Pseudo Partial Likelihood Method for Proportional Hazards Models when Time Origin Is Missing for Control Group with Applications to SARS-CoV-2 Seroprevalence Study
Pub. online: 7 October 2025
Type: Statistical Data Science
Open Access
Open Access
Received
7 December 2024
7 December 2024
Accepted
18 September 2025
18 September 2025
Published
7 October 2025
7 October 2025
Abstract
Time-to-event data analysis without a well-defined time origin commonly occurs in observational studies that retrospectively collect survival endpoints. For instance, after enrolling participants who have or have not received a specific treatment, an event status can be observed for all participants; however, the start date of treatment is only observable for the treatment group. The corresponding time origin does not exist for the control group, resulting in missing survival time data. Complete-case analysis is often considered the standard approach, but it disregards information from all participants in the control group and does not allow us to compare their survival distributions. To address this challenge, we propose a novel semiparametric proportional hazards model by regarding these missing time origins as nuisance parameters. We approximate the risk sets as cumulative normal distributions to deal with these nuisance parameters and develop estimation and inference procedures for our proposed estimator. We study the asymptotic properties of this model and conduct the simulation studies to validate its finite sample property. Analysis of data from a recent SARS-CoV-2 seroprevaluence study illustrates the applicability of our methods. The proposed methods are implemented in the R package coxphm.
Supplementary material
Supplementary MaterialSections A and B of the Supplementary Material provide the proofs of Theorems 1–2 and additional simulation results, respectively. The SARS-CoV-2 serological prevalence data and corresponding R code used for analysis are also included in the Supplementary Material. The coxphm package (Chung, 2025), which implements the methods developed in this article, is publicly available on CRAN.
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