We study the asymptotic behavior of the maximum partial likelihood estimator in the Cox proportional hazards model in the presence of nuisance parameters when the entry of patients is staggered. When entry of patients is simultaneous and there is only one regression parameter in the Cox model, the efficient score process of the partial likelihood is martingale and converges weakly to a time-chnaged Brownian motion. Our problem is to get a similar result in the presence of nuisance parameters when entry of patient is staggered.