Zero-inflated Poisson regression for non-proportional hazard models: parameter estimation, Monte Carlo simulation, and application to educational retention data

The Cox proportional hazards (PH) model assumes constant hazard ratios, a condition frequently violated in practice. This paper derives the zero-inflated Poisson non-proportional hazard (ZIP-NPH) model, embedding stratified-extended Cox regression within a zero-inflated Poisson response distribution. Maximum partial likelihood estimators are obtained via Newton–Raphson iteration with closed-form score equations, Hessian, and observed information matrix. A Monte Carlo simulation study (n = 3 000–12 000; censoring 0–50%; 500 replications) demonstrates that ZIP-NPH substantially outperforms Cox PH and stratified-extended Cox (SE Cox) in bias, MSE, and AIC when the data-generating process contains genuine zero-inflation. Applied to semester-level retention data from 4 483 students at Universitas Terbuka, Indonesia, the van den Broek test reveals that the apparent zero excess is a structural artefact of the survSplit expansion rather than genuine behavioural zero-inflation. Consequently, SE Cox emerges as the appropriate specification, reducing AIC by 4 099 units over Cox PH. These findings delineate the boundary conditions under which ZIP-NPH improves upon SE Cox.