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I have read in many places that power in survival analysis depends on the number of events rather than the total number of observations (events + non-events).

Suppose I have 10 events and 90 non-events and I want to test for survival differences between two groups: High Risk and Low Risk as classified by a diagnostic test.

Then suppose I add in 100 non-events, which, with my reasonably good diagnostic test, are more likely to be classified as low risk. Wouldn’t this increase the effect size (hazard ratio for High Risk v Low Risk), and therefore the power, without changing the number of events?

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  • $\begingroup$ What do you mean by "non-event"? Survival analyses are for data collected as the elapsed time until a one-time event. For some people/animal/object, that event may not have occurred by the time of collection. Survival analysis accounts for these censored observations. But "censored" means the event had not happened by time of data collection, or you don't know if it happened past a certain time point, or maybe it happened but the experimental protocol wasn't followed so the data must be censored. But "non-event" doesn't really enter into survival analysis. Details on experimental design??? $\endgroup$ – Harvey Motulsky Feb 26 '17 at 17:25
  • $\begingroup$ I'm analysing a cohort study where people were followed for 10 years. By "non-event" I mean that they were not dead at ten years $\endgroup$ – Scarper Feb 26 '17 at 17:43
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Adding in censored ("non-event") cases does not improve power in terms of precision of estimating regression coefficients/hazard ratios in Cox regression. This paper, for example, and the papers that it cites demonstrate that fact.

The issue is that the calculations relating predictor variables to outcome are only performed at the times of events. Censored cases thus don't help relate survival to predictors in regression. Censored cases might help refine the shape of the baseline hazard, and thus do add useful information, but they don't add to the precision of the hazard ratios that act on that baseline hazard.

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  • $\begingroup$ You said the censored cases don't improve the precision of the regression coefficients; can they change the magnitude of the coefficients/hazard ratios? Would a general conclusion be that censored cases can change the effect size between groups you want to compare, but won't make it more likely that the effect is significant? $\endgroup$ – Scarper Mar 1 '17 at 15:07
  • $\begingroup$ @Scarper that is how I understand it. The censored cases do contribute to the hazard and to the relation of hazard to the predictors at each event time, but the censored cases don't increase the effective N for the regression, which is the number of events. This is one of the more depressing aspects of survival analysis; it's the number of people who don't survive that matters. $\endgroup$ – EdM Mar 1 '17 at 16:06
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What you are calling a "non-event" is a person/animal/object with a very long survival time, so long that the event hasn't occurred at the time of data collection. These individual provide lots of information, so of course affect the power of the study. They are not missing values. Rather, they have a very long survival time.

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