Ewart A.C. Thomas
Department of Psychology, Stanford University
Title: Applications of linear mixed effects models to assessing the functional efficacy of CFTR-directed therapeutics in single patients
Cystic Fibrosis (CF) results from mutations of the CFTR gene that adversely affect chloride ion and water transport in sweat glands, lungs and other organs. As suggested in the Schwartz-Thaysen model of sweat (or other exocrine) gland secretion, there are two parallel pathways for sweat transport in the gland. The first is a cholinergic pathway, usually stimulated by cholinergic agonists, such as methacholine, to produce so-called M-sweat. This pathway is normal in CF patients, i.e., it is CFTR-independent. The second is a b-adrenergic pathway that can be stimulated by a b-adrenergic cocktail to produce so-called b-sweat (also called C-sweat) while simultaneously blocking M-sweat. This second pathway is compromised (often severely) in CF patients, i.e., it is CFTR-dependent. Recently, Wine et al. (2013) developed an experimental paradigm that monitors the amount of M-sweat and C-sweat secretion in parallel for multiple (say, 30-140) individual, identified glands in a single subject. The same glands can be measured repeatedly across experimental conditions that vary in, e.g., the dosage of the cholinergic or b-adrenergic reagents used to stimulate sweating, or, importantly, the dosage of a target drug, Ivacaftor (Kalydeco®, VX-770), that improves CFTR function in certain CF patients. Because of the constraints of sweat stimulation in this bioassay, off-drug measurements are obtained on different occasions (indexed by ‘Week’) from on-drug measurements. Linear mixed effects models (LMMs) offer a convenient, flexible framework for analyzing the repeated measurements across glands within a single subject, inasmuch as the analysis can include both the fixed effects of dosage and ‘Sweat’ (M- versus C-sweat) mentioned above, and the random effects of ‘Gland’ and ‘Week’, and it can easily accommodate unbalanced data sets in which observations are missing at random. Further, when data are pooled across subjects, e.g., to assess the generalizability of the effect of ‘Drug’ (Off versus On), ‘Subject’ can be included as an additional random effect.
Our main finding is that Ivacaftor increases the volume of C-sweat in CF patients who have certain mutations of the CFTR gene, suggesting, therefore, that this drug can yield significant clinical improvement in such patients. In the present talk, I will describe the family of LMMs we used to reach this conclusion and other conclusions concerning C-sweat and M-sweat in CF and non-CF subjects. In the basic LMM, the fixed effects include the interaction between ‘Sweat’ and ‘Drug’, and the random effects include the effects of ‘Gland’, ‘Week’ and the interaction between ‘Sweat’ and ‘Gland’. I will report also on an under-appreciated algebraic property of this LMM, namely, the dependence of the predicted correlation between 2 variables across glands (often taken as an index of ‘reliability’ of the bioassay) on whether M- or C-sweat is being measured, and whether the 2 measurements are taken in the same week or not. Finally, the Schwartz-Thaysen model suggests that, when a sweat gland is stimulated appropriately, a primary fluid is produced in the gland’s secretory coil, and is then expressed through the gland’s reabsorptive duct to the skin, where it is observed as sweat. During the passage through the duct, some fraction of the fluid is absorbed and does not reach the skin, and this fraction is high when C-sweat secretion is low. Thus, observed sweat volume is an underestimate of CFTR function, the error being proportionally larger when CFTR function is low, as it is in CF patients. I will discuss how an LMM can be used to estimate the loss of fluid and, in this way, to better estimate CFTR function in CF patients.
Reference: Wine, J.J., J.E. Char, J. Chen, H.J. Cho, C. Dunn, E. Frisbee, N.S. Joo, C. Milla, S.E. Modlin, I.H. Park, E.A.C. Thomas, K.V. Tran, R. Verma, and M.H. Wolfe. In Vivo Readout of CFTR Function: Ratiometric Measurement of CFTR-Dependent Secretion by Individual, Identifiable Human Sweat Glands. PLoS One, 2013. 8(10): p. e77114.