Some clinical trials perform repeated measurements on patients over time, plot those measures against time, and summarize the results in terms of the area under the curve. If the measured variable is health status, the summary outcome is sometimes referred to as years of healthy life (YHL), or quality-adjusted life years (QALY). This paper investigates some theoretical and practical aspects of randomized trials designed to assess measures such as YHL. We first derived algebraic expressions for the effect size of YHL measures under several theoretical models of the treatment's effect on health. We used these expressions to examine how the length of the study, the number of measurements per person and the correlations among health measurements over time influence the effect size. We also explored the relative statistical power of analyses based on YHL versus analyses based on change-scores using the same data. We present an example. Findings suggest that: (i) the number of measurements per person need not be large; (ii) high correlation among measures over time tends to lower the power of a study using YHL; (iii) a longer study will not always provide more power than a shorter study, and (iv) analyses based on YHL may have less power than change-score analyses. Some of these findings depend on the model of change in health status caused by the treatment. Such models require further study.