Statistical analysis
REGRESSION
We used frequencies and percentages to describe the distribution of the sample population and count data relating to contacts and consultations made in the control and intervention arms, and StataSE 17 (StataCorp. 2021. Stata Statistical Software: Release 17. College Station, TX: StataCorp LLC) for the statistical analyses.The Poisson regression is the basic model used for modelling count data. It assumes that the mean and the variance of the count variable are approximately equal. We checked this model assumption using the dispersion statistic, which should be equal to one. However, our Poisson model output gave the dispersion statistic equal to 24.2. In addition, the appropriateness of the negative binomial model over the Poisson regression model was checked using the Bayesian information criterion (BIC), which states that the model with the smaller BIC estimate is preferred over the model with a larger BIC. The negative binomial model had the smaller BIC estimate. Thirdly, we obtained a Z score test of 16.1, with a t-probability < 0.01. This test evaluates whether the data are Poisson or negative binomial. Based on this result, we rejected the null hypothesis of no overdispersion in the data. Further, we used the likelihood-ratio test of alpha = 0, to test if the dispersion parameter, was equal to zero, which would have reduced the model to a Poisson regression. Our results showed that alpha was significantly greater than zero. This implies that the data were over-dispersed, hence using the negative binomial model instead of the Poisson model was appropriate.The negative binomial regression model was used with random effects at the level of out-of-hours GP cooperatives to check for any baseline differences between the two groups (Table We obtained estimates of incidence rate ratios (IRRs) for the negative binomial regression model. An IRR > 1 indicates an increase in counts in one group relative to the reference group or one period relative to the reference period, whereas an IRR < 1 indicates a decrease in these parameters. An IRR = 1 indicates no difference in the number of counts between the groups or periods.