A simple method for analyzing data from a randomized trial with a missing binary outcome.
BACKGROUND
Many randomized trials involve missing binary outcomes. Although many previous adjustments for missing binary outcomes have been proposed, none of these makes explicit use of randomization to bound the bias when the data are not missing at random.


METHODS
We propose a novel approach that uses the randomization distribution to compute the anticipated maximum bias when missing at random does not hold due to an unobserved binary covariate (implying that missingness depends on outcome and treatment group). The anticipated maximum bias equals the product of two factors: (a) the anticipated maximum bias if there were complete confounding of the unobserved covariate with treatment group among subjects with an observed outcome and (b) an upper bound factor that depends only on the fraction missing in each randomization group. If less than 15% of subjects are missing in each group, the upper bound factor is less than.18.


RESULTS
We illustrated the methodology using data from the Polyp Prevention Trial. We anticipated a maximum bias under complete confounding of.25. With only 7% and 9% missing in each arm, the upper bound factor, after adjusting for age and sex, was.10. The anticipated maximum bias of.25 x.10 =.025 would not have affected the conclusion of no treatment effect.


CONCLUSIONS
This approach is easy to implement and is particularly informative when less than 15% of subjects are missing in each arm.
Biometry Research Group, Division of Cancer Prevention, National Cancer Institute, USA. sb16i@nih.gov
Stuart G
SG
Baker
Laurence S
LS
Freedman
D000236:Adenoma / Q000517:prevention & control; D015179:Colorectal Neoplasms / Q000517:prevention & control; D005260:Female; D006801:Humans; D007417:Intestinal Polyps / Q000517:prevention & control; D008297:Male; D015233:Models, Statistical; D009364:Neoplasm Recurrence, Local / Q000517:prevention & control; D016032:Randomized Controlled Trials as Topic; D016896:Treatment Outcome