Latency function estimation under the mixture cure model when the cure status is available

Abstract

This paper addresses the problem of estimating the conditional survival function of the lifetime of the subjects experiencing the event (latency) in the mixture cure model when the cure status information is partially available. The approach of past work relies on the assumption that long-term survivors are unidentifiable because of right censoring. However, in some cases this assumption is invalid since some subjects are known to be cured, e.g., when a medical test ascertains that a disease has entirely disappeared after treatment. We propose a latency estimator that extends the nonparametric estimator studied in López-Cheda et al. (TEST 26(2):353-376, 2017b) to the case when the cure status is partially available. We establish the asymptotic normality distribution of the estimator, and illustrate its performance in a simulation study. Finally, the estimator is applied to a medical dataset to study the length of hospital stay of COVID-19 patients requiring intensive care.

Estimating causal effects in observational studies for survival data with a cure fraction using propensity score adjustment

“…Additionally, for the latency function estimation, Bernhardt (2016) presented a semiparametric method, Safari et al. (2023) developed an extension based on a nonparametric estimator studied by López‐Cheda, Jácome, et al. (2017), among others.…”

“…For the nonparametric estimation of the survival function, Safari et al (2021) proposed an extension of KM and Beran estimators, while Betensky and Schoenfeld (2001) and Safari et al (2022) provide methods for the nonparametric estimation of the cure rate. Additionally, for the latency function estimation, Bernhardt (2016) presented a semiparametric method, Safari et al (2023) developed an extension based on a nonparametric estimator studied by , among others. Therefore, it would be valuable to explore absolute causal inference when the cure status information is partially available.…”

“…In this data set, identifying which individuals are cured and which are not can be challenging, as censoring hinders the classification of censored individuals into cured and uncured subjects. If there are some individuals identified as cured, alternative methods designed to consider this cure status information should be used instead of the usual cure models to estimate survival probability (Safari et al., 2021), latency (Safari et al., 2023), and cure rates (Safari et al., 2022). Figure 1 shows the KM curves of survival functions by the type of treatment.…”