Detecting telomere elongation in longitudinal datasets: analysis of a proposal by Simons, Stulp and Nakagawa.

Telomere shortening has emerged as an important biomarker of aging. Longitudinal studies consistently find that, although telomere length shortens over time on average, there is a subset of individuals for whom telomere length is observed to increase. This apparent lengthening could either be a genuine biological phenomenon, or simply due to measurement and sampling error. Simons, Stulp & Nakagawa (2014) recently proposed a statistical test for detecting when the amount of apparent lengthening in a dataset exceeds that which should be expected due to error, and thus indicating that genuine elongation may be operative in some individuals. However, the test is based on a restrictive assumption, namely that each individual's true rate of telomere change is constant over time. It is not currently known whether this assumption is true. Here we show, using simulated datasets, that with perfect measurement and large sample size, the test has high power to detect true lengthening as long as the true rate of change is either constant, or moderately stable, over time. If the true rate of change varies randomly from year to year, the test systematically returns type-II errors (false negatives; that is, failures to detect lengthening even when a substantial fraction of the population truly lengthens each year). We also consider the impact of measurement error. Using estimates of the magnitude of annual attrition and of measurement error derived from the human telomere literature, we show that power of the test is likely to be low in several empirically-realistic scenarios, even in large samples. Thus, whilst a significant result of the proposed test is likely to indicate that true lengthening is present in a data set, type-II errors are a likely outcome, either if measurement error is substantial, and/or the true rate of telomere change varies substantially over time within individuals.