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.