Comparing Observed Life Table Data with a Known Survival Curve in the Presence of Random Censorship

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Abstract
A simple statistic is presented for comparing grouped survival data, which may be variably right censored, with a known survival curve. The known or hypothesized survival curve may be specified either analytically or in terms of a life table. This statistic has good power against local proportional hazard alternatives. The asymptotic distribution theory of the test is valid provided terms of order O(.DELTA.3) in the actuarial interval lengths .DELTA. are negligible. For comparison an actuarial modification of a statistic studied by Breslow (1977) is given which has the desired asymptotic distribution if terms of order O(.DELTA.2) are negligible. In the presence of intrainterval censorship, a statistic proposed by Oleinick and Mantel (1970) has the asserted asymptotic distribution only if terms of order O(.DELTA.) are negligible. The statistic proposed is preferable for coarsely grouped data. For short intervals with small death and censorship probabilities, the 3 statistics are numerically close. [This study is relevant to human epidemiological statistics.].