Abstract

Group testing has been used extensively to reduce screening costs in

epidemiological studies involving low-prevalence diseases. This testing strategy

involves combining specimens (e.g., blood, urine, swabs, etc.) from several individuals to form a pool and then testing the pooled specimen for infection.

When the endpoint of interest is a time-to-event outcome, for example, the time

until infection or disease, and pools are measured only once, the resulting data

are called group-tested current status data (Petito and Jewell, 2016). In this

paper, we propose a new type of regression analysis for these data using a semiparametric probit model, an alternative to the proportional hazards model in

survival analysis. A sieve maximum likelihood estimation approach is developed

that approximates the model’s nonparametric nuisance function by using logarithmic monotone splines, and an efficient expectation-maximization algorithm

is proposed. Asymptotic properties of the resulting estimators are investigated

by using empirical process techniques and sieve estimation theory. Numerical results from simulation studies suggest our estimation methods perform nominally,

even when pools are possibly misclassified due to assay error, and can outperform individual testing when the number of assays (tests) is fixed. We illustrate

our work by estimating a time-to-event regression model for chlamydial infection

using group testing data from a large public health laboratory in Iowa.

Information

Preprint No.SS-2024-0099
Manuscript IDSS-2024-0099
Complete AuthorsLijun Fang, Tao Hu, Shuwei Li, Lianming Wang, Christopher S. McMahan, Joshua M. Tebbs
Corresponding AuthorsShuwei Li
Emailsseslishuw@gzhu.edu.cn

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Acknowledgments

We are grateful to two anonymous referees who provided helpful comments

on an earlier version of this article. This research is supported by Grants

12471251 and 12171328 from the National Nature Science Foundation of

China and and Grant Z210003 from the Beijing Natural Science Foundation.

Authors at institutions in the United States are supported by the National

Institutes of Health and the National Science Foundation.

Supplementary Materials

The online Supplementary Material contains conditional expectation derivations, detailed proofs for Theorems 1-3, a second simulation study, and an

analysis of the Iowa SHL data under the PH model. R code for data analysis

is available at https://github.com/lishuwstat/GTEMProbit.

Supplementary materials are available for download.