Use of Concomitant Variables and Incomplete Survival Information in the Estimation of an Exponential Survival Parameter

Abstract

This paper generalizes previous work of Feigl and Zelen, who assumed survival time of a chronic disease (e.g. cancer) patient to follow an exponential distribution. Expected survival time, the reciprocal of the parameter of the exponential, is considered to be linearly related to a measure (concomitant variable) of the severity of the disease. The present paper extends the statistical model to permit maximum likelihood estimation of the parameters of the linear regression where not all patients in a follow-up study have died by the end of the study. For different study lengths the effect on the size of the asymptotic standard errors is determined first assuming all patients to enter together and next assuming entry at regular time intervals. Approximate standard errors are also obtained assuming uniform entry rate and small random variation in the concomitant variable.