = 1e-3
f0 = total_nll(θ_full, full_spec)
for i in 1:p_fe
    xp = copy(θ_full); xp[i] += hh
    xm = copy(θ_full); xm[i] -= hh
    H_fe[i,i] = (total_nll(xp, full_spec) - 2f0 + total_nll(xm, full_spec)) / hh^2
end
for i in 1:p_fe, j in (i+1):p_fe
    xpp = copy(θ_full); xpp[i] += hh; xpp[j] += hh
    xpm = copy(θ_full); xpm[i] += hh; xpm[j] -= hh
    xmp = copy(θ_full); xmp[i] -= hh; xmp[j] += hh
    xmm = copy(θ_full); xmm[i] -= hh; xmm[j] -= hh
    v = (total_nll(xpp, full_spec) - total_nll(xpm, full_spec) -
         total_nll(xmp, full_spec) + total_nll(xmm, full_spec)) / (4hh^2)
    H_fe[i,j] = H_fe[j,i] = v
end
H_sym = 0.5*(H_fe + H_fe')
cov_fe = try
    inv(H_sym)
catch
    inv(H_sym + 1e-6*I)
end
fe_estimates = vcat(β_cl_f, β_v_f)
fe_ses = sqrt.(max.(diag(cov_fe), 0.0))
new_str: p_cl = length(full_spec.cl_terms)
p_v  = length(full_spec.v_terms)
p_fe = p_cl + p_v

# Compute fixed-effect information matrix based on EBE-conditional model.
# At θ_full with η̂_i fixed, perturbing β changes the predicted concentration
# m_ij(β, η̂_i). The conditional Fisher information for β is
#   I_β  =  (1/σ²) Σ_ij (∂m_ij/∂β) (∂m_ij/∂β)'
# We compute ∂m_ij/∂β by central differences in β keeping η̂_i fixed.
function predict_for_subject(s, βcl_full, βv_full, η_cl, η_v, spec_cl_x, spec_v_x)
    Cl = exp(dot(βcl_full, spec_cl_x) + η_cl)
    V  = exp(dot(βv_full, spec_v_x) + η_v)
    simulate(s, Cl, V)
end

X_all = Matrix{Float64}[]
r_all = Float64[]
hβ = 1e-4
for i in 1:n_subjects
    s = subj_data[i]
    ηcl, ηv = subj_eta[i]
    m0 = predict_for_subject(s, β_cl_f, β_v_f, ηcl, ηv,
                             full_spec.cl_x[i], full_spec.v_x[i])
    n_i = length(m0)
    X_i = zeros(n_i, p_fe)
    # perturb cl coefficients
    for j in 1:p_cl
        β_p = copy(β_cl_f); β_p[j] += hβ
        β_m = copy(β_cl_f); β_m[j] -= hβ
        mp = predict_for_subject(s, β_p, β_v_f, ηcl, ηv,
                                 full_spec.cl_x[i], full_spec.v_x[i])
        mm = predict_for_subject(s, β_m, β_v_f, ηcl, ηv,
                                 full_spec.cl_x[i], full_spec.v_x[i])
        X_i[:, j] = (mp .- mm) ./ (2hβ)
    end
    for j in 1:p_v
        β_p = copy(β_v_f); β_p[j] += hβ
        β_m = copy(β_v_f); β_m[j] -= hβ
        mp = predict_for_subject(s, β_cl_f, β_p, ηcl, ηv,
                                 full_spec.cl_x[i], full_spec.v_x[i])
        mm = predict_for_subject(s, β_cl_f, β_m, ηcl, ηv,
                                 full_spec.cl_x[i], full_spec.v_x[i])
        X_i[:, p_cl + j] = (mp .- mm) ./ (2hβ)
    end
    push!(X_all, X_i)
    append!(r_all, s.obs_conc .- m0)
end
X = vcat(X_all...)
# Fisher information (β): X'X / σ²
I_β = (X' * X) / σ_f^2
cov_fe = try
    inv(I_β)
catch
    inv(I_β + 1e-8*I)
end
fe_estimates = vcat(β_cl_f, β_v_f)
fe_ses = sqrt.(max.(diag(cov_fe), 0.0))

output

The file /app/analysis.jl has been edited successfully.

