Linear Regression with Interval Censored Data
نویسندگان
چکیده
Ž . are observed instead of the usual Y , Z , where I for some censori i i Y T 4 i i ing times T . This observation scheme is also called the binary choice model i Ž . Coslett 1987 and Case 1 interval censoring Groeneboom and Wellner Ž . 4 4 1992 . We assume that the errors are independent of Z , T and are i i i Ž . i.i.d. variables with a common distribution F t . Situations involving interval censoring arise commonly in engineering and Ž . medicine. In some clinical settings e.g., final follow-up after treatment , an examination at time T determines whether or not an endpoint Y has i i occurred. In reliability studies, destructive tests are often used to find whether Ž . an item e.g., fire extinguisher has failed. In rodent bioassay experiments, the presence or absence of a tumor may only be detected through sacrifices. For certain designs of experiments, T are i.i.d. random variables with a i known probability density. In general, T and Z are associated. In Case 2 i i interval censoring, two censoring variables T T are observed with the i i knowledge that Y is inside the interval T , T . In both cases of interval i i i Ž . censoring and with known 0 , the estimation of the common distribuŽ . tion F of in 1.1 has been considered by many authors under parametric i and nonparametric assumptions; see, for example, Ayer, Brunk, Ewing, Reid Ž . Ž . Ž . and Silverman 1955 , Brunk 1970 , Groeneboom and Wellner 1992 and Ž . Peto et al. 1980 among others. Linear and hazards regression models for Ž . interval censored data have been considered by Finkelstein 1986 , Finkel-
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