M. Pagano et al., REGRESSION-ANALYSIS OF CENSORED AND TRUNCATED DATA - ESTIMATING REPORTING-DELAY DISTRIBUTIONS AND AIDS INCIDENCE FROM SURVEILLANCE DATA, Biometrics, 50(4), 1994, pp. 1203-1214
AIDS surveillance provides a vital source of information for health de
partments to assess the AIDS epidemic and to plan for future health-ca
re needs. However, the use of surveillance data requires proper adjust
ments for the underreporting of AIDS cases caused by the delay in repo
rting diagnosed AIDS cases to the surveillance system. The statistical
problem of adjusting for this underreporting concerns making inferenc
es about an unobservable random sample of which only a portion is obse
rved in a chronologic time interval defined by the analysis. Most regr
ession methods for making inferences using right-truncated data employ
a reverse-time hazard function, which requires that the observed data
be transformed so that methods for left-truncated data can be applied
. In this paper, we discuss fitting regression models to data that can
be truncated and even censored in arbitrary intervals. The proposed m
ethodology was applied to the national AIDS surveillance data provided
by the Centers for Disease Control to analyze the trend of delays ove
r chronologic time and variation among different geographic regions as
well as across risk groups.