Survival analysis with censored data: a further twist on ignorability conditions

A key assumption for the application of methods concerning censored data is that the random nature of the censoring mechanism should be ignorable when making likelihood-based inferences. The constant-sum property is an ignorability assumption that is critical for the correct use of a simplified version of the likelihood function and for the identifiability of the survival function [Oller R, Gomez G, Calle ML. Interval censoring: identifiability and the constant-sum property. Biometrika. 2007;94(1):61-70]. It has been proven to be weaker than the assumption of independence between the lifetime variable and the assessment process that leads to censored data. An important caveat is that the theoretical framework established in the class of constant-sum censoring models requires full knowledge of the support of the lifetime variable. In the present work we investigate the consequences of a wrong specification of the support. One might naively expect that this information is not necessary and that, for instance, the estimation of the survival function would assign null or almost null probabilities to regions outside the support. We reveal via examples that this premise is generally true but there are also several exceptions. To shed light on this issue, we introduce a new ignorability condition that extends the constant-sum property and removes the knowledge of the support from the equation. We also show that the independence assumption is stronger than the new extended constant-sum condition.