Categorical endpoints — [binary_model]

Categorical (discrete-state) endpoints let a model score a non-Gaussian observation — a category index rather than a continuous concentration. The first member of the family is the binary / Bernoulli endpoint: mixed-effects logistic regression, declared with a [binary_model] block.

Ordinal (proportional-odds), Poisson, and negative-binomial endpoints are planned follow-ups in the same family. This page documents the binary endpoint only.

The [binary_model] block

[binary_model]
cmt   = 3
logit = TH0 + THX * X + THT * TIME     ; log-odds of P(DV = 1)
; link = logit                          ; optional; logit is the default

Observations for the block’s cmt carry DV ∈ {0, 1} (EVID = 0). The model computes a per-observation probability

\[ p = \operatorname{logit}^{-1}(\eta_\text{lp}) = \frac{1}{1 + e^{-\eta_\text{lp}}}, \]

where the linear predictor logit (the log-odds) is any expression over the same namespace the hazard and error blocks use — population parameters θ, random effects η, data covariates, values from [individual_parameters], and the per-record TIME builtin. The data term is the negative Bernoulli log-likelihood

\[ -\log L = -\sum_j \big[\, y_j \log p_j + (1 - y_j)\log(1 - p_j) \,\big]. \]

Keys

Key	Required	Meaning
cmt	yes	Data-file CMT column value for this endpoint’s rows.
logit	yes	Linear predictor (log-odds of DV = 1). Any θ/η/covariate/[individual_parameters]/TIME expression.
link	no	Link function. Only logit is available; probit/cloglog are planned.

Random effects and the fixed-effects special case

A per-subject random effect in the predictor (logit = TH0 + ETA_I) gives a mixed-effects logistic model — a random intercept (or slope). Omitting all random effects (no omega, n_eta = 0) gives ordinary fixed-effects logistic regression, exactly analogous to base-R glm(..., family = binomial). Both are supported; the fixed-effects case needs no [structural_model], [error_model], or [individual_parameters] blocks (a logistic-only model can be just [parameters] + [binary_model] + [fit_options]).

Covariates on the predictor may vary with time via the TIME builtin (evaluated per observation). A time-varying covariate column on the predictor is not yet supported; declare a [covariates] value used at baseline instead.

Data format

DV holds the 0/1 outcome directly (there is no censoring code). One row per observation; no dose rows are needed for a logistic-only model.

ID,TIME,DV,CMT,EVID,MDV,X
1,0,0,3,0,0,1.07
1,1,0,3,0,0,1.07
1,2,1,3,0,0,1.07
2,0,1,3,0,0,-1.01

A DV value of 2 or more on a binary CMT is a data error — the fit stops with a clear message (an ordered response with more than two categories needs an ordinal endpoint, which is not yet available).

Example

examples/binary_logistic.ferx (with data/binary_logistic.csv) fits a fixed-effects logistic model with a subject covariate X and a TIME effect:

[parameters]
  theta TH0(0.0, -10.0, 10.0)
  theta THX(0.0, -10.0, 10.0)
  theta THT(0.0, -10.0, 10.0)

[covariates]
  X continuous

[binary_model]
  cmt   = 3
  logit = TH0 + THX * X + THT * TIME

See Categorical estimation for the estimator guidance and the validation against R glm.