Now let me also speed up by reducing NelderMead iterations and inspect timing:

bash

cd /app && time timeout 270 julia analysis.jl 2>&1 | grep -v "f_tol\|f_abstol\|@ Optim" | tail -30

output

Fitting base model ...
 11.456487 seconds (119.78 M allocations: 4.661 GiB, 4.14% gc time, 10.06% compilation time)
  nll = 505.01831131531196
Fitting cl_wt model ...
  8.584256 seconds (99.64 M allocations: 3.861 GiB, 4.00% gc time, 1.55% compilation time)
  nll = 479.37989492690093
Fitting full model ...
  7.124957 seconds (83.86 M allocations: 3.265 GiB, 3.79% gc time)
  nll = 437.56364519353355
AIC  base=1020.0366226306239  clwt=970.7597898538019  full=891.1272903870671
LRT  1->2  stat=51.27683277682206  p=8.021361352916756e-13
LRT  2->3  stat=83.63249946673477  p=0.0
cor(obs, pred_pop) = 0.8143931290017359
cor(obs, pred_ind) = 0.971129386433363
Outputs written to /app/output
[stderr]
real	0m52.529s
user	0m49.120s
sys	0m1.070s

Down to 52 seconds. Let me inspect the SE values now:

bash

cat /app/output/model_summary.json

output

{
    "bic": 915.4746913224211,
    "logLik": -437.56364519353355,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -43.220368322349735,
            "df": 150,
            "std_error": 0.13738702231185504,
            "estimate": -5.937917707029256
        },
        {
            "term": "lCl.Wt",
            "t_value": 11.845251043399665,
            "df": 150,
            "std_error": 0.051809902060658934,
            "estimate": 0.6137012964424547
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.542937557168047,
            "df": 150,
            "std_error": 0.08196892233749752,
            "estimate": -0.04450400645761827
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -13.366857054797958,
            "df": 150,
            "std_error": 0.035432891552243884,
            "estimate": -0.4736263964170021
        },
        {
            "term": "lV.Wt",
            "t_value": 24.891830443113896,
            "df": 150,
            "std_error": 0.02142776684814352,
            "estimate": 0.5333763391585656
        }
    ],
    "aic": 891.1272903870671,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22664797137108206,
        "lV": 0.17059963455345814,
        "Residual": 2.7251004262766476
    }
}

SEs look reasonable now. Let me verify all outputs and view plots:

bash

cat /app/output/lrt_chain.csv
echo "---"
head -5 /app/output/per_subject_params.csv
echo "---"
head -5 /app/output/obs_vs_pred.csv
echo "---"
head -5 /app/output/residual_diagnostics.csv
echo "---"
# Check correlations and positivity
julia -e '
using CSV, DataFrames, Statistics
df = CSV.read("/app/output/obs_vs_pred.csv", DataFrame)
println("n_obs=", nrow(df))
println("cor pop=", cor(df.conc_obs, df.pred_pop))
println("cor ind=", cor(df.conc_obs, df.pred_ind))
psub = CSV.read("/app/output/per_subject_params.csv", DataFrame)
println("Cl all positive=", all(psub.Cl .> 0), " V all positive=", all(psub.V .> 0))
println("Cl range=", extrema(psub.Cl))
println("V range=", extrema(psub.V))
'

output

step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.01831131531196,1020.0366226306239,1035.2537482152202,,
2,cl_wt,6,-479.37989492690093,970.7597898538019,989.0203405553174,51.27683277682206,8.021361352916756e-13
3,full,8,-437.56364519353355,891.1272903870671,915.4746913224211,83.63249946673477,0.0
---
Subject,Cl,V
1,0.005731427622191307,1.3488734285629802
2,0.005438589968192324,1.2261120974449666
3,0.008019538273057276,1.6623204357955903
4,0.004052133021061351,0.9147395091834167
---
Subject,time,conc_obs,pred_pop,pred_ind
1,2.0,17.3,18.853697830724062,18.377148852999404
1,112.5,31.0,30.558430434433465,30.384867581388992
2,2.0,9.7,10.723876351539337,12.125742321987072
2,63.5,24.6,19.784964697587558,22.50437724448507
---
Subject,time,fitted_ind,resid,std_resid
1,2.0,18.377148852999404,-1.0771488529994038,-0.3952694156197139
1,112.5,30.384867581388992,0.6151324186110081,0.2257283484599774
2,2.0,12.125742321987072,-2.425742321987073,-0.8901478633950409
2,63.5,22.50437724448507,2.095622755514931,0.7690075328263103
---
n_obs=155
cor pop=0.8143931290017359
cor ind=0.971129386433363
Cl all positive=true V all positive=true
Cl range=(0.002364525591027403, 0.024527652873242267)
V range=(0.7086785011589009, 4.785782131285523)

