Estimating the cognitive effects of statins from observational data using the survival-incorporated median: a summary measure for clinical outcomes in the presence of death

The issue of "truncation by death" commonly arises in clinical research: subjects may die before their follow-up assessment, resulting in undefined clinical outcomes. This article addresses truncation by death by analyzing the Long Life Family Study (LLFS), a multicenter observational study involving over 4000 older adults with familial longevity. We are interested in the cognitive effects of statins in LLFS participants, as the impact of statins on cognition remains unclear despite their widespread use. In this application, rather than treating death as a mechanism through which clinical outcomes are missing, we advocate treating death as part of the outcome measure. We focus on the survival-incorporated median, the median of a composite outcome combining death and cognitive scores, to summarize the effect of statins. We propose an estimator for the survival-incorporated median from observational data, applicable in both point-treatment settings and time-varying treatment settings. Simulations demonstrate the survival-incorporated median as a simple and useful summary measure. We apply this method to estimate the effect of statins on the change in cognitive function (measured by the Digit Symbol Substitution Test), incorporating death. Our results indicate no significant difference in cognitive decline between participants with a similar age distribution on and off statins from baseline. Through this application, we aim to not only contribute to this clinical question but also offer insights into analyzing clinical outcomes in the presence of death.