Estimates of relative risk

Summary For the two-sample problem with proportional hazard functions, we consider estimation of the constant of proportionality, known as relative risk, using complete uncensored data. For this very special case of Cox’s (1972) regression model for survival data, we find a two-step estimate which is asymptotically equivalent to Cox’s partial likelihood estimate, and we show that both estimates are asymptotically optimal (in the sense of minimum asymptotic variance) among all regular rank estimates of relative risk. Supported by NSF grant 81-00748.