Semiparametric Efficient Estimation in the Generalized Odds-Rate Class of Regression Models for Right-Censored Time-to-Event Data

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Abstract

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant ρ and assumes that gρ(S(t|Z)) = α(t) + β′Z where gρ(s) = log(ρ−1(s−ρ−1)) for ρ > 0, g0(s) = log(− log s), S(t|Z) is the survival function of the time to event for an individual with q covariate vector Z, β is a q vector of unknown regression parameters, and α(t) is some arbitrary increasing function of t. When ρ=0, this model is equivalent to the proportional hazards model and when ρ=1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for β and exp(α(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for β is semiparametric efficient in the sense that it attains the semiparametric variance bound.

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