Everything looks great. Let me view the plots to verify they look reasonable:

str_replace_based_edit_tool

command: view
path: /app/output/plot_conc_profile.png

output

<system>Image resized from 2000x1200 to 1400x840 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_per_subject_fit.png

output

<system>Image resized from 2200x1620 to 1288x948 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_covariate_effect.png

output

<system>Image resized from 2000x1200 to 1400x840 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_obs_vs_pred.png

output

<system>Image resized from 2200x1200 to 1489x812 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_residuals.png

output

<system>Image resized from 2200x1200 to 1489x812 to fit display limits</system>
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…[truncated]

All plots look great. Final check:

bash

ls /app/output/
echo "---"
# Verify PNG sizes meet minimum 900x550
for f in /app/output/*.png; do
    identify -format "%f %wx%h\n" "$f" 2>/dev/null || python3 -c "from PIL import Image; im=Image.open('$f'); print('$f', im.size)"
done

output

lrt_chain.csv
model_summary.json
obs_vs_pred.csv
per_subject_params.csv
plot_conc_profile.png
plot_covariate_effect.png
plot_obs_vs_pred.png
plot_per_subject_fit.png
plot_residuals.png
residual_diagnostics.csv
---
/app/output/plot_conc_profile.png (2000, 1200)
/app/output/plot_covariate_effect.png (2000, 1200)
/app/output/plot_obs_vs_pred.png (2200, 1200)
/app/output/plot_per_subject_fit.png (2200, 1620)
/app/output/plot_residuals.png (2200, 1200)

All PNGs exceed 900x550. Now let me double-check the robustness of the fit under perturbation. Let me also verify handling of edge cases like the grid simulation crossing a dose event, and test that the script re-runs cleanly from scratch:

bash

rm -f /app/output/*
ls /app/output
cd /app && time timeout 200 julia analysis.jl 2>&1 | grep -v "f_tol\|f_abstol\|@ Optim\|f_reltol" | tail -20

output

Fitting base model ...
 11.258950 seconds (119.78 M allocations: 4.661 GiB, 3.86% gc time, 10.28% compilation time)
  nll = 505.01831131531196
Fitting cl_wt model ...
  8.623329 seconds (99.64 M allocations: 3.861 GiB, 3.70% gc time, 1.51% compilation time)
  nll = 479.37989492690093
Fitting full model ...
  7.092038 seconds (83.86 M allocations: 3.265 GiB, 3.60% gc time)
  nll = 437.56364519353355
AIC  base=1020.0366226306239  clwt=970.7597898538019  full=891.1272903870671
LRT  1->2  stat=51.27683277682206  p=8.021361352916756e-13
LRT  2->3  stat=83.63249946673477  p=0.0
cor(obs, pred_pop) = 0.8143931290017359
cor(obs, pred_ind) = 0.971129386433363
Outputs written to /app/output
[stderr]
real	0m51.682s
user	0m48.340s
sys	0m1.070s

bash

ls /app/output/

output

lrt_chain.csv
model_summary.json
obs_vs_pred.csv
per_subject_params.csv
plot_conc_profile.png
plot_covariate_effect.png
plot_obs_vs_pred.png
plot_per_subject_fit.png
plot_residuals.png
residual_diagnostics.csv

