Transformation techniques for cross-sectional and longitudinal endocrine data: Application to salivary cortisol concentrations

Endocrine time series often lack normality and homoscedasticity most likely due to the non-linear dynamics of their natural determinants and the immanent characteristics of the biochemical analysis tools, respectively. As a consequence, data transformation (e.g., log-transformation) is frequently applied to enable general linear model-based analyses. However, to date, data transformation techniques substantially vary across studies and the question of which is the optimum power transformation remains to be addressed. The present report aims to provide a common solution for the analysis of endocrine time series by systematically comparing different power transformations with regard to their impact on data normality and homoscedasticity. For this, a variety of power transformations of the Box-Cox family were applied to salivary cortisol data of 309 healthy participants sampled in temporal proximity to a psychosocial stressor (the Trier Social Stress Test). Whereas our analyses show that un- as well as log-transformed data are inferior in terms of meeting normality and homoscedasticity, they also provide optimum transformations for both, cross-sectional cortisol samples reflecting the distributional concentration equilibrium and longitudinal cortisol time series comprising systematically altered hormone distributions that result from simultaneously elicited pulsatile change and continuous elimination processes. Considering these dynamics of endocrine oscillations, data transformation prior to testing GLMs seems mandatory to minimize biased results.