CADUMS and CTADS each employ a complex sample design, with stratification, multiple stages of selection and unequal probabilities of selection. Using data from complex surveys such as these can present problems as the survey design and selection probabilities could affect estimates of exposure and variance, particularly for small areas and subgroups when samples are small. Statistics Canada apply reporting restrictions on survey-based estimates of prevalence which result in the suppression of estimates with a sample size below 30 or with very high CVs (above 33.3%). Secondly, CADUMS was conducted in ten provinces in 2008–2012 and the CTADS was conducted in ten provinces in 2013, 2015 and 2017. Missing are exposure estimates of SU prevalence for the provinces in 2006, 2007, 2014 and 2016. Thirdly, there is a need to assess SU of particular populations such as those in the three Territories and also age and sex subgroups regionally in order to plan the delivery of treatment and harm reduction services efficiently.
There are several approaches to small area estimation (SAE) that have been developed and used to produce estimates when reliable estimates cannot be obtained directly from surveys for any of the above reasons [3, 4]. One approach is the composite estimator called empirical best linear unbiased prediction (EBLUP). EBLUP has been used to combine cross-sectional and time-series data [4].
To develop our estimates, we first used the method of direct estimates to estimate SU for six age-sex groups in each of ten provinces for survey years adjusted for survey design effects [5]. Using multilevel models [6] make direct estimates of SU prevalence (i.e., mean annual alcohol consumption, tobacco sales, wholly SU attributable hospitalisations, prevalence of SU and relevant auxiliary data to predict the estimates using the empirical best linear unbiased prediction (EBLUP) approach [3]. These estimates were produced by age-sex groups in provinces/territories for each year between 2006 and 2017. All the estimates were broken down by sex and age groups (15–34, 35–64 and 65+) for ten provinces, three territories and the whole of Canada from 2006 to 2017.
Data sources
Analyses were based on two national surveys: the Canadian Alcohol and Drug Use Monitoring Survey (CADUMS), which was conducted annually from 2008 to 2012 by Health Canada [7–11], and the Canadian Tobacco Alcohol and Drugs Survey (CTADS), which replaced the CADUMS in 2013 and was conducted in 2013, 2015 and 2017 by Statistics Canada [12–14]. The CTADS is conducted every two years. Details on the surveys can be found elsewhere [7–14].
Several auxiliary data sources were used to produce reliable estimates for province-age-sex groups when no reliable estimates can be produced directly from the surveys, or when no survey data are available (i.e., 2006, 2007, 2014 and 2016). These auxiliary data include age-sex population counts, per capita alcohol and tobacco sales data, and counts of wholly SU-attributable hospitalizations. Age-sex population data in provinces/territories over years [15] as well as per capita alcohol consumption data for the provinces/territories across the years 2006–2017 [16] were obtained from Statistics Canada. Annual tobacco sales data by province/territory were obtained from Health Canada [17]. The data of wholly SU (alcohol, cannabis, opioids, CNS depressant, CNS stimulant, cocaine and any other psychoactive substances)-attributable hospitalizations covered 10 provinces and three territories from 2006 to 2017 where obtained from the Canadian Institute for Health Information. Our analyses showed that official provincial per capita alcohol and tobacco consumption rates for the years 2006 to 2017 were significantly correlated with the survey-based estimates of alcohol and tobacco use produced by CADUMS/CTADS (Tables A1, A2 and A3 in Appendix A). A US study conducted also found that per capita sales and per capita self-reported consumption were highly correlated across individual states [18].
Survey sampling and population coverage
The CADUMS was a yearly survey on alcohol and other SU among Canadians initiated in April 2008 by the Controlled Substances and Tobacco Directorate, Health Canada [7–11]. The survey was derived from the Canadian Addiction Survey administered in 2004 and contained questions on substance use (including prescription drug misuse) and associated harms [19]. From 2013, the same SU questions were carried forward into the CTADS [12, 13]. Both the CADUMS and CTADS used random digit dialing to obtain a stratified sample across all 10 provinces with equal representation of subjects each month and based on a two-stage (telephone household, respondent) random sample stratified by province. The surveys used random-digit dialing (RDD) methods via Computer Assisted Telephone Interviewing (CATI). The sampling approach was designed to produce maximum precision of estimates when reporting at the provincial level by sex and the national level by sex and major age groups.
