Simple approaches to assess the possible impact of missing outcome information on estimates of risk ratios, odds ratios, and risk differences

Abstract

Often in clinical trials, the primary outcome is binary and the impact of an intervention is summarized using risk ratios (RRs), odds ratios (ORs), or risk differences (RDs). It is typical that in such studies, the binary outcome variable is not observed for some study participants. When there is missing data, it is well known that analyses based on those participants with complete data can be biased unless it can be assumed that the probability of a missing outcome is unrelated to the value of the missing binary outcome (i.e., missing at random). Unfortunately, this assumption cannot be assessed with the data since the missing outcomes, by definition, are not observed. One approach to this problem is to perform a sensitivity analysis to see the degree to which conclusions based only on the complete data would be affected given various degrees of departure from the missing at random assumption. In this paper we provide researchers formulae for doing such a sensitivity analysis. We quantify the departure from the missing at random assumption with a parameter we call the “response probability ratio” (RPR). This is the ratio between the probability of a nonmissing outcome among those with one value of the binary outcome and the probability of a nonmissing outcome among those with the other value of the outcome. Then we provide simple formulae for the estimation of the RRs, ORs, and RDs given any specific values of the RPRs. In addition to being useful for sensitivity analyses, these formulae provide some insight into the conditions that are necessary for bias to occur. In particular, it can be seen that, under certain plausible assumptions, OR estimates based on participants with complete data will be asymptotically unbiased, even if the probability of missing outcome depends on both the treatment and the outcome.