A Goodness-of-Fit Test for One-Sample Life Table Data
针对分组删失数据，提出一种不依赖删失分布假设的拟合优度检验，用于检验假设的生存曲线与观测数据的一致性，适用于寿命测试和医学试验。
Abstract Grouped censored data are common in life testing, medical trials, and other fields. Individuals, subject to a disease, have their lifetimes recorded as belonging to a certain interval. If the individuals are censored or removed before death, then it is only known that their lifetimes were at least as great as the beginning of the interval in which the individuals were censored. A goodness-of-fit problem is to test the agreement of a hypothesized survival curve with the observed data. Several tests have been proposed in the literature that require various assumptions about the censoring distribution. It is shown in this article that if these conditions are relaxed, then the tests may no longer have the stated properties, such as the correct size. To derive a test under minimal conditions, the maximum likelihood estimates of the probability of death or censoring in an interval are found, given that the probability of death in the absence of censoring is a certain quantity. The estimates are used to construct the maximum likelihood test of the fit of the postulated survival curve. The test does not require any assumptions about the censoring marginal distribution. If the assumptions for the more specific tests hold, however, then there may be some loss of power.