AN EM ALGORITHM FOR SMOOTHING THE SELF-CONSISTENT ESTIMATOR OF SURVIVAL FUNCTIONS WITH INTERVAL-CENSORED DATA

Interval-censored data arise in a wide variety of application and rese arch areas such as, for example, AIDS studies (Kim et al., 1993) and c ancer research (Finkelstein, 1986; Becker & Melbye, 1991). Peto (1973) proposed a Newton-Raphson algorithm for obtaining a generalized maxim um likelihood estimate (GMLE) of the survival function with interval-c ensored observations. Turnbull (1976) proposed a self-consistent algor ithm for interval-censored data and obtained the same GMLE. Groeneboom & Wellner (1992) used the convex minorant algorithm for constructing an estimator of the survival function with ''case 2'' interval-censore d data. However, as is known, the GMLE is not uniquely defined on the interval [0, infinity). In addition, Turnbull's algorithm leads to a s elf-consistent equation which is not in the form of an integral equati on. Large sample properties of the GMLE have not been previously exami ned because of, we believe, among other things, the lack of such an in tegral equation. In this paper, we present an EM algorithm for constru cting a GMLE on [0, infinity). The GMLE is expressed as a solution of an integral equation. More recently, with the help of this integral eq uation, Yu et al. (1997a, b) have shown that the GMLE is consistent an d asymptotically normally distributed. An application of the proposed GMLE is presented.