All the methods that we have discussed so far require “complete” observations, in the sense that we know the outcome of the treatment or intervention we are studying. For example, in Chapter 5 we considered a study that compared the rate of filing advance directives in people who received in-person counseling or written instructions (Table 5-1). We compared these two groups of people by computing the expected pattern of thrombus formation in each of the two comparison groups under the null hypothesis that there was no difference in the rate of thrombus formation in the two treatment groups, then used the chi-square test statistic to examine how closely the observed pattern in the data matched the expected pattern under the null hypothesis of no treatment effect. The resulting value of χ2 was “big,” so we rejected the null hypothesis of no treatment effect and concluded that aspirin reduced the risk of thrombus formation. In this study we knew the outcome in all the people in the study after a fixed length of time following treatment. Indeed, in all the methods we have considered in this book so far, we knew the outcome of the variable under study for all the individuals in the study being analyzed. There are, however, situations, in which we do not know the ultimate outcome for all the individuals in the study because the study ended before the final outcome had been observed in all the study subjects or because the outcome in some of the individuals is not known.* In addition, it would be desirable to take into account the outcomes in people who were enrolled in the study for varying lengths of follow-up that allows for the fact that the more time that passes after treatment the more likely it is that there would be the outcome of interest. We now turn our attention to developing procedures for such data.
The most common type of study in which we have incomplete knowledge of the outcome are clinical trials or survival studies in which individuals enter the study and are followed up over time until some event—typically death or development of a disease—occurs. Since such studies do not go on forever, it is possible that the study will end before the event of interest has occurred in all the study subjects. In such cases, we have incomplete information about the outcomes in these individuals. In clinical trials it is also common to lose track of patients who are being observed over time. Thus, we would know that the patient was free of disease up until the last time that we observed them, but we do not know what happened later. In both cases, we know that the individuals in the study were event free for some length of time, but not the actual time to an event. These people are lost to follow-up; such data are known as censored data.** Censored data are most common ...