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Abstract We propose a broad class of so-called Cox–Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function within a transformation. The proposed models provide a highly flexible and versatile class of semiparametric models that include the transformation models and the Cox–Aalen model as special cases. Specifically, it extends the transformation models by allowing potentially time-dependent covariates to work additively on the baseline hazard and extends the Cox–Aalen model through a predetermined transformation function. We propose an estimating equation approach and devise an expectation-solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via modern empirical process techniques. The ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we demonstrate the performance of our procedures through extensive simulation studies and applications in two randomized, placebo-controlled human immunodeficiency virus (HIV) prevention efficacy trials. The data example shows the utility of the proposed Cox–Aalen transformation models in enhancing statistical power for discovering covariate effects. 

Summary Deployment of the recently licensed tetravalent dengue vaccine based on a chimeric yellow fever virus, CYD-TDV, requires understanding of how the risk of dengue disease in vaccine recipients depends jointly on a host biomarker measured after vaccination (neutralization titre—neutralizing antibodies) and on a ‘mark’ feature of the dengue disease failure event (the amino acid sequence distance of the dengue virus to the dengue sequence represented in the vaccine). The CYD14 phase 3 trial of CYD-TDV measured neutralizing antibodies via case–cohort sampling and the mark in dengue disease failure events, with about a third missing marks. We addressed the question of interest by developing inferential procedures for the stratified mark-specific proportional hazards model with missing covariates and missing marks. Two hybrid approaches are investigated that leverage both augmented inverse probability weighting and nearest neighbourhood hot deck multiple imputation. The two approaches differ in how the imputed marks are pooled in estimation. Our investigation shows that nearest neighbourhood hot deck imputation can lead to biased estimation without properly selected neighbourhoods. Simulations show that the hybrid methods developed perform well with unbiased nearest neighbourhood hot deck imputations from proper neighbourhood selection. The new methods applied to CYD14 show that neutralizing antibody level is strongly inversely associated with the risk of dengue disease in vaccine recipients, more strongly against dengue viruses with shorter distances.