Regression modelling of interval censored data based on the adaptive ridge procedure

Fast approximations of pseudo-observations in the context of right censoring and interval censoring

In the context of right-censored and interval-censored data, we develop asymptotic formulas to compute pseudo-observations for the survival function and the restricted mean survival time (RMST). These formulas are based on the original estimators and do not involve computation of the jackknife estimators. For right-censored data, Von Mises expansions of the Kaplan-Meier estimator are used to derive the pseudo-observations. For interval-censored data, a general class of parametric models for the survival function is studied. An asymptotic representation of the pseudo-observations is derived involving the Hessian matrix and the score vector. Theoretical results that justify the use of pseudo-observations in regression are also derived. The formula is illustrated on the piecewise-constant-hazard model for the RMST. The proposed approximations are extremely accurate, even for small sample sizes, as illustrated by Monte Carlo simulations and real data. We also study the gain in terms of computation time, as compared to the original jackknife method, which can be substantial for a large dataset.

Cox models with time-varying covariates and partly-interval censoring-A maximum penalised likelihood approach

Time-varying covariates can be important predictors when model based predictions are considered. A Cox model that includes time-varying covariates is usually referred to as an extended Cox model. When only right censoring is presented in the observed survival times, the conventional partial likelihood method is still applicable to estimate the regression coefficients of an extended Cox model. However, if there are interval-censored survival times, then the partial likelihood method is not directly available unless an imputation, such as the middle point imputation, is used to replaced the left- and interval-censored data. However, such imputation methods are well known for causing biases. This paper considers fitting of the extended Cox models using the maximum penalised likelihood method allowing observed survival times to be partly interval censored, where a penalty function is used to regularise the baseline hazard estimate. We present simulation studies to demonstrate the performance of our proposed method, and illustrate our method with applications to two real datasets from medical research.

Penalized likelihood estimation of the proportional hazards model for survival data with interval censoring

This paper considers the problem of semi-parametric proportional hazards model fitting where observed survival times contain event times and also interval, left and right censoring times. Although this is not a new topic, many existing methods suffer from poor computational performance. In this paper, we adopt a more versatile penalized likelihood method to estimate the baseline hazard and the regression coefficients simultaneously. The baseline hazard is approximated using basis functions such as M-splines. A penalty is introduced to regularize the baseline hazard estimate and also to ease dependence of the estimates on the knots of the basis functions. We propose a Newton-MI (multiplicative iterative) algorithm to fit this model. We also present novel asymptotic properties of our estimates, allowing for the possibility that some parameters of the approximate baseline hazard may lie on the parameter space boundary. Comparisons of our method against other similar approaches are made through an intensive simulation study. Results demonstrate that our method is very stable and encounters virtually no numerical issues. A real data application involving melanoma recurrence is presented and an R package 'survivalMPL' implementing the method is available on R CRAN.