Estimation in a Competing Risks Proportional Hazards Model Under Length-biased Sampling with Censoring

Abstract

Consider a population of individuals who experience two causes of death.We observe the ones alive at time t0 and follow them until death or possiblecensoring time. Given this length biased sample, we introduce an estimator ofthe survival function of "initial survival times" (i.e. for the entire population)under the assumption of proportional hazards for the two causes of death. Thelarge sample behavior of our estimator is also studied.