# Approaches to the parametric modeling of hormone concentrations

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- Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden
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## Abstract

Transdisciplinary research in general, and stress research in particular, requires an efficient integration of methodological knowledge of all involved academic disciplines, in order to obtain conclusions of incremental value about the investigated constructs. From a psychologist’s point of view, biochemistry and quantitative neuroendocrinology are of particular importance for the investigation of endocrine stress systems (i.e., the HPA axis, and the SNS). Despite of their fundamental role for the adequate assessment of endocrine activity, both topics are rarely covered by conventional psychological curriculae. Consequently, the transfer of the respective knowledge has to rely on other, less efficient channels of scientific exchange. The present thesis sets out to contribute to this exchange, by highlighting methodological issues that are repeatedly encountered in research on stress-related endocrine activity, and providing solutions to these issues. As outlined within this thesis, modern stress research tends to fall short of an adequate quantification of the kinetics and dynamics of bioactive cortisol. Cortisol has gained considerable popularity during the last decades, as its bioactive fraction is supposed to be reliably determinable from saliva and is therefore the most conveniently obtainable marker of HPA activity. However, a substantial fraction of salivary cortisol is metabolized to its inactivated form cortisone by the enzyme 11β-HSD2 in the parotid glands, which is likely to restrict its utility. Although the commonly used antibody-based quantification methods (i.e. immunoassays) might “involuntarily” qualify this issue to some degree (due to their inherent cross-reactivity with matrix components that are structurally-related to cortisol; e.g., cortisone), they also cause differential within-immunoassay measurement bias: Salivary cortisone has (as compared to salivary cortisol) a substantially longer half-life, which leads to an overestimation of cortisol levels the more time has passed since the onset of the prior HPA secretory episode, and thus tends to distort any inference on the kinetics of bioactive cortisol. Furthermore, absolute cortisol levels also depend on the between-immunoassay variation of antibodies. Consequently, raw signal comparisons between laboratories and studies, which are favorable as compared to effect comparisons, can hardly be performed. This finding also highlights the need for the long-sought standardization of biochemical measurement procedures. The presumably only way to circumvent both issues is to rely on quantification of ultrafiltrated blood cortisol by mass-spectrometric methods. Being partly related to biochemical considerations with research on HPA activity, a second topic arises concerning the operationalization of the construct itself: In contrast to the simple outcome measures like averaged reaction times, inclined stress researchers can only indirectly infer on the sub-processes being involved in HPA activity from longitudinally sampled hormone concentrations. HPA activity can be quantified either by (a) discrete-time, or by (b) continuous-time models. Although the former is the most popular and more convenient approach (as indicated by the overly frequent encounter of ANOVAs and trapezoidal AUC calculations in the field of psychobiological stress research), most discrete time models form rather data-driven, descriptive approaches to quantify HPA activity, that assume the existence of some endocrine resting-state (i.e., a baseline) at the first sampling point and disregard any mechanistic hormonal change occurring in between all following sampling points. Even if one ignores the fact, that such properties are unlikely to pertain to endocrine systems in general, many generic discrete time models fail to account for the specific structure of endocrine data that results from biochemical hormone measurement, as well as from the dynamics of the investigated system. More precisely speaking, cortisol time series violate homoscedasticity, residual normality, and sphericity, which need to be present in order to enable (mixed effects) GLM-based analyses. Neglecting these prerequisites may lead to inference bias unless counter-measures are taken. Such counter-measures usually involve alteration of the scale of hormone concentrations via transformation techniques. As such, a fourth-root transformation of salivary cortisol (being determined by a widely used, commercially available immunoassay) is shown to yield the optimal tradeoff for generating homoscedasticity and residual normality simultaneously. Although the violation of sphericity could be partly accounted for by several correction techniques, many modern software packages for structural equation modeling (e.g., Mplus, OpenMX, Lavaan) also offer the opportunity to easily specify more appropriate moment structures via path notation and therefore to relax the modeling assumptions of GLM approaches to the analysis of longitudinal hormone data. Proceeding from this reasoning, this thesis illustrates how one can additionally incorporate hypotheses about HPA functioning, and thus model all relevant sub-processes that give rise to HPA kinetics and dynamics. The ALT modeling framework being advocated within this thesis, is shown to serve well for this purpose: ALT modeling can recover HPA activity parameters, which are directly interpretable within a physiological framework, that is, distinct growth factors representing the amount of secreted cortisol and velocity of cortisol elimination can serve to interpret HPA reactivity and regulation in a more unambiguous way, as compared to GLM effect measures. For illustration of these advantages on a content level, cortisol elimination after stress induction was found to be elevated as compared to its known pharmacokinetics. While the mechanism behind this effect requires further investigation, its detection would obviously have been more difficult upon application of conventional GLM methods. Further extension of the ALT framework allowed to address a methodological question, which had previously been dealt with by a mere rule of thumb; what’s the optimal threshold criterion, that enables a convenient but comparably accurate classification of individuals whose HPA axis is or is not activated upon encountering a stressful situation? While a rather arbitrarily chosen baseline-to-peak threshold of 2.5 nmol/L was commonly used to identify episodes of secretory HPA activity in time series of salivary cortisol concentrations, a reanalysis of a TSST meta- dataset by means of ALT mixture modeling suggested that this 2.5 nmol/L criterion is overly conservative with modern biochemical measurement tools and should be lowered according to the precision of the utilized assay (i.e., 1.5 nmol/L). In sum, parametric ALT modeling of endocrine activity can provide a convenient alternative to the commonly utilized GLM-based approaches that enables the inference on and quantification of distinct HPA components on a theoretical foundation, and thus to bridge the gap between discrete- and continuous-time modeling frameworks. The implementation of the outlined modeling approaches by the respective statistical syntaxes and practical guidelines being derived from the comparison of cortisol assays mentioned above, are provided in the appendix of the present thesis, which will hopefully help stress researchers to directly quantify the construct they actually intend to assess.

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