Current status observation on survival times has recently been widely studied. An extreme form of interval censoring, this data structure refers to situations where the only available information on a survival random variable, T, is whether or not T exceeds a random independent monitoring time C, a binary random variable, Y. To date, nonparametric analyses of current status data have assumed the availability of i.i.d. random samples of the random variable (Y, C), or a similar random sample at each of a set of fixed monitoring times. In many situations, it is useful to consider a case-control sampling scheme. Here, cases refer to a random sample of observations on C from the sub-population where T is less than or equal to C. On the other hand, controls provide a random sample of observations from the sub-population where T is greater than C. In this paper, we examine the identifiability of the distribution function F of T from such case-control current status data, showing that F is identified up to a one parameter family of distribution functions. With supplementary information on the relative population frequency of cases/controls, a simple weighted version of the nonparametric maximum likelihood estimator for prospective current status data provides a natural estimate for case-control samples. Following the parametric results of Scott and Wild (1997), we show that this estimator is, in fact, nonparametric maximum likelihood.
Epidemiology | Statistical Methodology | Statistical Theory | Survival Analysis
Jewell, Nicholas P. and van der Laan, Mark J., "Case-Control Current Status Data" (September 2002). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 116.