Flexible hazard regression for generalised interval-censored time-to-event data and the gicsurv Rshiny app

Abstract Time-to-event analysis is a core tool in epidemiological and clinical research. While right-censoring is commonly addressed, many studies involve more complex forms of censoring, such as interval- and double-interval-censoring, particularly in settings with routine follow-up. Existing methods and software provide limited support for regression modelling under these conditions, especially when combining different censoring types within the same dataset. We introduce a flexible semi-parametric hazard regression model for generalised interval-censored time-to-event data. This includes right-censored, interval-censored, double-interval-censored, and mixed censoring structures, where event and/or origin times may be partially or exactly observed. The baseline hazard is modelled using penalised B-splines, allowing complex, smooth hazard shapes without assuming a parametric form. Spline coefficients and the smoothing parameter (controlling penalisation) are jointly estimated using a two-step algorithm, each based on likelihood maximisation. This approach prevents overfitting while remaining computationally efficient. Covariate effects are estimated under a proportional hazards framework, with standard errors derived from the inverse Hessian of the penalised likelihood. The method accommodates arbitrary censoring combinations, making it suitable for longitudinal studies where timing of events varies across participants. We evaluated the model’s performance through a simulation study across ten scenarios, varying in sample size, interval width, censoring proportion, and hazard shape. Across all scenarios, the model yielded unbiased coefficients, accurate standard errors, and nominal coverage. Performance remained stable under mixed data types and non-uniform start-time distributions. Compared to existing methods, including the Cox model for exact times and icenReg for interval-censored data, our model showed strong consistency and reduced estimation error. To enhance accessibility, we developed a user-friendly Rshiny app, gicsurv, implementing the method. Application to malaria cohort data demonstrated the model’s utility in estimating hazards of infection clearance while accounting for relevant host and parasite factors.