We calculated frequency distributions of individual variables and assessed univariate associations between each variable and the prescription of antibiotics. We developed a model to obtain a valid estimate of the relationship between perceived patient demand for an antibiotic and GPs' antibiotic prescribing. We used a hierarchical backwards elimination procedure described by Kleinbaum,22 taking clustering of the data into account (Box 2). Before starting the procedure, all categorical variables were dichotomised. Since we aimed to estimate the effect of perceived patient demand for an antibiotic, and since we wanted to control the above relationship only for the presence of the other covariates, we dichotomised comorbidity and risk, symptoms, signs, and the circumstances ‘demands antibiotics’ and ‘demands other medication’ by recoding ‘don't know’ into ‘no’, and the circumstances ‘workload’ and ‘impression’ by recoding ‘very high’ into ‘high’, and ‘very ill’ into ‘ill’, respectively. To deal with co-linearity, the variables ‘reduced breathing sounds’, ‘wheezing’, ‘ronchi’, and ‘crepitations’ were replaced by the variable ‘lung auscultation’, representing the number of abnormal auscultatory findings, while a new dichotomous variable ‘higher risk’ was created based upon Fine's prediction rule to identify patients with community-acquired pneumonia at low risk for mortality or complications,23 and equals one, if the patient's age is over 50 years or if the patient has congestive heart failure, cerebrovascular disease, liver disease, renal disease or neoplastic disease, or has altered consciousness, pulse rate >125/min, respiratory rate >30/min, temperature >38°C or systolic blood pressure >90 mmHg, and which equals zero otherwise (Table 2).
Box 2. Hierarchical backwards elimination procedure and cluster data.
To obtain a valid estimate of the relationship between perceived patient demand for an antibiotic and GPs’ antibiotic prescribing, we estimated a logistic model which contained all covariates as possible confounders and all interaction terms between perceived patient demand and the covariates as possible effect modifiers. The covariates were the other information the GPs recorded about the patients, as well as their characteristics (Table 2). We also added the interaction terms of patient sex and age, and GP's sex and year of birth, respectively, as well as the variables year, group and year*group to control for the randomised controlled trial design. If some of the covariates or interaction terms dropped out of the starting model due to co-linearity, confounding and interaction were evaluated in a stratified analysis of perceived patient demand versus GPs' antibiotic prescribing, controlling for each covariate separately.
First, interactions were assessed by eliminating one by one the interaction term with least significant type 3 score statistics. Only significant interactions were retained in a ‘gold standard’ model. P values of their parameter estimates would be considered significant if smaller than 0.01 instead of smaller than 0.05 only if necessary for a clear interpretation of the effect of perceived patient demand on GPs antibiotic prescribing.
Second, the confounding effect of all covariates not in significant interaction terms in the full model was assessed, followed by precision considerations. We looked for a subset of covariates for which the model gave roughly the same parameter estimates for perceived patient demand and the significant interaction terms, but with narrower confidence intervals.
Alternating logistic regression (ALR),24 a technique closely related to generalised estimating equations (GEE),25,26 was used to adjust the logistic regression estimates for clustering within our data (patients are nested within GPs).27 The marriage of GEE or ALR with goodness-of-fit (GOF) is not an easy one.28–31 In addition to the original Hosmer and Lemeshow GOF statistic,32 we used an extension of that to marginal regression models for repeated binary responses.31 Our approach to fit a broader model with interactions and to test whether the additional terms are significant is regarded as an appropriate way to determine the fit as well.31
Statistical analyses were performed with SAS statistical software.
