Semi- and Non-parametric Methods for Interval Censored Data with Shape Constraints PDF Download

Author: Clifford Isaac Anderson-Bergman
Publisher:
ISBN: 9781303810138
Category :
Languages : en
Pages : 213

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Book Description
Interval censoring occurs when event times are known to have occurred within an interval, rather than observing the exact time of event. This includes observations that are right censored, left censored and contained in intervals such that the left side is greater than the origin and the right side is finite (i.e. neither right censored or left censored). For interval censored data, the most common survival estimator used is the non-parametric maximum likelihood estimator (NPMLE), a generalization of the Kaplan-Meier curve which does not require any uncensored event times. The popularity of this estimator is due in part to the fact that assessing model fit for interval censored data can be very difficult. However, the extreme flexibility of the estimator comes at the cost of high variance, often providing an n^(1/3) convergence rate rather than the more typical n^(1/2). In a compromise between a highly constrained parametric estimator and the overly flexible NPMLE, we apply the popular log-concave density constraint to the NPMLE. By constraining a non-parametric estimator to have a log-concave density, an inves- tigator can improve the performance without needing to select a parametric family or smoothing parameter. We describe a fast algorithm we have developed for finding the log-concave NPMLE for interval censored data. We demonstrate that using the constraint significantly reduces the variance of the survival estimates in comparison to the unconstrained NPMLE via simulations. Next, we present three inference methods for our new estimator. This includes a goodness of fit test, two methods of confidence interval construction and a Cox PH model which incorporates a baseline log-concave distribution. We evaluate the power of the goodness of fit test and compare the other inference methods with the unconstrained counterparts via simulation. We apply these methods to a study on the effects of different environments on the rates of lung cancer among mice and another study investigating age at menopause. While our work demonstrates that the application of the shape constraints can be very helpful in the context of interval censored data, in some situations the log- concave constraint may not allow for as heavy tailed distributions as the investigator would like. To address this, we propose a new, more flexible "inverse convex" shape constraint, examine its behavior via simulation and show that it provides a better fit than the log-concave estimator when applied to real income data, which is well known to be heavy tailed. We are very optimistic about applying this new estimator to censored data, although we have yet to implement an algorithm to do so. We end this work with an algorithm for finding the (unconstrained) bivariate NPMLE for interval censored data. The bivariate NPMLE is used when each subject has two censored outcomes and the investigator is interested in modeling the relation between the two outcomes. Quickly finding the NPMLE has proven to be a challenging computational problem, as the number of parameters to consider is of order O(n^2). We present an efficient EM algorithm to find the bivariate NPMLE. We note that this is not related to shape constrained estimation.