Comment: Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies.

The authors suggest an interesting way to measure the fraction of missing information in the context of hypothesis testing. The measure seeks to quantify the impact of missing observations on the test between two hypotheses. The amount of impact can be useful information for applied research. An example is, in genetics, where multiple tests of the same sort are performed on different variables with different missing rates, and follow-up studies may be designed to resolve missing values in selected variables. In this discussion, we offer our prospective views on the use of relative information in a follow-up study. For studies where the impact of missing observations varies greatly across different variables and where the investigators have the flexibility of designing studies that can have different efforts on variables, an optimal design may be derived using relative information measures to improve the cost-effectiveness of the followup. Using the simple motivation example in their paper, we examine the estimation of relative information by RI1 and RI0 in terms of unbiasedness and variability, and discuss issues that require further research. Although the relative information measure developed in their paper estimates the mean impact of the missing data, the actual impact may be highly variable when the amount of information in the observed data is moderate or small, which makes the estimated mean relative information a less reliable prediction of the actual impact of missing observations. For this reason, we suggest a simple way to estimate the variability of relative information between complete data and observed data in the simple motivation example. Further investigation is required in incorporating these variability estimates into the optimal design of follow-up studies.