A Chi-Squared Type Goodness of Fit Test for Recurrent Event Data

• Activity Number: 169
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Akim Adekpedjou*+ and Gideon Zamba+
• Companies: Missouri University of Science and Technology and University of Iowa
• Keywords: Recurrent Events ; Gaussian Process ; Pitman's Alternative ; Goodness of Fit

Abstract

Goodness of fit of the distribution function governing the time to occurrence of a recurrent event is considered. We develop a chi-squared type of test based on a nonparametric maximum likelihood estimator (NPMLE) for testing the distribution function of the inter event time of recurrent event data. The test is of the inter-event time distribution for recurrent events. The test compares a parametric null to the NPMLE over $k$ partitions of a calendar time $s$. We investigate small sample and asymptotic properties of the test as well as power analysis against a sequence of Pitman's alternatives. Four variants of the test resulting from a combination of variance estimators and censoring were studied. The conclusion that transpires from the finite sample simulation study is that significant level is achieved when the right-censoring random variable is not ignored and $k > 3$. For exponential model, the tests are less powered to detect lighter right tail distribution than they are for left tails (contrary to Weibull model findings). The Weibull model has a slow response to heavier left tail distributions. We apply the test to a real-life recurrent event data.