Semiparametric Estimation of the Mean and Coefficient of Variation of the Interevent Distribution of a Renewal Process from Cross-Sectional Count Data

• Activity Number: 344 - Semiparametric Modeling
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): John D. Rice* and Robert L. Strawderman and Brent A. Johnson
• Companies: University of Colorado, Denver and University of Rochester and University of Rochester
• Keywords: Renewal process; Regularity; Medical screening tests; Count data models

Abstract

It is important to evaluate both the frequency and regularity of medical screening tests: these quantities are embodied by the mean and coefficient of variation (CV), respectively, of the inter-test time distribution. We are motivated by a situation in which available data consist only of counts of events occurring within a known time interval rather than exact event times. We base our approach to this problem on asymptotic results for renewal processes and propose three estimators for the mean and CV (which may include covariates): the first uses the asymptotic normality of the renewal process, the second an extended quasi-likelihood criterion, and the third two moment conditions providing a system of estimating equations. Crucially, the proposed methods do not require knowledge of the inter-test time distribution. We apply these methods to cross-sectional survey data consisting of 1300 subjects' responses to questions about lifetime number of HIV tests, sexual risk behaviors, and demographics. Our results suggest that having more than 20 lifetime sex partners significantly increases frequency of testing, but decreases regularity; male gender has the reverse effect.