Semiparametric Sieve Maximum Likelihood Estimation Under Cure Model with Partly Interval Censored and Left Truncated Data for Application to Spontaneous Abortion Data

TL;DR

This paper develops a semiparametric sieve maximum likelihood method for analyzing complex pregnancy data involving spontaneous abortion, accounting for left truncation, interval censoring, and cure rates, with proven consistency and asymptotic normality.

Contribution

It introduces a novel semiparametric sieve MLE approach for cure models with complex censored data, extending existing methods to more realistic pregnancy study scenarios.

Findings

Method is consistent and asymptotically normal.

Simulation studies confirm good finite sample performance.

Applied to real spontaneous abortion data successfully.

Abstract

This work was motivated by observational studies in pregnancy with spontaneous abortion (SAB) as outcome. Clearly some women experience the SAB event but the rest do not. In addition, the data are left truncated due to the way pregnant women are recruited into these studies. For those women who do experience SAB, their exact event times are sometimes unknown. Finally, a small percentage of the women are lost to follow-up during their pregnancy. All these give rise to data that are left truncated, partly interval and right-censored, and with a clearly defined cured portion. We consider the non-mixture Cox regression cure rate model and adopt the semiparametric spline-based sieve maximum likelihood approach to analyze such data. Using modern empirical process theory we show that both the parametric and the nonparametric parts of the sieve estimator are consistent, and we establish the asymptotic normality for both parts. Simulation studies are conducted to establish the finite sample performance. Finally, we apply our method to a database of observational studies on spontaneous abortion.