TY - JOUR

T1 - Semiparametric Efficient Estimation in the Generalized Odds-Rate Class of Regression Models for Right-Censored Time-to-Event Data

AU - Scharfstein, Daniel O.

AU - Tsiatis, Anastasios A.

AU - Gilbert, Peter B.

N1 - Funding Information:
This research was sponsored in part by National Institute of Health Grants R01-AI-31789 from NIAID, R01-CA-51962 from NCI, R01-AI-32475 from NIAID, R01-MH-56639 from NIMH, and R01-DA-10184 from NIDA . The authors are grateful to Drs. James Robins and Aad van der Vaart for their help in the preparation of this manuscript.

PY - 1998

Y1 - 1998

N2 - 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×1 covariate vector Z, β is a q×1 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.

AB - 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×1 covariate vector Z, β is a q×1 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.

KW - Nonparametric maximum likelihood

KW - Proportional hazards model

KW - Proportional odds model

KW - Survival analysis

UR - http://www.scopus.com/inward/record.url?scp=0032245819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032245819&partnerID=8YFLogxK

U2 - 10.1023/A:1009634103154

DO - 10.1023/A:1009634103154

M3 - Article

C2 - 9880995

AN - SCOPUS:0032245819

VL - 4

SP - 355

EP - 391

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

SN - 1380-7870

IS - 4

ER -