This is a retrospective cohort study on the factors associated with COVID-19 infection and mortality in care homes for the elderly in the Basque Country (Spain). Data for the study was provided by the Basque Health Service, covering 298 of the 300 facilities in the region and 20,186 elderly people living in those care homes from 1 March 2020 to 31 October 2020. For each individual in the cohort, the following information was obtained:

• Care home where the person was living
• Date of birth and sex
• COVID-19 test (Yes/no)
• Date of first positive test for COVID-19
• Date of death

Additionally, the following information was gathered from public social services registers for each LTC facility:

• Ubication: Province, Integrated Health Organisation Area (IHOA) and Health Care Division Area (HCDA) where the facility is located.
• Ownership (public, private non-profit, private for-profit)
• Size (<25 beds, 26-70 beds, >70 beds)

A Multilevel Analysis of individual Heterogeneity and Discriminatory Accuracy (MAIHDA) was carried out following a three-step approach where three consecutive logistic regression models are built, for two separate dependent variables: positive COVID-19 test and all-cause mortality.

• Step 1: a conventional single-level logistic regression was estimated for each dependent variables, including only the individual-level covariates age and sex. Post-estimation predicted probabilities are calculated for each individual and are used to calculate the AUC (Area Under the ROC Curve) for the model. The AUC is constructed by plotting the true positive fraction (TPF) (i.e., sensitivity) against the false positive fraction (FPF) (i.e., 1 ? specificity) for different binary classification thresholds of the predicted probabilities. The AUC measures the ability of the model to correctly classify individuals with or without the outcome (e.g., having a COVID-19 test positive or negative) as a function of individuals’ predicted probabilities. The AUC takes a value between 1 and 0.5 where 1 is perfect discrimination and 0.5 would be as equally as informative as flipping a coin (i.e., the covariates have no predictive power). The AUC of the Step 1 model quantifies the accuracy of using individual-level information alone for identifying individuals with the outcome.
• Step 2: a general contextual effects model is built, expanding the Step 1 model from a conventional single-level logistic regression model to a multilevel logistic regression model with 4 levels: individual (level 1), LTC-facility (level 2), HCDA (level 3), IHOA (level 4). The general contextual effect is appraised using the estimated between-units variance (e.g., care homes variance) as this quantifies the variability in unobserved influences on the outcome (positive COVID-19 test and overall mortality) common to all individuals living in in the same care homes. We then refer the between-unit variance to the total variance in the model using two different measures of general contextual effects: (i) The Intraclass Correlation Coefficient (ICC); and (ii) The increment in the AUC in step 2 compared with the Step 1 (?AUC).
• Step 3: we add the care home covariates to the model for estimating the specific OR for those contextual variables. We focused on measuring the association (ORs) between positive COVID-19 test and three variables, the province where the care home was placed, the type of ownership of the care home and the size of the facility. Step 3 also provides a way of understanding the mechanism behind the observed general contextual effects of the care homes. For this purpose, we calculated the proportional change in variance (PCV) defined as the proportion of the care home variance (which correspond with the total contextual variance) in Model 2 explained by adding specific contextual information (i.e., province and ownership variables) in Model 3.

In the models for overall mortality, positive COVID-19 test was included as a fixed effect in the Step 1 model. Additionally, in step 2, we include a random effect for the slope of the association between COVID-19 test and mortality, that is, we drop the assumption that the slope of this association is the same in all care homes. Therefore, the variance between the care homes becomes a function of the COVID-19 test variable and, consequently, this variance can be different for individuals with a positive COVID-19 test and individuals with a negative test. Accordingly, there also are two VPCs and two AUCs one for COVID-19 positive individuals and other for COVID-19 negative individuals.

The main output of this study will be an estimation of the amount of individual variance in the risk for a positive COVID-19 test (and in the risk of death) that is captured by contextual factors (the care home where the person lives and health area to which it belongs) as opposed to individual characteristics (age and sex). This will indicate the relevance of considering the specific care home where the person was living to explain the risk of infection with SARS-CoV-2 and the risk of death.

The models will also give information on the relative risk of death for COVID-19 positive versus non infected individuals living in care homes for the elderly in the Basque Country.

Finally, if significative general contextual effects are found, the models will provide an estimation of the associations between analysed care home characteristics (size, ownership, and province) and risk of infection or death, as well as the amount of total contextual variance that is explained by these factors.