Statistical analyses
We calculated mean and median payments per allergist and proportion of allergists receiving payments. We assessed the concentration of payments among allergists using the Gini index, a measure traditionally applied to analyze income inequality in economics[32,33]. The index ranges from 0 (indicating uniform payment distribution) to 1 (where a single allergist receives all payments), with higher values signaling greater disparity. We also analyzed payment data by category and the pharmaceutical companies making these payments. Trends in the number of allergists receiving payments and the payment amounts from 2016 to 2020 were evaluated using generalized estimating equation (GEE) models. Due to the non-normal distribution of payments, the analyses were conducted using a log-linked GEE model with a Poisson distribution and a negative binomial GEE model[6-8,29]. The study period was bifurcated into two intervals (2016-2019 and 2020) to determine the impact of the COVID-19 pandemic on payments, as indicated by a notable reduction in payments to physicians in the United States in 2020[15,20,34-36]. A sensitivity analysis was also conducted for companies that consistently made payments over the five-year span. For trend analysis, we adjusted for inflation, converting all payment values to their 2020-Japanese yen equivalent. Statistical significance was set at a p-value of less than 0.05.