Statistical analysis

Three methodological approaches were considered: minimum estimation, standardized mortality rates, and geographically weighted regression models, which are described below. Additionally, to detect significant differences between the number of deaths for each location in prepandemic and pandemic periods, we applied Welch’s t-statistic, which is defined at the end of this section.

The “minimal estimate” [9, 11] considers 10 diseases (Table 1) that may potentially require palliative care, such as cancer, heart failure, kidney failure, liver failure, chronic obstructive pulmonary disease, amyotrophic/motor neuron disease, lateral sclerosis, Parkinson’s disease, Huntington’s disease, Alzheimer’s disease, and HIV/AIDS. In this study, to determine the number of people potentially requiring palliative care in the Biobío Region, the minimal estimate approach was applied, calculating the age-and sex-specific proportions of deaths from the chronic progressive diseases defined in Table 1.

With this approach, a geographic analysis was carried out on the standardized mortality rates in the Biobío region between 2010 and 2021, omitting 2019 since no information was found on deaths for that year. This methodology was based on [11], who estimated the need for palliative care in a geographic study on mortality in Colombia between 2012 and 2016, calculating the crude rate per year in a population density graph. However, the levels of health and mortality rates between the regions and communes of Chile are not homogeneous, manifesting in particular in the heterogeneity in the age groups of the different communes considered in this study.

Due to the aforementioned factors, age-standardized death rates (ASDR) obtained by the direct method were used. In this regard, what was stated in the literature on ASDR was considered in this study to study the geographical behavior of the causes of mortality; for example, [20] used ASDR to examine aggregate divergence in mortality among southern US states, and [21, 22] investigated temporal trends through ASDR of deaths from all causes and from the leading causes of death in the US. Other investigations with this same approach were carried out by the authors cited in the references below [23, 24].

To determine the effect of the COVID-19 pandemic on deaths from COD and CNOD that could have required palliative care, the average ASDR in the pandemic period (2020–2021) was used to formulate a linear relationship with the average mortality from COVID-19 and the historical average of ASDR in the prepandemic period (2010–2018). After that, the geographically weighted regression (GWR) method was applied ([25]), which allows the regression coefficients to depend on covariates such as the longitude and latitude of the communes of the Biobío Region [26]. In the GWR model, the classical or global regression coefficients are replaced by local parameters, as described in Eq (1).

where:

The coefficient function vector β(u_i, v_i) for the i–th observation in GWR can be estimated via the locally weighted least square procedure, which is available in the free R statistical software [27], through the GWmodel package developed by the authors in reference [28].

To determine the trends in the number of deaths from COD and CNOD in all communes registered before and after COVID-19, the mean-variance tests before and after were considered, where the data from 2020 to 2021 corresponded to the pandemic period and 2010 to 2018 were from before the pandemic. To differentiate cases of nonhomogeneity of variance, the Welch ([29]) test was used in this study. The most important difference between Student’s t-test and Welch’s t-test is that, when both the variances and the sample size differ between groups, the t-value, degrees of freedom, and p-value all differ between Student’s t-test and Welch’s t-test. Welch’s t-statistic is defined as follows:

where X¯j=1nj∑i=1njXij and sj2=1nj-1∑i=1nj(Xij-X¯j)2 represent the sample mean of the j–th population (j = 1, 2) and sample variance, respectively. As indicated by [30], the exact distribution of Welch’s t-statistic can be approximated, under the assumption of normality, by a t-distribution with degrees of freedom

When both variances and sample sizes are the same in each independent group, the t-values, degrees of freedom, and p-values in Student’s t-test and Welch’s t-test are the same. Regarding the assumption of normality, several authors ([31, 32]) have studied the power of the Welch test and have agreed that the sampling distribution of means is close to being a normal distribution when means are based on sample sizes greater than 40. R software [27] (version 4.1.2, R 4.1.2: R Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2019. Available online at: https://www.R-project.org/) was used for data analysis and graphs.