Effect of length biased sampling of unobserved sojourn times on the survival distribution when disease is screen detected

Abstract

Data can arise as a length-biased sample rather than as a random sample; e.g. a sample of patients in hospitals or of network cable lines (experimental units with longer stays or longer lines have greater likelihoods of being sampled). The distribution arising from a single length-biased sampling (LBS) time has been derived (e.g. (The Statistical Analysis of Discrete Time Events. Oxford Press: London, 1972)) and applies when the observed outcome relates to the random variable subjected to LBS. Zelen (Breast Cancer: Trends in Research and Treatment. Raven Press: New York, 1976; 287-301) noted that cases of disease detected from a screening program likewise form a length-biased sample among all cases, since longer sojourn times afford greater likelihoods of being screen detected. In contrast to the samples on hospital stays and cable lines, however, the length-biased sojourns (preclinical durations) cannot be observed, although their subsequent clinical durations (survival times) are. This article quantifies the effect of LBS of the sojourn times (or pre-clinical durations) on the distribution of the observed clinical durations when cases undergo periodic screening for the early detection of disease. We show that, when preclinical and clinical durations are positively correlated, the mean, median, and quartiles of the distribution of the clinical duration from screen-detected cases can be substantially inflated-even in the absence of any benefit on survival from the screening procedure. Screening studies that report mean survival time need to take account of the fact that, even in the absence of any real benefit, the mean survival among cases in the screen-detected group will be longer than that among interval cases or among cases that arise in the control arm, above and beyond lead time bias, simply by virtue of the LBS phenomenon

Size bias for one and all

“…Nearer to the present, the 2009 paper [50] considers issues arising in assessing the value of medical screening and the effects of subsequent early treatment on survival time. As discussed in [50], for reasons analogous to waiting-time bias, the durations of preclinical disease states detected by certain screening protocols are subject to length bias. Even though the durations themselves are not observed, longer durations are likely to derive from slower-acting instances of the disease under consideration, and hence are correlated a priori with longer survival times.…”

Improving safety climate through a communication and recognition program for construction: a mixed methods study

“…The workers who are on-site >30 days are different in their distribution of trade, job title, race/ethnicity, and baseline musculoskeletal pain than workers who are on-site <30 days (16). The surveys analyzed in this study may not reflect a population representative of the true worksite composition, with those captured tending to be healthier (26). Within our sample, we addressed this issue of potential bias by controlling for time-varying parameters (total time on-site and month started) in our analysis.…”

Quantification of length‐bias in screening trials with covariate‐dependent test sensitivity

“…Screen‐detected incident cases are those for which , for otherwise the case presented clinically before it could be screen detected. The probability P is conditional on being in at the time of screen, and is denoted by the cumulative distribution function (cdf) (Kafadar and Prorok, ). …”

“…Most of the literature on LBS has focused not on quantification of its consequences but rather on estimation of its density (Cox, ; Walter and Day, , ; Blumenthal, ), and on survivor function estimation (Vardi, ; Vardi and Zhang, ). Kafadar and Prorok () quantify the LBS effect under different scenarios based on a joint model for the preclinical and clinical durations as a bivariate gamma density. While this density is flexible, the sensitivity of the inferences to results using the bivariate gamma model was not investigated.…”

“…In this paper, we extend the method of Kafadar and Prorok () for deriving the joint density of preclincal and clinical duration (survival time) in the length‐biased sample to the bivariate lognormal distribution to accommodate an expanded range of correlations, shapes, and scales, and also model test sensitivity as a function of subject‐level covariates. The overall correlation from the bivariate gamma joint density is constrained (Jones et al., 2000), forces the same correlation for the two disease states, and the densities are forced to lose skewness to obtain high correlations between sojourn time and clinical duration.…”