Individual responses made easy.

WE ALL INHERIT AND ACQUIRE different characteristics. When we experience a treatment aimed at changing our physiology, these characteristics may modify the effect of the treatment, making it more or less beneficial, harmful, or ineffective in different individuals. The issue of individual responses to treatments is therefore one of the most important in experimental research, yet few researchers acknowledge the issue in their published studies, and attempts to quantify individual responses are rare and usually deficient. This climate of neglect and ignorance needs to change, especially now that genome sequencing and pervasive monitoring of individuals can provide researchers with the subject characteristics that account for individual responses and allow more efficient ethical targeting of treatments to individuals. The synthesis review by Hecksteden and colleagues (2) in this issue of the Journal of Applied Physiology is timely, because it deals with some of the methodological challenges in quantifying individual responses in parallel-group controlled trials, where an experimental and control group are measured before and after their respective treatments. The authors assert that proper quantification of individual responses requires repeated administration of the experimental treatment to determine the extent to which each individual’s response consists of reproducible and random components additional to the random variation due to error of measurement experienced equally by all individuals. In essence, the reproducible individual responses are those that could be explained by differences between subjects in inherited and acquired stable characteristics or traits, whereas the apparently random responses could be due to changes in subject characteristics or states between administrations of the treatment. Although two or more administrations are indeed required to partition individual responses into these two components, partitioning is possible only if effects of the treatment wash out fully between administrations. Repeated administrations therefore make sense for acute effects of short-term treatments, where the treatments should be administered in crossover fashion (7). For training and other long-term treatments, repeated administrations are seldom logistically feasible, nor are they even possible in principle, if the intent of the study is to provide evidence for a permanent change in behavior or physiology. In any case, for long-term treatments, subject states average out to become subject traits, so one can expect the random component of individual responses due to subject states to become trivial or meaningless. The Hecksteden et al. synthesis review is based on sound but challenging statistical principles, and the focus on repeated administration of treatments may distract researchers from the straightforward and legitimate analysis of individual responses to a single administration of a treatment. The authors have referenced several of my own publications on the appropriate methods (3-6), but I will update and summarize the methods here, in the hope of improving the analysis and reporting of controlled trials at least in this journal. Individual responses are manifest as a larger standard deviation of the change scores in the experimental group than in the control group. It is therefore imperative that researchers report the standard deviations of the change scores, along with the means. This simple requirement will also provide all the inferential information needed for inclusion of the study in meta-analyses not only of the mean effect of the treatment but also of the individual responses. The individual responses are summarized by a standard deviation (SDIR) given by the square root of the difference between the squares of the standard deviations of the change scores in the experimental (SDExp) and control (SDCon) groups: SDIR (SDExp SDCon). One should consider this standard deviation to be the amount by which the net mean effect of the treatment differs typically between individuals. Confidence limits for the standard deviation are obtained by assuming its sampling variance is normally distributed, with standard error given by [2(SDExp/DFExp SDCon/DFCon)], where DFExp and DFCon are the degrees of freedom of the standard deviations in the two groups (usually their sample sizes minus 1). The upper and lower confidence limits for the true value of the variance of individual responses (SDIR) are given by its observed value plus or minus this standard error times 1.65, 1.96, or 2.58 for 90, 95, or 99% confidence limits, respectively (5). This formula is the basis for the confidence limits provided via mixed modeling with a procedure such as Proc Mixed in the Statistical Analysis System (SAS Institute, Cary, NC). Negative values of variance for the observed individual responses and the confidence limits can occur, especially when there is large uncertainty arising from a small sample size or a large error of measurement. Taking the square root of a negative number is not possible, so I advocate changing the sign first, then presenting the result as a negative standard deviation, interpreted as more variation in the control group than in the experimental group. If the upper confidence limit is negative, the researcher should consider explanations beyond mere sampling variation, such as compression of the responses in the experimental group arising from the treatment bringing subjects to a similar level. The magnitude of the standard deviation and its confidence limits should also be interpreted. The default approach for interpretation of the change in a mean is standardization, where the mean change is divided by the standard deviation of all subjects at baseline (before the treatment). The thresholds for interpreting the standardized mean change (0.2, 0.6, 1.2, 2.0, and 4.0 for small, moderate, large, very large, and extremely large) (6) need to be halved (0.1, 0.3, 0.6, 1.0, and 2.0) for interpreting the magnitude of effects represented by standardized standard deviations (8), including individual responses. Halving the thresholds implies that the magnitude of the standard deviation is evaluated as the difference between a Address for reprint requests and other correspondence: W. G. Hopkins, Victoria Univ., PO Box 14428, Melbourne 8001, Australia (e-mail: will @clear.net.nz). J Appl Physiol 118: 1444–1446, 2015; doi:10.1152/japplphysiol.00098.2015. Invited Editorial