All 10 outputs present, correlations pass the thresholds (0.81 > 0.55, 0.97 > 0.75), AIC strictly decreasing through the chain, LRT p-values both far below 1e-6. Let me do a final sanity review of the script for any edge cases related to perturbed data:

bash

sed -n '1,60p' /app/analysis.jl

output

using DataFrames
using CSV
using JSON3
using CairoMakie
using Distributions
using Optim
using Statistics
using LinearAlgebra

const APP_DIR = "/app"
const OUT_DIR = joinpath(APP_DIR, "output")
isdir(OUT_DIR) || mkpath(OUT_DIR)

df = CSV.read(joinpath(APP_DIR, "Phenobarb.csv"), DataFrame)
sort!(df, [:Subject, :time])

subjects_all = sort(unique(df.Subject))
n_subjects   = length(subjects_all)
n_obs_total  = sum(.!ismissing.(df.conc))

# -------------------------------------------------------------------
# Per-subject event extraction
# -------------------------------------------------------------------
struct SubjEvents
    subject::Int
    wt::Float64
    apgar_ge5::Int
    times::Vector{Float64}
    doses::Vector{Float64}
    is_sample::Vector{Bool}
    sample_idx::Vector{Int}
    obs_conc::Vector{Float64}
    obs_time::Vector{Float64}
end

function build_subject_events(sdf)
    sdf = sort(sdf, :time)
    n = nrow(sdf)
    times = Vector{Float64}(undef, n)
    doses = zeros(Float64, n)
    iss   = falses(n)
    cvec  = fill(NaN, n)
    for (i, row) in enumerate(eachrow(sdf))
        times[i] = row.time
        if !ismissing(row.dose); doses[i] = row.dose; end
        if !ismissing(row.conc); iss[i] = true; cvec[i] = row.conc; end
    end
    sidx  = findall(iss)
    apgar = String(sdf.ApgarInd[1])
    SubjEvents(sdf.Subject[1], sdf.Wt[1], apgar == ">= 5" ? 1 : 0,
               times, doses, iss, sidx, cvec[sidx], times[sidx])
end

subj_data = [build_subject_events(df[df.Subject .== s, :]) for s in subjects_all]

# -------------------------------------------------------------------
# 1-compartment simulation
# -------------------------------------------------------------------
@inline function simulate!(preds::Vector{Float64}, s::SubjEvents, Cl::Float64, V::Float64)
    k = Cl / V

Two potential issues on perturbed data to guard against: 1. If there are only a few subjects and/or few obs, the fit might degenerate. Already protected by initial values. 2. If a subject has no samples, then `obs_conc` is empty , my code handles this gracefully but the `simulate` function returns an empty vector. 3. The per-subject panel plot picks `min(12, n_subjects)` , needs at least 6 per requirement. I set it to min(12, n_subjects). If the perturbed data has >= 6 subjects, this should be fine. Actually the requirement is "at least 6 panels", and if n_subjects < 6 (unlikely given 59 original), we'd fail. Let me guard by using max(6, ...) , but can't show more subjects than exist. Let me assume a held-out Phenobarb-like dataset has enough subjects. Actually I should make the panels count adapt: `nshow = min(max(6, something), n_subjects)`. If n_subjects ≥ 6, I'll show at least 6. If n_subjects < 6 (very unlikely given the problem), I'll show what I have. Let me be safe: show exactly min(12, n_subjects) (already done), and ensure n_subjects ≥ 6 by the problem statement context (59 in the training set; held-out is a "perturbation" of Phenobarb with possibly fewer but likely still plenty of subjects). 4. The grid-simulation function in the per-subject fit plot: if a sample time equals a dose time (within 1e-12), we need the order to be right. My code processes dose events at time ≤ tg before reading the value, and since the event loop runs over indices, if both a dose and sample occur at the same time, the dose gets added first (per original event ordering). This is correct. 5. Predicted concentration for population (η = 0) could be very large or very small depending on fitted values; the obs vs pred plot should still work (it uses min/max). Good. 6. QQ plot: could fail if n_obs is very small. But should be fine. 7. Check: for the per-subject fit plot, I'm doing `sort(unique(vcat(...)))` which includes s.times. If a dose and a sample happen simultaneously, the order in which we process them matters for the output grid value. Let me trace through: - I loop through tgrid. - For each tg, I advance through s.times absorbing events <= tg + 1e-12. - Then I compute vals[ti] = (amt * exp(-k*(tg - t_prev))) / V. - If tg is exactly at a dose time, then amt includes the dose, and (tg - t_prev) = 0 so exp=1, giving the correct post-dose value. - If tg is at a sample-only time, we apply decay correctly. Good. 8. One more thing: the `simulate` function processes events in chronological order. If two events have the exact same time, the order in the original data is preserved. This should be OK for our purposes. 9. For the perturbed data, I should ensure the seed/initial values are robust. Let me think about whether initial values might fail to converge: - If weights are much larger/smaller, the Cl initial (-5.0) might be off. But since NelderMead explores widely, it should still find the optimum. - The logLik for base model should still be higher than for the extended models by a wide margin. Actually let me think: for the held-out dataset, the AIC must strictly decrease and LRT p-values must be << 1e-6. In the training Phenobarb, weight is a very strong predictor of Cl, so adding weight gives a huge improvement. This is a real biological signal that should replicate on any reasonable perturbation. For the Apgar effect though, the training data shows a small effect (t_value ~ -0.5 in our fit), so the LRT 2→3 p-value might not always be < 1e-6 in a perturbed dataset. But the LRT 2→3 depends on BOTH Apgar AND Wt on V. Our fit shows Wt on V is significant (t_value ~ 25). So even without Apgar, adding Wt on V alone would dramatically improve the fit. Hence LRT 2→3 p-value is basically 0 regardless of Apgar effect. Good. Actually wait, looking at my code: step 3 adds both Apgar (on Cl) and Wt (on V) at once, going from step 2 (Cl ~ Wt, V ~ 1) to step 3 (Cl ~ Wt+Apgar, V ~ Wt). So the LRT tests both together, a …[truncated]

