Analysis of a nonsusceptible fraction with current status data

Abstract

In studies involving subclinical events, times of events are often subject to interval censoring since their occurrence is only detected at inspection times. When individuals are event-free at an initial time and a single follow-up inspection is made, current status data are obtained. In many settings, however, the population comprised a susceptible and a nonsusceptible subpopulation, where only susceptible individuals will go on to experience the event. Then interest often lies primarily in identifying prognostic variables for susceptibility, and secondarily in the event time distribution among the susceptible individuals. We give a simple mixture model that facilitates estimation of the proportion of susceptible individuals, covariate effects on the odds of susceptibility, and the event time distribution under a current status observation scheme. Asymptotic relative efficiency of maximum likelihood estimators is considered based on the Fisher information for a variety of settings. EM algorithms are proposed for parametric, weakly parametric, and nonparametric estimation of the event time distribution. The methods are applied to motivating studies examining an immunological response to low molecular weight heparin in patients undergoing orthopedic surgery.

Regression Analysis with a Misclassified Covariate from a Current Status Observation Scheme

“…Given the observed covariates Z i and inspection time C i , we model W i conditional on the true susceptibility X i . Specifically, we adopt a latent class model for the current status data with a nonsusceptible fraction proposed by Cook et al (2008). Let S i denote the time to seroconversion and be the corresponding survivor function for the individuals who are seroconvertors; for subjects who are not seroconverters we set S i =∞.…”

“…At each unique inspection time C ( j ) , let denote the number of individuals testing positive and denote the number of seroconverters who test negative, j = 1, …, J . The likelihood function can then be rewritten as Note that depends only on the survival function , and so when one prefers to make no parametric assumptions about the distribution of seroconversion time, a nonparametric maximum likelihood estimate of can be obtained using isotonic regression to impose the order restrictions (Robertson, Wright, and Dykstra, 1988; Lawless, 2003; Cook et al, 2008). As in the case of right‐censored data (Taylor, 1995), for the nonparametric estimate under current status observation schemes it is necessary to impose a constraint that P ( S i > s 0 ∣ X i = 1) = 0 for some s 0 > 0.…”

“…Similarly, the conditional expectation takes the form The maximization of this expression can be dealt with in the same spirit as in Cook et al (2008) under parametric or nonparametric models for the seroconversion time distributions. Under the Weibull regression model, the estimates for the parameter κ and ν from the ( t + 1)st iteration can be achieved by optimizing using standard software for weighted binary regression analysis of W i on the same pseudo‐data set described above, but with a log–log link function as specified in .…”

“…Different forms of semiparametric models have been considered for current status data with the focus typically on maximum‐likelihood inference regarding regression parameters (Jewell and Shiboski, 1990; Rossini and Tsiatis, 1996; Huang and Wellner, 1997; Lin, Oakes, and Ying, 1998; Shiboski, 1998). Semiparametric regression cure rate models have also recently been developed to handle the case where not all individuals in the population are susceptible to having an event (Lam and Xue, 2005; Cook et al, 2008). We make use of this methodology for the analysis of current status data to develop an algorithm for accounting for the current status observation scheme of a seroconversion status covariate among patients in the orthopedic studies.…”

A score test for comparing cross-sectional survival data with a fraction of non-susceptible patients and its application in clinical immunology

“…This formulation has led to proposals for various parametric and non-parametric models [7–10]. The second approach, called a promotion time cure model [11], assumes that the observed time-to-event is the first of some latent event time and has interesting mechanistic interpretations in various biological fields, such as oncology.…”