Censoring observations

Note that the term censor is introduced in the preceding table. The log-rank test (invoked in SAS with PROC LIFETEST) and the Cox proportional hazards model (invoked in SAS with PROC PHREG) allow for censoring observations in a time-to-event analysis. These tests adjust for the fact that at some point a patient may no longer be able to experience an event. The censor date is the last known time that the patient did not experience a given event and the point at which the patient is no longer considered able to experience the event. Often the censor date is the last known date of patient follow-up, but a patient could be censored for other reasons, such as having taken a protocol-prohibited medication. 

The Kaplan-Meier survival estimates plots are instantiated by specifying PLOTS = (S) in the PROC LIFETEST statement. To show just the line itself, CENSOREDSYMBOL = NONE is specified to hide the censored observations in the plot. EVENTSYMBOL = NONE is specified here to hide the event points, although this is the default setting for... 

Gehan-Breslow Modification of Kruskal-Wallis Test is a nonparametric test on censored observations. It assigns more weight to early incidences compared to Cox-Tarone test. 

The Wilcoxon Rank-Sum Test could be used to analyze the event times in the absence of censoring. A Generalized Wilcoxon Test, sometimes called the Gehan Test, based on an approximate chi-square distribution, has been developed for use in the presence of censored observations. 

A statistical technique used to test the significance of differences between the survival curves associated with two different treatments. It is often used to analyze survival (life vs. death) data when there are censored observations (observations that are unknown because a subject has not been in the study long enough for the outcome to be observed) or to analyze the effects of different treatment procedures. ... 

Censoring in clinical trials usually occurs because the patient is still alive at the end of the period of follow-up. In the above example, if this were the only cause of censoring then all the censored observations would be equal to 24 months. There are, however, other ways in which censoring can occur, such as lost to follow-up or withdrawal. These can sometimes raise difficulties and we will return to discuss the issues in a later section. Also, at an interim analysis the period of follow-up for the patients still alive in the trial would be variable and this would produce a whole range of censored event times our methodology needs to be able to cope with this. 

The proportion of participants with the event is still equal between the groups (this time 0.6 in both). As seen in Figure 8.2, some participants dropped out of the study before reporting the AE, which are denoted by the open circles at days before day 20. When analyzing data in this way, observations for which the event of Interest was not recorded during the time at risk are called censored observations. As noted earlier it... 

When analyzing the time to the AE, we need an analytic way to deal with these censored observations. Although we do not know what would have happened for these participants, we do know that they were at risk for some period of time and "survived" their time in the study without experiencing the AE. Accordingly, the main objective of this analysis is to describe how long participants survive without experiencing the event. 

The event times for the placebo and active groups are provided below ("C" indicates a censored observation) ... 

The unique times at which events occurred (not censored observations) are on days 2, 3, 4, 5,... 

Censoring Type I Type I censoring occurs when observations are made within prespecified fixed time limits, resulting in a random number of censored observations. An example of such censoring occurs when subjects are enrolled in a study of a given duration, and the event of interest has not occurred in some of the subjects by the end of the observation period. The censoring time will be identical for all such subjects and will equal the prespecified study duration. It is also possible that some subjects will drop out of the study or be lost to follow-up and will have censored observations that are less than the study duration. 

Table 2 Percentages of censored observations (less than LOD) for each site included in this study (2004-2006)...

Susarla, V and Van Ryzin, J. 1978. Empirical Bayes estimation of a distribution (survival) function from right censored observations.Tnn. Statist. 6 740-754. 

---