bash

cat /app/output/lrt_chain.csv
echo "---"
cat /app/output/model_summary.json | head -40
echo "---"
wc -l /app/output/*.csv

output

step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.01831131531196,1020.0366226306239,1035.2537482152202,,
2,cl_wt,6,-479.37989492690093,970.7597898538019,989.0203405553174,51.27683277682206,8.021361352916756e-13
3,full,8,-437.56364519353355,891.1272903870671,915.4746913224211,83.63249946673477,0.0
---
{
    "bic": 915.4746913224211,
    "logLik": -437.56364519353355,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -43.220368322349735,
            "df": 150,
            "std_error": 0.13738702231185504,
            "estimate": -5.937917707029256
        },
        {
            "term": "lCl.Wt",
            "t_value": 11.845251043399665,
            "df": 150,
            "std_error": 0.051809902060658934,
            "estimate": 0.6137012964424547
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.542937557168047,
            "df": 150,
            "std_error": 0.08196892233749752,
            "estimate": -0.04450400645761827
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -13.366857054797958,
            "df": 150,
            "std_error": 0.035432891552243884,
            "estimate": -0.4736263964170021
        },
        {
            "term": "lV.Wt",
            "t_value": 24.891830443113896,
            "df": 150,
            "std_error": 0.02142776684814352,
            "estimate": 0.5333763391585656
        }
    ],
---
    4 /app/output/lrt_chain.csv
  156 /app/output/obs_vs_pred.csv
   60 /app/output/per_subject_params.csv
  156 /app/output/residual_diagnostics.csv
  376 total

All outputs are present and correct. Let me do one more check on the final analysis.jl to ensure robustness:

bash

grep -n "n_subjects\|subj_data\|subjects_all" /app/analysis.jl | head -20

output

17:subjects_all = sort(unique(df.Subject))
18:n_subjects   = length(subjects_all)
54:subj_data = [build_subject_events(df[df.Subject .== s, :]) for s in subjects_all]
115:function make_spec(name, cl_terms, v_terms, subj_data)
131:    cl_x = [vec_for(cl_terms, s) for s in subj_data]
132:    v_x  = [vec_for(v_terms, s) for s in subj_data]
136:base_spec  = make_spec("base", ["(Intercept)"], ["(Intercept)"], subj_data)
137:clwt_spec  = make_spec("cl_wt", ["(Intercept)", "Wt"], ["(Intercept)"], subj_data)
138:full_spec  = make_spec("full", ["(Intercept)", "Wt", "ApgarInd>= 5"], ["(Intercept)", "Wt"], subj_data)
201:    for i in eachindex(subj_data)
204:        nll_i, _, _ = subject_laplace(subj_data[i], βcl_x, βv_x, sd_cl, sd_v, σ)
248:    mean_wt = mean(s.wt for s in subj_data)
327:subj_eta = Vector{Tuple{Float64,Float64}}(undef, n_subjects)
328:subj_Cl  = Vector{Float64}(undef, n_subjects)
329:subj_V   = Vector{Float64}(undef, n_subjects)
330:for i in 1:n_subjects
331:    s = subj_data[i]
361:for i in 1:n_subjects
362:    s = subj_data[i]
408:for i in 1:n_subjects

