ROBUSTNESS OF CONFIDENCE INTERVALS FOR RARE EVENTS
Author(s)
Su Z1, Mendelsohn A1, Kim J2, Gemmen E31Outcome Sciences, a Quintiles Company, Cambridge, MA, USA, 2Quintiles Global Consulting, London, Reading Berkshir, United Kingdom, 3Quintiles Global Consulting, Rockville, MD, USA
OBJECTIVES: Accurately estimating the upper bounds of confidence intervals for rare events such as hospitalization or death is an important activity in safety studies and outcomes research. Confidence intervals, however, for rare events are subject to considerable variation based upon the overall sample size and total number of observed events. This has led to a challenging convention that a minimum of 2 or 3 events are needed for computing meaningful confidence intervals. The objective of this study was to quantify the variation of the upper bound of confidence intervals for a binomial proportion in the setting of rare events. METHODS: Clopper-Pearson confidence intervals were constructed for sample sizes ranging from 50 to 1000, and numbers of events from 0 to 5. The robustness of the confidence interval was evaluated by calculating additional confidence intervals assuming: 1) one more observed event than in the original sample and, 2) that the proportion of events is equal to the upper bound of the confidence interval for the original sample. RESULTS: With sample sizes of 50, 100, 200, 500 and 1000, the upper bounds of the confidence intervals were 13.71%, 7.04%, 3.57%, 1.44% and 0.72%, respectively, with 2 observed events in the original sample; 16.55%, 8.52%, 4.32%, 1.74% and 0.87%, respectively, (3 observed events); and, 26.40%, 13.94%, 7.16%, 2.91% and 1.47%, respectively, when the proportion of events was equal to the upper bound of the confidence interval for the original sample with 2 events. Similar trends were seen when using other numbers of observed events. CONCLUSIONS: The upper bounds of confidence intervals for rare events vary greatly with sample sizes and the numbers of events observed when the sample size is small. A minimum of 500 subjects is optimal for constructing confidence intervals for rare events, even if 2 events or less are observed.
Conference/Value in Health Info
2012-06, ISPOR 2012, Washington, D.C., USA
Value in Health, Vol. 15, No. 4 (June 2012)
Code
PRM43
Topic
Methodological & Statistical Research
Topic Subcategory
Confounding, Selection Bias Correction, Causal Inference
Disease
Multiple Diseases