In standard linear regression, though one samples from the joint distribution of the variable of interest and covariates, the analysis is carried out conditionally because the marginal distribution of the covariates is considered ancillary to the parameters of interest. When sampling is done with length-bias with respect to the response variable, as can be the case with survival data from prevalent cohorts, the covariates are also sampled with a bias. The question is whether the marginal distribution holds any information about the parameters and, if so, should one adapt the usual methods of analysis to account for it? We present an adjusted (joint) likelihood approach for length-biased survival data with left truncation and right censoring and compare it with a conditional approach which ignores the information in the sampling distribution of the covariates. It is shown that taking the covariates into consideration yields more efficient estimates. The methods are applied to data on survival with dementia from the Canadian Study on Health and Aging (CSHA). If time permits, extension of these ideas to data on recurrent events will be addressed.
Group for Research in Decision Analysis