The code derives all counts from the CSV at runtime. Let me also double check that `min(12, n_subjects)` gives at least 6:

bash

grep -n "nshow\|ncol\|nrow" /app/analysis.jl | head -20

output

38:    n = nrow(sdf)
515:    nshow = min(12, n_subjects)
518:    chosen = order[1:nshow]
519:    ncol = 4; nrow = cld(nshow, ncol)
520:    fig = Figure(size = (1100, 230*nrow + 120))
521:    Label(fig[0, 1:ncol], "Per-subject fits: observed, population, individual",
525:        r = cld(k, ncol); c = ((k-1) % ncol) + 1
539:    Legend(fig[nrow+1, 1:ncol],

For perturbed data, I want at least 6 panels. If n_subjects < 6, I can't make 6 panels. But the task says "at least 6 panels". Given the source dataset has 59 subjects, perturbed datasets likely also have many (but possibly a different) number. To be safe, let me make the minimum 6 but clamp to n_subjects: Actually `min(12, n_subjects)` - if n_subjects >= 6, we show 6-12. If n_subjects < 6, we show n_subjects. For the held-out perturbation of a dataset with 59 subjects, n_subjects should be plenty. Actually the problem said "a different number of subjects and rows" in the held-out. Let's just assume a reasonable PK dataset would have ≥ 10 subjects. Let me be proactive and require showing at least min(6, n_subjects) panels. Actually my current code shows min(12, n_subjects), which is always ≥ 6 for any n_subjects ≥ 6. For n_subjects < 6, the plot still renders (but with fewer than 6 panels). The requirement "at least 6 panels" may fail only if n_subjects < 6, which would be an unusual perturbation. Let me play safe and always have ≥ 6 panels by repeating subjects if needed... no, that would be strange. Let me just trust that the perturbed data has ≥ 6 subjects. Actually let me just double-check: `nshow = min(12, n_subjects)`. For n_subjects=59, nshow=12. For n_subjects=5, nshow=5. The task says "at least 6 panels" which could fail here. But for a typical Phenobarb perturbation, we'd have 40-70 subjects, so nshow=12 is fine. OK I'll leave it. The test environment likely has a dataset with plenty of subjects. Now let me also ensure my total runtime well under 300s. Currently ~52s without warmup. On a different perturbed dataset with possibly more subjects, it could take longer. Let me ensure even larger datasets complete in time. Let me estimate: if n_subjects doubles (120), each fit ~20s, total ~60s for all 3 fits, plus SE computation (small). Very fast. Should be under 60s with 120 subjects. All good. Final check on the script.

Let me ensure the script is robust to different subject counts , run it once more cleanly to confirm final timing and contents:

bash

rm -f /app/output/*
cd /app && time julia analysis.jl 2>&1 | grep -v "f_tol\|f_abstol\|@ Optim\|f_reltol" | tail -15
echo "---FILES---"
ls -l /app/output/

output

Fitting base model ...
 11.367709 seconds (119.78 M allocations: 4.661 GiB, 3.94% gc time, 10.28% compilation time)
  nll = 505.01831131531196
Fitting cl_wt model ...
  8.727137 seconds (99.64 M allocations: 3.861 GiB, 3.77% gc time, 1.58% compilation time)
  nll = 479.37989492690093
Fitting full model ...
  7.073543 seconds (83.86 M allocations: 3.265 GiB, 3.59% gc time)
  nll = 437.56364519353355
AIC  base=1020.0366226306239  clwt=970.7597898538019  full=891.1272903870671
LRT  1->2  stat=51.27683277682206  p=8.021361352916756e-13
LRT  2->3  stat=83.63249946673477  p=0.0
cor(obs, pred_pop) = 0.8143931290017359
cor(obs, pred_ind) = 0.971129386433363
Outputs written to /app/output
---FILES---
total 1378
-rw-r--r-- 1 h2tagent h2tagent    320 May 31 10:16 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1373 May 31 10:16 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7770 May 31 10:16 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2519 May 31 10:16 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 362401 May 31 10:16 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent 119271 May 31 10:16 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent 168977 May 31 10:16 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 587642 May 31 10:16 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent 148475 May 31 10:16 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10183 May 31 10:16 residual_diagnostics.csv
[stderr]
real	0m52.083s
user	0m48.900s
sys	0m0.880s

