A Nonparametric Maximum Likelihood Approach for Partially Observed Cured Data with Left Truncation and Right-Censoring

TL;DR

This paper introduces a nonparametric maximum likelihood method for analyzing partially observed cured data with left truncation and right-censoring, specifically applied to spontaneous abortion studies, addressing bias and computational challenges.

Contribution

It develops a novel EM algorithm-based approach for cure rate modeling with left truncation and right-censoring, including theoretical proofs and practical application to SAB data.

Findings

The proposed method accurately estimates cure rates and timing in SAB data.

Simulation studies demonstrate good finite sample performance.

Application to SAB data shows improved analysis over existing methods.

Abstract

Partially observed cured data occur in the analysis of spontaneous abortion (SAB) in observational studies in pregnancy. In contrast to the traditional cured data, such data has an observable `cured' portion as women who do not abort spontaneously. The data is also subject to left truncate in addition to right-censoring because women may enter or withdraw from a study any time during their pregnancy. Left truncation in particular causes unique bias in the presence of a cured portion. In this paper, we study a cure rate model and develop a conditional nonparametric maximum likelihood approach. To tackle the computational challenge we adopt an EM algorithm making use of "ghost copies" of the data, and a closed form variance estimator is derived. Under suitable assumptions, we prove the consistency of the resulting estimator involving an unbounded cumulative baseline hazard function, as well as the asymptotic normality. Simulation results are carried out to evaluate the finite sample performance. We present the analysis of the motivating SAB study to illustrate the power of our model addressing both occurrence and timing of SAB, as compared to existing approaches in practice.