Testing the assumptions for the analysis of survival data arising from a prevalent cohort study with follow-up

Abstract

In a prevalent cohort study with follow-up subjects identified as prevalent cases are followed until failure (defined suitably) or censoring. When the dates of the initiating events of these prevalent cases are ascertainable, each observed datum point consists of a backward recurrence time and a possibly censored forward recurrence time. Their sum is well known to be the left truncated lifetime. It is common to term these left truncated lifetimes "length biased" if the initiating event times of all the incident cases (including those not observed through the prevalent sampling scheme) follow a stationary Poisson process. Statistical inference is then said to be carried out under stationarity. Whether or not stationarity holds, a further assumption needed for estimation of the incident survivor function is the independence of the lifetimes and their accompanying truncation times. That is, it must be assumed that survival does not depend on the calendar date of the initiating event. We show how this assumption may be checked under stationarity, even though only the backward recurrence times and their associated (possibly censored) forward recurrence times are observed. We prove that independence of the lifetimes and truncation times is equivalent to equality in distribution of the backward and forward recurrence times, and exploit this equivalence as a means of testing the former hypothesis. A simulation study is conducted to investigate the power and Type 1 error rate of our proposed tests, which include a bootstrap procedure that takes into account the pairwise dependence between the forward and backward recurrence times, as well as the potential censoring of only one of the members of each pair. We illustrate our methods using data from the Canadian Study of Health and Aging. We also point out an equivalence of the problem presented here to a non-standard changepoint problem.

Survival and life-expectancy in a young-onset dementia cohort with six years of follow-up: the NeedYD-study

“…The strength of our study is the sensitivity analysis we did on left truncation. Cohort studies are frequently influenced because some potential participants do not enter the study because they pass away before the date of inclusion, which is considered left truncation (Addona et al, 2012;Vansteelandt et al, 2017). However, we found that survival time after the date of diagnosis in our cohort was not influenced due to this effect, and this was confirmed with the sensitivity analysis.…”

“…A t-test was used in a sensitivity analysis whether or not to consider left truncation. Left truncation means that a correction may be needed for potential participants who did not survive until the date of inclusion, and, thus, did not enter the study population, resulting in possible overestimation of survival (Addona et al, 2012;Vansteelandt et al, 2017). For this sensitivity analysis, the study population was divided into two groups, one with the participants who had the longest baseline survival time from symptom onset and one with the shortest.…”

A nonparametric test for equality of survival medians using right-censored prevalent cohort survival data

“…the underlying onset dates are drawn from a stationary Poisson point process) the observed failure times are typically referred to as being “length-biased.” For details on testing the validity of the stationary onset process assumption, see the literature. 16–19 Let F L B false( ⋅ false) = 1 − S L B false( ⋅ false) denote the length-biased distribution function for which it may be shown 8 : In this setting, it is sufficient to only use the observed failure/censoring times without the observed truncation times in order to make inferences regarding the unbiased survival function. For a set of length-biased right-censored failure time data, Asgharian and Wolfson established uniform consistency and weak convergence for the NPMLE of S ^ L B and showedwhere U is a Gaussian process.…”

“…For details on testing the validity of the stationary onset process assumption, see the literature. [16][17][18][19] Let F LB (•) = 1 − S LB (•) denote the length-biased distribution function for which it may be shown 8 :…”