2.7 Statistical analysis
Categorical variables were described by proportions, and intergroup differences were tested by chi-square test. Continuous variables of normal distribution were described by means and standard deviations (SD), and tested by one-way analysis (ANOVA) of variance. Continuous variables of skewed distribution, including the concentrations of arsenic in blood, urine, and hair and level of serum β-endorphin, were described by median and interquartile range (IQR), and tested by Kruskal-Wallis H test.
The does-response relationship between hair arsenic and NRS was estimated by a generalized additive model with cubic spline, and presented in figures. To derive parametric estimates, a multiple linear model was used for continuous NRS score, and partial regression coefficient of hair arsenic was reported. For dichotomous outcomes (NRS≥3 or NRS≥7), logistic models were used, and odds ratios (ORs) with 95% confidence intervals (CIs) were reported. Potential risk factors16 for itch were introduced into the following models for the purpose of adjustment.
In the MR analysis, the associations of genetically predicted urinary MMA% and DMA% with pruritus in participants of the UK Biobank was estimated using logistic regression models, adjusting for age, sex, race, Townsend deprivation index, smoking status and alcohol drinking. PRSs were analyzed as either continuous or categorical (above vs. under median) variables.
In the randomized controlled trial, an intention-to-treat (ITT) analysis was performed to evaluate the efficacy of naloxone. The last observation carry-forward (LOCF) imputation method was used for unmeasured data in drop-out participants. Mixed effect models were used to estimate the efficacy, by constructing a model: Y =β 0+ β 1Group + β 2Time +β 3(Group×Time) + ei +υ ij, where β 2 is the estimate for efficacy; ei andυ ij refer to the errors between individuals and within an individual (repeated measurements), respectively.
Statistical analyses were performed in R Statistical Software 3.4.1. The significance level for all statistical tests was 0.05.