Statistical analysis
chronic pain, pain
REGRESSION, CHRONIC PAIN
We used SAS software version 9.4 for Windows (copyright © 2013, SAS Institute Inc.) and R version 4.0.3We analysed data using a modified intention-to-treat approach, including participants for whom at least one PIQ-6 score was available and analysing them in the groups to which they were assigned. We compared the distribution of baseline characteristics between participants who were included and excluded from the analysis using chi-squared tests.We used linear regression to analyse PIQ-6 score as a continuous variable, and log-linked regression to estimate prevalence ratios (PR) for binary outcomes (i.e. some or more pain impact and some bodily pain). All models included the randomisation stratification variables of age, sex and state of residence. We analysed data from each survey separately and fitted a model integrating data from all surveys, using generalised estimating equations with an exchangeable correlation matrix to account for intra-person correlation. We included time (1, 2 or 5 years) in the generalised estimating equations models. To investigate whether the effect of supplementation varied with time since randomisation, we fitted an additional model that included a time by study group interaction term.To assess whether the effect of vitamin D supplementation on PIQ-6 score was modified by baseline values of age, sex, BMI, history of chronic pain or predicted baseline 25(OH)D concentration, we incorporated an interaction term (separately for each covariable) in the generalised estimating equations models that did not include a time by study group interaction term. We used these models to generate stratum-specific effect estimates.To confirm that variables previously shown to be associated with pain were evident in our study cohort, we estimated associations between baseline factors and each pain outcome using generalised estimating equations models (linear and log-linked). The study groups were combined for these analyses and models included potential confounders, identified using directed acyclic graphs.