Can you increase power in survival analysis by increasing the number of non-events? 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?
 A: 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, Hsieh and Lavori, Control Clin Trials 2000;21:552–560, 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 Cox 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.
With a fully parametric survival model, censored cases do make contributions to the likelihood and thus can increase power in terms of more precise coefficient estimates.
A: 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. 
