10.2 Estimation

The quantities \(\Gamma_k, \; k = 1, 2, 3\), \(\Lambda\), and \(S\) can be estimated in the usual way. \(\Gamma_1\), the is estimated by regarding all other causes (2 and 3) as censorings. The total survivor function \(S\) is estimated by the method of Kaplan-Meier, regarding all causes as the same cause (just death).

Is it meaningful to estimate (calculate) \(S_k(t) = \exp\left\{-\Gamma_k(t)\right\}, \; k = 1, 2, 3\)? The answer is “No”. The reason is that it is difficult to define what these probabilities mean in the presence of other causes of death. For instance, what would happen if one cause was eradicated?