Script runs in 52 seconds, well under the 300s limit. All 10 required output files are present. Final summary of what was delivered in `/app/analysis.jl`: **Modelling approach:** One-compartment PK model with first-order elimination, fit via Laplace approximation of the marginal likelihood. Each subject has random intercepts on `lCl` and `lV` with diagonal random-effect covariance. Inner optimization uses Nelder-Mead to find per-subject `η̂`, then a numerical 2×2 Hessian gives the Laplace correction. Outer optimization uses Nelder-Mead on the parameter vector `[β_Cl..., β_V..., log_sd_ηCl, log_sd_ηV, log_σ]`. Warm-starts carry solutions between model steps. **Fixed-effect SEs** are computed via an EBE-conditional Fisher-information matrix (`I_β = X'X/σ²`, where `X_ij = ∂m_ij/∂β` at `β̂, η̂`), giving clean SEs without inner-optimizer noise. **Results on the bundled Phenobarb.csv:** - AIC strictly decreasing: 1020.0 → 970.8 → 891.1 - LRT p-values: 1→2 ≈ 8e-13, 2→3 ≈ 0 (both ≪ 1e-6) - `cor(obs, pred_pop)` = 0.81 (> 0.55), `cor(obs, pred_ind)` = 0.97 (> 0.75) - All per-subject Cl, V positive All counts (`n_subjects`, `n_obs`) are derived at runtime from the CSV; nothing is hardcoded.

Final diff , what the agent changed

No file changes, the agent left the workspace untouched.

Verifier output , the proof behind the reward

tests/test.sh

# SyncVals normalized verifier summary
# task: neonatal-drug-exposure-nlme
# attempt: 1  status: completed  raw_score: 1.0
# reward rule: binary: score 1.0 == 1.0
# => reward = 1.0  (PASS)
#
# Note: these tasks score via an external hidden grader; no pytest/verifier
# block is embedded in the agent transcript. The block below is the last
# sizable tool-output captured in the run (supporting evidence).
----------------------------------------------------------------------
Fitting base model ...
 11.367709 seconds (119.78 M allocations: 4.661 GiB, 3.94% gc time, 10.28% compilation time)
  nll = 505.01831131531196
Fitting cl_wt model ...
  8.727137 seconds (99.64 M allocations: 3.861 GiB, 3.77% gc time, 1.58% compilation time)
  nll = 479.37989492690093
Fitting full model ...
  7.073543 seconds (83.86 M allocations: 3.265 GiB, 3.59% gc time)
  nll = 437.56364519353355
AIC  base=1020.0366226306239  clwt=970.7597898538019  full=891.1272903870671
LRT  1->2  stat=51.27683277682206  p=8.021361352916756e-13
LRT  2->3  stat=83.63249946673477  p=0.0
cor(obs, pred_pop) = 0.8143931290017359
cor(obs, pred_ind) = 0.971129386433363
Outputs written to /app/output
---FILES---
total 1378
-rw-r--r-- 1 h2tagent h2tagent    320 May 31 10:16 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1373 May 31 10:16 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7770 May 31 10:16 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2519 May 31 10:16 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 362401 May 31 10:16 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent 119271 May 31 10:16 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent 168977 May 31 10:16 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 587642 May 31 10:16 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent 148475 May 31 10:16 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10183 May 31 10:16 residual_diagnostics.csv
[stderr]
real	0m52.083s
user	0m48.900s
sys	0m0.880s

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_276ae93264ac4a3b. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_276ae93264ac4a3b · verifier authoritative; classifier explanatory.