Estimating Survivorship when the Subjects are Visited Periodically

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Abstract
Statistical methods for estimating and comparing constant survival rates are developed here for sampling designs in which survival of a subject is checked at irregular intervals. The maximum likelihood estimator is derived and shown to be readily calculated using an iterative procedure that starts with the Mayfield (1975) estimate as a trial value. Sampling distributions of this estimator and of the product of two or more estimates are skewed, and normalizing transformations are provided to facilitate valid confidence interval estimation. The sampling distribution of the difference between two independent estimates is found to be sufficiently normal without transformation to allow valid use of conventional normal theory procedures for testing differences and determining sample size for specified power. Statistical validity under the variable intensity sampling design does require that the duration of intervisit periods vary independently of observer perceptions concerning the survival status of the subject and, in order to achive robustness with respect to the assumption of constant survivorship, sampling intensity must vary independently of any temporal changes in the daily survival rate. Investigators are warned not to return earlier than planned to subjects thought to have died, as this observer behavior may cause serious bias in the survivorship estimate.

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