Many randomized clinical trials schedule subjects to undergo some assessment at a fixed time (or times) after the initiation of treatment. Often, these follow-up measurements may be missing for some subjects because a disease-related event occurred prior to the time of the follow-up observation. For example, a study of congestive heart failure may schedule patients to undergo exercise testing at 12 weeks, but this measurement may be missing for those who died of heart disease during the study. In such cases, the measurements are informatively missing because mortality from heart disease and a decline in exercise both indicate progression of the underlying disease. It is inappropriate, therefore, to treat these missing observations as missing-at-random and ignore them in the analysis. In one approach to this problem, investigators have included such patients in the analysis of the follow-up data by assigning a rank that represents a "worst-rank score" relative to those actually observed. Some, however, have criticized this procedure as having the potential to produce biased results. In this paper, we explore the statistical properties of such an analysis. We show under a specific model that the imputation of a worst-rank score for informatively missing observations provides an unbiased test against a restricted alternative. We also describe generalizations that employ the actual times of the informative event. We present an example from a study of congestive heart failure. Last, we discuss the implications of this approach and of other methods.