Joint Analysis of Longitudinal and Survival Data Measured on Nested Timescales by Using Shared Parameter Models: An Application to Fecundity Data

Abstract

Summary We consider the joint modelling, analysis and prediction of a longitudinal binary process and a discrete time-to-event outcome. We consider data from a prospective pregnancy study, which provides day level information regarding the behaviour of couples attempting to conceive. Reproductive epidemiologists are particularly interested in developing a model for individualized predictions of time to pregnancy (TTP). A couple’s intercourse behaviour should be an integral part of such a model and is one of the main focuses of the paper. In our motivating data, the intercourse observations are a long series of binary data with a periodic probability of success and the amount of available intercourse data is a function of both the menstrual cycle length and TTP. Moreover, these variables are dependent and observed on different, and nested, timescales (TTP is measured in menstrual cycles whereas intercourse is measured on days within a menstrual cycle) further complicating its analysis. Here, we propose a semiparametric shared parameter model for the joint modelling of the binary longitudinal data (intercourse behaviour) and the discrete survival outcome (TTP). Further, we develop couple-based dynamic predictions for the intercourse profiles, which in turn are used to assess the risk for subfertility (i.e. TTP longer than six menstrual cycles).

Harnessing repeated measurements of predictor variables for clinical risk prediction: a review of existing methods

“…Similar to the TSM framework, a ME model was often employed for the covariate trajectory and a Cox proportional hazards model for a time-to-event outcome [ 57 ]. However, variations of the event prediction sub-model exist in the CPM literature such as binary event models [ 52 , 58 – 61 ], parametric survival models [ 9 ], models for discrete-time data [ 9 , 62 , 63 ], models for competing risks [ 64 ], generalised linear models [ 58 ], and models for left-truncated data [ 65 , 66 ]. Furthermore, the ME models could be for different types of data (e.g.…”

Natural history of diseases: Statistical designs and issues

“…Much of the research here was developed in investigations of the natural history of human immunodeficiency virus disease, although the ideas have now been extended to studies of biomarkers of disease development in a wide variety of applications, including cancer, cardiovascular disease, and kidney transplantation. A quite different application occurs in the study of sexual intercourse data in prospective pregnancy studies . Various statistical approaches have been suggested for joint modeling of longitudinal and survival data.…”

“…A quite different application occurs in the study of sexual intercourse data in prospective pregnancy studies. 47 Various statistical approaches have been suggested for joint modeling of longitudinal and survival data. Early general surveys of these ideas in this context are given by Tsiatis & Davidian 48 and Kurland et al 49 Asar et al 50 provided a recent introductory tutorial on the topic.…”

Joint modeling of longitudinal functional feature and time to event: an application to fecundity studies

“…We assess the performance of the proposed estimates through simulation studies in Section 4. In Section 5, we present analysis of the Stress and Time to pregnancy, a sub-component of the Oxford Conception Study (McLain et al, 2015)…”