Can serum biomarkers predict the outcome of systemic immunosuppressive therapy in adult atopic dermatitis patients?

Abstract Background Atopic dermatitis (AD or eczema) is a most common chronic skin disease. Designing personalised treatment strategies for AD based on patient stratification is of high clinical relevance, given a considerable variation in the clinical phenotype and responses to treatments among patients. It has been hypothesised that the measurement of biomarkers could help predict therapeutic responses for individual patients. Objective We aim to assess whether serum biomarkers can predict the outcome of systemic immunosuppressive therapy in adult AD patients. Methods We developed a statistical machine learning model using the data of an already published longitudinal study of 42 patients who received azathioprine or methotrexate for over 24 weeks. The data contained 26 serum cytokines and chemokines measured before the therapy. The model described the dynamic evolution of the latent disease severity and measurement errors to predict AD severity scores (Eczema Area and Severity Index, (o)SCORing of AD and Patient Oriented Eczema Measure) two‐weeks ahead. We conducted feature selection to identify the most important biomarkers for the prediction of AD severity scores. Results We validated our model in a forward chaining setting and confirmed that it outperformed standard time‐series forecasting models. Adding biomarkers did not improve predictive performance. Conclusions In this study, biomarkers had a negligible and non‐significant effect for predicting the future AD severity scores and the outcome of the systemic therapy.

total variance. 2 can be interpreted similarly to an R-squared, the proportion of the explained variance (the variance of the measurements) in the total variance. The priors for t and 2 are given by • t ∼ log (− log 20 , (0.5 log 5) 2 ), a lognormal prior with a 95% confidence interval of [0.01 , 0.25 ], and • 2 ∼ (4, 2), a Beta distribution to reflect our expectation that future severity scores are predictable ( l < m ).
We assumed a hierarchical prior for the autocorrelation parameter, where is the population mean of the Beta distribution and is the population pseudo sample size of the Beta distribution. The priors for and are given by • ∼ Beta(2, 2), a symmetric Beta distribution that slightly favours values around 0.5 as opposed to 0 or 1, and • ∼ log (log 10 , (0.5 log 10) 2 ), a log-normal prior with a 95% confidence interval being approximately [1, 100], allowing a wide variety of distributions for from well spread to concentrated.
We defined the prior for the intercept, , by introducing the expected value of the autoregressive process, ∞ , such that = (1 − ) ∞ . We assumed a Gaussian hierarchical prior on ∞ ∼ ( ∞ , ∞ 2 ), where ∞ is the population mean of ∞ and ∞ is the population standard deviation of ∞ . The priors for ∞ and ∞ are given by • ∞ ∼ (0.5, 0.25 2 ), a Gaussian distribution that covers the range [0, ] of the score, and • ∞ ∼ + (0, 0.125 2 ), a half-Gaussian distribution to reflect an assumption that ∞ is at most 0.25 , resulting in the width of the distribution for ∞ to be at most .
We assumed a regularised horseshoe prior for the coefficients, (i=1, …, 30 = D), defined by • ∼ (0,̃2 2 ), where ̃= 2 2 2 + 2 2 is the local shrinkage parameter, is the global shrinkage parameter and is the scale of the signal, • ∼ + (0, 1), where + denotes a half-Cauchy distribution, where 0 = 5 is the expected number of covariates with non-zero coefficients, = 30 is the number of covariates, = 42 is the number of patients, and = l is the standard deviation of the residuals, and • 2~ Inv-2 ( , 2 ), a scaled-inverse chi-squared prior, where we assume the degree of freedom, = 5, and the scale, = 1. This prior corresponds to following a Student-t slab with degrees of freedom and scale , if is far from 0. This prior reflects an assumption that the order of magnitude of non-zero coefficients is around 1 but could be higher. To

B. Reference models
We implemented four reference models, a uniform forecast model and three models of increasing complexity leading to our state-space model. The models were implemented in a Bayesian setting and provided probabilistic predictions for a fair comparison. These models are more advanced than standard off-the-shelf implementation as missing values are treated as parameters to be inferred in a semi-supervised setting.
• The uniform forecast model (Uniform) is described by ( ) ∼ (0, ), where each outcome is assigned the same probability density.
• The random walk model (RW) provides a flat forecast, ( + 1) ∼ ( ( ), 2 ), centred on the last observation with the uncertainty quantified by a variance, 2 . The prior for is the same as that for t in our SSM.
• The autoregressive model (AR) is an extension of the random walk model and is described by ( + 1) ∼ ( ( ) + , 2 ), with a fixed autocorrelation, , and an intercept, = (1 − ) ∞ . We assumed a uniform prior for ~ (0, 1). The prior for ∞ is the same as that for ∞ in our SSM.
• The mixed effect autoregressive model (MixedAR) extends the autoregressive model and is described by ( + 1) ∼ ( ( ) + , 2 ), with a patient-dependent autocorrelation, , and a patient-dependent intercept, = (1 − ) ∞ . The priors for and are the same as those in our SSM.   Figure S1: K-fold cross-validation ( = 5 in this example) in a forward chaining setting, which reflects how the model would be used in a clinical setting. For each fold, the model was pre-trained with ( − 1) subsets of patients and validated on the remaining subset of patients in a forward chaining setting, in which the model was trained with the first timepoint and tested on the remaining timepoints, then the model was trained with the first two timepoints and tested on the remaining timepoints, etc. Figure S2: Performance of our model (SSM) and reference models (MixedAR, AR, RW and Uniform) to predict EASI. The performance was evaluated by lpd (higher the better). The values of lpd as a function of the prediction horizon for various training weeks (panels) and models (colours).