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We extend Cox's classical regression model to accomodate partially informative censored data. In this type of data, each observation is the minimum of one lifetime and two censoring times. The survival function of one of these censoring times is a power of the survival function of the lifetime. We call this the informative censoring time. The distribution of the other censoring time has no relation with the distribution of the lifetime. It is called the non-informative censoring time. In thisdoi:10.1081/sta-200066346 fatcat:kzfeibdkyjczzckkj2wgufmg2q