3
$\begingroup$

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?

Improve this question
$\endgroup$
2
  • $\begingroup$ 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
    Commented Feb 26, 2017 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
    Commented Feb 26, 2017 at 17:43

2 Answers 2

Reset to default
7
$\begingroup$

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.

Improve this answer
$\endgroup$
4
  • $\begingroup$ 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
    Commented Mar 1, 2017 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
    Commented Mar 1, 2017 at 16:06
  • 1
    $\begingroup$ This claim bothers me. In current status data, all events are right or left censored and we can fit a semi-parametric Proportional Hazards regression models to them. I'm trying to determine how both could be true. One explanation would be that we fit the current status PH model using the full likelihood rather than partial. This also suggests we may get significantly more power from using the full likelihood rather than the partial likelihood if we have a heavily censored dataset? $\endgroup$
    – Cliff AB
    Commented May 15, 2022 at 15:48
  • 1
    $\begingroup$ @CliffAB It can be frightening to come back to an answer 5 years later, as I did today to update a broken link. I think that the full versus partial likelihood distinction is key here; my original answer was focused on Cox regressions, while the question was perhaps more generic. Even if censored cases don't increase power for distinguishing differences in regression coefficients, they increase the precision of baseline-survival estimates from a Cox model. They clearly contribute to likelihoods in fully parametric models. I've expanded a bit on that distinction. Thanks. $\endgroup$
    – EdM
    Commented May 15, 2022 at 16:06
0
$\begingroup$

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.

Improve this answer
$\endgroup$
3
  • $\begingroup$ That is not necessarily true. If a subject is right censored at $t = 1$ and typical event time is $t = 100$, we have very little information of whether they had a long survival time. $\endgroup$
    – Cliff AB
    Commented May 15, 2022 at 15:03
  • $\begingroup$ @CliffAB Depends on what the OP meant by "nonevents". I interpret to mean the event hasn't happened by the end of data collection. It seems that you interpret it to mean any reason for censoring at any time. With that definition, of course you are right. $\endgroup$
    – Harvey Motulsky
    Commented May 26 at 22:28
  • $\begingroup$ I don't think we are disagreeing about what non-events mean, I simply mean that whether the data is "informative" can be is dependent on the relation between the censoring time/study end and expected event time. As a stupid example, if we observed a cohort 1k patients for 1 hour and observed that none of them got cancer, we didn't really learn anything about their cancer risk. But if we observed 1k patients for 20 years and none of them got cancer that's an interesting finding. $\endgroup$
    – Cliff AB
    Commented May 27 at 4:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.