Sieve estimation in a Markov illness-death process under dual censoring

Abstract

Semiparametric methods are well-established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials.

Joint modelling of colorectal cancer recurrence and death after resection using multi-state model with cured fraction

“…In the other words, recurrence can only be ascertained at a discrete evaluation time. However, some researchers have proposed estimation methods for the illness-death model under this type of dual censoring 49 , this is yet to be extended to the multi-state cure model.…”

Bias in progression‐free survival analysis due to intermittent assessment of progression

“…Frydman and Szarek discuss the issue of interval‐censored progression times in the context of nonparametric estimation of progression‐free survival distribution. Boruvka and Cook consider estimation and inference with the Cox model when two competing events are subject to different censoring schemes and interest lies in the transition intensity ratios. They point out that the present problem can be cast in this dual censoring framework, and hence, their methods could be utilized in this context.…”

Design of cancer trials based on progression‐free survival with intermittent assessment

“…Treating the progression time as interval‐censored is more appropriate, which yields a composite endpoint with one component (progression) subject to interval censoring and another (death) to right censoring. The bias in the regression coefficient estimator of a semiparametric Cox model is examined in Zeng et al, and Boruvka and Cook discuss semiparametric estimation for this problem. The purpose of this article was to develop valid design criteria when analyses are appropriately based on an illness‐death model with the progression status assessed intermittently and deaths are subject to right‐censoring.…”

“…Frydman and Szarek consider this problem and discuss nonparametric estimation of the progression‐free survival time distribution. Boruvka and Cook consider semiparametric methods for the incorporation of treatment effects, which are most appealing when the assessment times are highly irregular as in uncontrolled (eg, registry‐based) observational studies. When assessment times are regularly scheduled and common across individuals, identifiability problems can arise with general semiparametric models.…”