The sampling frame was based on an electronic inventory of all active telephone area codes and exchanges in Canada. Within each of the 10 provincial strata, a random sample of telephone numbers was selected with equal probability in the first stage of selection (i.e., households). Within selected households, one respondent aged 15 years or older who could complete the interview in English or French was chosen. The person who would celebrate his/her birthday next within the household was asked to complete the interview. The surveys covered the population aged 15 years and older in ten provinces and excludes residents of the Yukon, the Northwest Territories and Nunavut, permanent residents of institutions, people living in households without a telephone and people with cell phones only. Some provinces purchased additional cases in some years. The sample size was 16,674 in 2008, 13,082 in 2009, 13,615 in 2010, 10,076 in 2011, 11,090 in 2012, 14,565 in 2013, 15,154 in 2015 and 16,349 in 2017. Each sample represented approximately 26,000,000 Canadians aged 15 years and older. Details of sample sizes for provinces each survey year can be found in Table A4 in Appendix A.
Measures of substance use
The CADUMS and CTADS core content included self-report questions concerning general health and well-being, smoking status, alcohol use and harms, pharmaceutical use, cannabis use and harms, other illicit SU (opioids, cocaine, other CNS stimulants and depressants and harms, alcohol and cannabis and driving, pregnancy and SU, and demographics. The questions on SU are presented in Table A5 in Appendix A. Specific indicators analyzed in this study are described below. These exposure estimates of SU were needed to help estimate the number of SU attributable conditions in the CSUCH the study [2].
Alcohol consumption
Measures of alcohol consumption included in the CADUMS and CTADS and used in CanSUED were prevalence of lifetime abstainers, former drinkers and current drinkers in the population aged 15+, percentage of binge drinkers among current year drinkers aged 15+, and annual litres of ethanol consumed in the population aged 15+. Lifetime abstainers were defined as those who have consumed no alcohol or less than one standard drink (SD) of alcohol in their lifetime (one SD = 13.6 g or 17.05 ml in Canada). Former drinkers are defined as those who have consumed alcohol within their lifetime but who have not consumed at least one SD of alcohol within the past year. Current drinkers are defined as those who have consumed at least one SD of alcohol in the past year. The quantity and frequency (QF) method [20] was used to estimate total annual litres of alcohol consumption for current drinkers.
Tobacco smoking
Measures of tobacco smoking included the prevalence of lifetime non-smokers, former smokers and current smokers. Lifetime non-smokers were those who smoked less than 100 cigarettes in their lifetime. Former smokers were those who smoked at least 100 cigarettes but did not smoke daily or occasionally. Current smokers are those who smoked daily or occasionally when they were surveyed.
Other substance use
The use of cannabis, opioids (illicit or prescribed pain relievers), other CNS depressants (sedatives, tranquilizers), cocaine, other CNS stimulants (amphetamine, methamphetamines, ecstasy and any other stimulants) and other psychoactive substances (hallucinogens, inhalants, etc.) in the past year was assessed. In addition, some SU-related conditions are causally associated with injection drug use (IDU) and an additional analysis was carried out regarding IDU, which was restricted to SU types with injection as a possible route of administration (opioids, cocaine, other CNS stimulants). The proportions of those reporting use of these substances among those aged 15 years and older in the past 12 months were estimated.
Analytical strategy to estimate substance use exposures
We developed a statistical model to estimate trends and patterns observed across all the available survey data sets so as to allow reliable estimates of suppressed or otherwise missing data. In our analyses, an estimate with a CV of greater than 33.3% was considered unreliable and was modelled using the methods described below. Specifically, we did so by using auxiliary information and borrowing strength from (1) data collected in neighbouring areas (2) data collected at other times (3) exploiting spatial correlation in the data across regions (4) exploiting the temporal correlation of the target variable in each area to indirect estimates of SU prevalence. Indirect estimators borrow strength from other area and/or time periods to increase effective sample size. These indirect estimates were based on implicit or explicit models that provides a link to related areas and/or time periods through supplementary information such as recent census counts or current administrative records related to the variable of interest.
