title: Statistical inference methods for recurrent event processes with shape and size parameters.
abstract: This paper proposes a unified framework to characterize the rate function of a recurrent event process through shape and size parameters. In contrast to the intensity function, which is the event occurrence rate conditional on the event history, the rate function is the occurrence rate unconditional on the event history, and thus it can be interpreted as a population-averaged count of events in unit time. In this paper, shape and size parameters are introduced and used to characterize the association between the rate functionλ(·) and a random variableX. Measures of association betweenXandλ(·) are defined via shape- and size-based coefficients. Rate-independence ofXandλ(·) is studied through tests of shape-independence and size-independence, where the shape-and size-based test statistics can be used separately or in combination. These tests can be applied whenXis a covariable possibly correlated with the recurrent event process throughλ(·) or, in the one-sample setting, whenXis the censoring time at which the observation ofN(·) is terminated. The proposed tests are shape- and size-based, so when a null hypothesis is rejected, the test results can serve to distinguish the source of violation.
authors.affiliation: Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University, 615 N. Wolfe Street, Baltimore, Maryland 21205, U.S.A.
authors.forename: Mei-Cheng
authors.initials: MC
authors.lastname: Wang
authors.affiliation: Division of Biostatistics and Bioinformatics, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University, 550 N. Broadway, Baltimore, Maryland 21205, U.S.A.
authors.forename: Chiung-Yu
authors.initials: CY
authors.lastname: Huang
keywords: Intensity function; Point process; Poisson process; Rate function; Rate-independence; Shape-independence; Size-independence