The effect of SARS-CoV-2 vaccination on post-acute COVID-19 syndrome (PASC): A prospective cohort study 8 263 Supplementary Text S1. Full formulation of models used in Bayesian analyses To compare neutralising antibody levels between those who did and did not develop PASC, we implemented a Bayesian hierarchical generalization of the one-way ANOVA model to estimate the bounds on the effects of individual groups j of a nominal predictor i on an observed metric variable. We assumed that the predicted mean-centered metric variable 〈Yi 〉 is given by: where Xi.j is a Boolean variable denoting if an individual belongs to subgroup j for the nominal predictor i. We assumed that the observed metric data (Yi ) can be described by the Student’s t-distribution with v degrees of freedom. the predicted location 〈Yi 〉 and heterogenous variances for individual groups σi.[j]: Y ~ T (v,〈Yi 〉,σi.[j]) The intercept was again placed with a weakly informative Gaussian prior: ~ N (0,1) We placed a prior of Student’s t-distribution on the effect size βi.j for each subgroup j of nominal predictor i centered around zero with a weakly-informative gamma prior on vβ degrees of freedom and positive-constrained half-normal prior on the standard deviation error-term σβ : βi.j ~ T (vβ ,0, σβ ) vβ ~ Gamma (2, 0.1) σβ ~ Half-Normal (0, 1) Following Kruschke1, We assumed that v is exponentially distributed with a mean of 30 such that high prior probability was allocated over parameter values that describe the range from normal to heavy-tailed data under the Student’s t-distribution:
RkJQdWJsaXNoZXIy MTk4NDMw