Target population and study design
The target population represents adult persons aged 40–70 (for age specification, see below) over the observational period from the 1st of March 2011 (the 2011 census moment) until the 1st of December 2019. The study population was restricted to the participants of the 2011 census aged 40–70 at any time during the study period (total N = 1,552,507). As the census only included permanent residents at the census moment, persons migrating to Lithuania after the census were excluded. Based on this population, we calculated monthly estimates of education-specific mortality rates, which were used to derive mortality differences as indicator of health inequalities. Using interrupted time series analyses, we examined whether changes in mortality differences were related to the 2017 taxation increase for beer and wine.
Data source and preparation
We obtained census-linked mortality data from the years 2011 to 2019 from Statistics Lithuania. The data linkage was performed by Statistics Lithuania following all rules of data confidentiality. The supplied file included time-invariant information collected from census participants (sex, date of birth, and highest educational achievement) as well as the date of death and the cause of death for those who died until December 2019, coded according to the International Classification of Diseases, 10th revision (4-digit code).
The individual-level data were aggregated to obtain a time series of monthly mortality rates, stratified by sex, age group and educational achievement (grouped according to the International Standard Classification of Education, see Additional File 1: “2. Classification of highest educational achievement”). To obtain monthly mortality rates, we calculated the number of deaths (numerator) and the person-months (denominator) by sex, age group and educational achievement. In contrast to cohort studies, the person-months were not accumulated over the study period but represented the number of persons which were at risk of dying in each month within each year of the observational period.
The stratification of deaths and person-months by sex and educational achievement was straightforward as this information was fixed at the 2011 census moment and does not change over time. For age groups, however, we were challenged with a changing composition of the population at risk of dying with each month. We used the age-of-death format proposed by Mackenbach and colleagues [35], which involved assigning individuals to that age group which represents their current age in a given month of the observational period. For example, a person turning 50 in January 2015 would be assigned the age group 40–49 in the months leading to December 2014 but would be assigned the age group 50–59 in January 2015 and following months. Lastly, persons emigrating from Lithuania were included in the calculations until the month in which they formally left the country.
Trajectories of the sex-age-education-stratified death counts and person-months are illustrated in Additional File 1: Figure S1 and S2. The age distribution of the person-months in July 2015 (midpoint of the time series) was used to derive weights for calculating a time series of sex-education-stratified age-standardized mortality rates (see Additional File 1: Figure S3). The implausibly low mortality rates in the first month (March 2011, see Additional File 1: Figure S4) was excluded from all analyses, resulting in a time series of n = 105 months (April 2011 to December 2019).
Outcome variables
As primary outcome, we calculated the difference in the age-standardized mortality rates between the population of lowest and highest educational achievement, which gives the excess mortality rate experienced in the lower educated population. As a secondary outcome, we calculated the mortality rate ratio between the population of lowest and highest educational achievement.
Both absolute and relative measures are important as they reflect different perspectives of inequality. The absolute measures show the overall public health importance of inequality in terms of the total excess deaths (per 100,000) related to inequality. Relative measures indicate a relative importance of inequality albeit not considering the number of excess deaths. For example, a relative mortality rate ratio of 1.8 times for rare cause of death may be less important (in terms of public health impact) than the corresponding rate ratio of 1.2 times for a major (frequent) cause of death. Importantly, more pronounced reductions in mortality rates among lower as compared to higher educated groups will result in reductions in absolute inequalities. For reductions in relative inequalities, the percentage change needs to be larger in lower as compared to higher educated groups, which may not always be achieved.
Intervention variables
To test the effect of the 2017 taxation increase, we considered both level and slope change. The level change was defined as a binary variable, with 0 in all months before (April 2011 to February 2017) and 1 in all months after the intervention (March 2017 to December 2019). The slope change was defined as a continuous variable, with 0 in all months up to (April 2011 to March 2017) and an incremental increase by 1 in all months after the intervention (April 2017 to December 2019; for parametrization of intervention variables, see [36]).
Confounding variables
In order to rule out alternative explanations, we considered to include time-varying confounders that have been linked to health inequalities in previous studies. Data from seven economic and social variables were available either at a quarterly or annual basis and imputed linearly to obtain monthly time series of each variable (see Additional File 1: Table S1).
Statistical analyses
As described in the study protocol, we employed generalized additive mixed models to evaluate the intervention impact, separately for primary and secondary outcomes and stratified by sex. The model selection strategy is summarized in the following and explained in greater detail in Additional File 1.
First, the secondary outcome was log-transformed to achieve normality (see Additional File 1: Figures S5 and S6).
Second, baseline models restricted to the pre-intervention period were built following three steps: (1) test for seasonal adjustment, (2) test for time trend, (3) test for confounding variables. For step 3, we examined possible correlations of each outcome variable by sex with the potential confounders (Additional File 1: Table S2). Statistically significant correlations with confounders in the hypothesized direction were only present for absolute mortality difference among men. Based on cross-correlations of confounders and outcome variables (Additional File 1: Figure S5), a 1-month lag of educational expansion was retained as single confounder for the absolute mortality difference among men. For the absolute mortality difference among women, as well as for mortality rates (secondary outcome), no confounders were included in the models (Additional File 1: Table S3).
Third, for the main analyses, three models were built for each outcome by sex, testing (1) an immediate level change, (2) a slope change and (3) a level and slope change. The best performing models were selected based on model fit indicators while taking autocorrelation and stationarity into account (Additional File 1: Table S4 and S5). As no autocorrelation or seasonality was present in the time series (see Additional File 1: Table S3, checked using auto.arima function from R package “forecast” [37]), the analyses were performed using simple generalized linear models (with normally distributed dependent variables) rather than generalized additive models.
The analyses were performed with R version 4.1.2 [38] and all data including the corresponding R code are publicly available (https://doi.org/10.6084/m9.figshare.21749651).
Additional analyses
In the study protocol, we described to perform additional interrupted time series analyses for alcohol-related mortality rates. However, this was not proven to be feasible given low or even 0 death counts in some months, in particular for the high-educated population. Instead of formal time series analyses on monthly data, we decomposed mortality inequalities into 16 cause-of-death groupings (for definition, see Additional File 1: Table S6) to identify those causes of death that are linked to changes in mortality inequalities.