Survival analysis: the importance of censored observations

We have considered the issue of predicting from diagnosis of a condition such as malignant melanoma survival past an often arbitrarily chosen fixed time-point, such as 5 years. Prediction of survival past any time-point becomes rather complicated due to the presence of 'censored observations', and these observations are often ignored in any analysis. Censored observations are subjects who either die of causes other than the disease of interest or are lost to follow-up. The aim of this paper is to show that the result of ignoring these 'censored observations' is an underestimation of the probability of survival beyond the fixed time-point. Ignoring these censored observations results in potentially valuable information on survival being thrown away. This underestimation will often prove to be of considerable magnitude and dependent on the proportion of censored observations present in the data. It is therefore essential to carry out a full actuarial survival analysis which will incorporate all the information contained in these censored observations.