Statistical analysis

The chi-square test assessed the impact of study variables on CRC screening participation. Results were deemed significant at the usual alpha level (0.05).

We calculated simple standardized adherence rates (SARs) by gender, age and SES. SARs over a selected area (S), i.e., triangular or hexagonal area, census section, or municipal level, were obtained using the following formula:

where aSi was the number of adherence events in the i-th stratum of the study population (e.g. sex, age classes are the variables to stratify the population), RSi was the adherence event rate in the i-th stratum of the regional standard invited population and ISi was the size of the i-th stratum of the invited population. The smallest partition considered was the triangular area (0.68 km², on average 111 invited residents, 48% males).

To investigate the role of FDs and FDs practices, we compared adherence in a FDs practice with adherence in the general population living in the same areas by local SARs. We defined the S_FD area as the polygon including areas (e.g., triangular areas) containing at least one FD patient (Fig 1A). The weighted FD SAR was:

where aFDi was the number of observed adherent FDs patients in the i-th stratum, wSFDi was the ratio of adherent population aSFDi over the invited population ISFDi in the area SFDi and IFDi was the invited FDs population. A 95% confidence interval was calculated for SAR_S and wSARSFD.

We fitted a set of multilevel logistic regression models to investigate the influence of study variables on screening adherence [22]. Invited individuals (level 1) were considered clustering by FDs practice (level 2).

First, we fitted a random intercept empty model (i.e., without fixed effects variables) to test the influence of FDs on adherence. A second logistic regression model investigated individual-level variables as independent determinants of adherence. Then, we fitted a multi-level model including significant individual variables (fixed effects) and allowed the adherence by FDs practice to vary randomly.

The final model was selected using the Bayesian information criterion (BIC)[23]. The selected model allowed the random variation of both the intercept for FDs practices and the coefficient for the percentage of foreigners in a FDs practice and it took the following form:

where the vector with fixed effects (x_ij) was denoted by β and the vector with the random effects (z_ij) shared by all level-1 units i, i = 1,…,n_j, belonging to the j-th level-2 unit j, i = 1,…,n, by u_j. π_ij = E(y_ij|x_ij,z_ij,u_j) was the conditional expectation of binary response y_ij.

Finally, we fitted two multilevel models for FDs practices respectively with significantly higher and lower local wSARSFD than the residents in the same areas.

The variance partition coefficient (VPC) was calculated as a measure of the variability explained by clustering variables (e.g., variance due to adherence levels by FDs practices or HD). In our two-level models with random intercept and random coefficient, VPC is the same as the intraclass correlation coefficient (ICC) due to a zero value for the slope variable, which is a measure of correlation among individuals belonging to the same cluster.

In a multilevel model, it is not possible to estimate the odds ratios for cluster-level variables and this poses some difficulties for the interpretation of the influence of such variables. To overcome this limitation, additional measures were proposed for cluster-level variables (reviewed in [24]). We also calculated the median odds ratio (MOR) to further illustrate the adherence heterogeneity between clusters [24]. MOR represents the median value of the odds ratio in the distribution of pairwise comparisons between subjects with equal values of covariates but belonging to different clusters. The MOR assumes values ≥1, with 1 indicating no variation among clusters. MOR is expressed in the odds ratio scale and can be properly compared to the fixed-effects odds ratios to quantify the cluster effect. The MOR can be interpreted as the (median) change in risk for an individual moving from a cluster at lower risk to another at higher risk [25].

Predicted adherence probabilities at average covariates values were calculated based on the two models above and, for comparison, using model 1, over the same selected FD practices.

We performed all analyses using Stata statistical software [26] and the GeoMap module of GeCOsys for geocoded data [21].