Direct estimates
Direct estimates of self-reported SU were obtained from the surveys with adjustment for design effects due to strata, clustering and disproportionate selection of subjects in the surveys [5]. Direct estimates were based on the CADUMS and CTADS surveys of 107,750 Canadians aged 15+ in the provinces in 2008–2017. There were a total of 600 direct estimates by six age-sex groups in ten provinces in 2008–2017. The estimates in 2014 were produced based on the pooled 2013 and 2015 CTADS and the estimates in 2016 were produced based on the pooled 2015 and 2017 CTADS. Equations for the estimates of per capita alcohol consumption and corresponding standard errors produced directly from the surveys are presented in Box I.
Prevalence of SU, estimated for computing SU attributable hospitalization and death includes proportions P¯̂ of lifetime non-smokers, former smokers and current smokers, lifetime non-drinkers, former drinkers and current drinkers, and other SUs in past year among the population aged 15, and proportion of binge drinkers among current drinkers. The equations for these direct estimates can be found in Box II.
Model-based empirical best linear unbiased prediction
Using the empirical best linear unbiased prediction (EBLUP) method [21, 22], we computed the estimates of per capita alcohol consumption and the SU prevalence for age-sex groups in ten provinces and three territories from 2006 to 2017. These computations were performed for cases in which the design-based direct estimates are unreliable due to small sample sizes or years when no surveys were conducted. The equations of the model-based estimates are presented in Box III.
The standard error of a model-based EBLUP estimate is the square root of the variance V̂m̂-m of the EBLUP estimate and the coefficient of variation of the EBLUP estimate can be computed using the standard error of the EBLUP estimate divided by the EBLUP estimate.
The fixed effect estimates β can be obtained from the mixed models [6, 23]. The mixed model is written as y = Xβ+Zγ+ε
where
- y denotes the vector of observed yi’s
- X is the known matrix of xij ' and the values of explanatory variables xij can be either regression-type continuous variables or dummy variables indicating class membership
- β is the unknown fixed effects parameter vector
- Z the known design matrix
- γ is the vector of unknown random-effects parameters
- ε is the unobserved vector of independent and identified distributed normal (Gaussian) random variables with mean 0 and variance σ2.
Statistical analyses were completed using SAS 9.3 [24]. Direct estimates of mean alcohol consumption were produced using the SAS SURVEYMEANS procedure and percentages of substance users and non-users were estimated using the SAS SURVEYFREQ procedure because these procedures analyze sample survey data taking into account the sample design effects [24]. Direct estimates were conducted by age, sex, province/territory and year. The SAS MIXED procedure estimates the fixed-effects parameters and further produce the EBLUP estimates. The SAS MIXED procedure was used to perform multilevel regression of the direct estimates in which province/territories and year are considered as random effects and auxiliary data such as year-province-age-sex population, rates of wholly SU attributable conditions available by age and gender for all 13 jurisdictions by year, annual per capita cigarettes data and litres of alcohol of official sales data at province level as covariates fixed effects [3, 25]. Using the EBLUP method [3] predicts the estimates for all six age-sex groups by years in ten provinces and three territories in 2006–2017.
Validity assessments
We conducted several internal validity checks of the model-based EBLUP estimates. First, we compared the EBLUP estimates against the CADUMS/CTADS design-based direct survey estimates of per capita alcohol consumption and the prevalence of SUs for age-sex groups by provinces and years where there were reliable estimates, i.e., CVs <33.3%. We further compared the EBLUP estimates with the prevalence estimates from the Canadian Community Health Survey (CCHS) where the CVs of the estimates by age-sex groups were smaller than 33.3%. The CCHS conducted by Statistics Canada has a large sample size (a total of 984,911 Canadians were surveyed in 2005–2014) but only provided equivalent questions for some key alcohol and tobacco indicators for the Yukon, the Northwest Territories and Nunavut. More details on the CCHSs can be found elsewhere [12, 13, 26, 27]. Bivariate correlation was used to assess the relationship between the EBLUP estimates and the direct estimates; we estimated the Pearson correlation coefficient for each pair of the estimates.