Temporal Associations of Alcohol and Tobacco Consumption With Cancer Mortality

Key Points Question Are changes in population-level alcohol and tobacco consumption associated with changes in overall cancer mortality? Findings In this population-based cohort study, temporal associations of alcohol and tobacco consumption with cancer mortality overall were found using Australian time series data (1935-2014). An estimated 1-L decrease in alcohol consumption per capita and a 1-kg decrease in tobacco consumption per capita were associated with a decline of 3.9% and 16%, respectively, in overall cancer mortality across a 20-year period. Meaning Health policy interventions that can decrease population alcohol and tobacco consumption may lead to a reduction in cancer mortality over a 20-year period.


Data collection
A proxy for per-capita alcohol consumption was constructed, using data on alcohol sales sourced from the Australian Bureau of Statistics (ABS). Data on alcohol consumption per person aged 15+ for the years 1961 to 2014 are taken from a recent synthesis of historical data, 1 while data from earlier years  were extracted manually from the relevant yearbooks 2 [e.g. Commonwealth Bureau of Census and Statistics report], and converted from gallons or proof gallons to litres of pure alcohol. This was then converted to litres of pure alcohol per resident aged 15 and older, using population data provided by the Australian Institute of Health and Welfare (AIHW). 3 Data on per capita tobacco consumption (aged 15+) from 1935 to 2014 were collected from Cancer Council Victoria 4 and KPMG's report, Illicit Tobacco in Australia. 5

Time series model
The autoregressive integrated moving average (ARIMA) modelling technique was employed to estimate the association between per-capita alcohol consumption and overall cancer mortality. ARIMA models require stationary time series to reduce the risk of obtaining a spurious relation between two series that have common trends. 6 The Augmented Dickey-Fuller (ADF) unit root test is commonly used for testing for stationarity. 7 Furthermore, the error term (which includes explanatory variables not considered in the model) is allowed to have a temporal structure that is modelled and estimated in terms of autoregressive or moving average parameters. 8 In most cases, a differencing of the time series is sufficient to eliminate non-stationarity. 9 In this study, a semi-log ARIMA model was selected (because the slope coefficient measures the relative change in dependent variable for a given absolute change in the value of the explanatory variable at time t), as the risk for chronic diseases is a convex function of alcohol or/and tobacco intake. 10 The final model can be written as follows: where ∆ is the differencing operator, is the natura l logari thm of mor tal ity rates of overall cancer diseases in Australia per 100,000 inhabitants, is la g w eigh ted per-capita alcohol consumption, is lag weighted per-capita tobacco consumption, , are the oth er con trol var iables con sidered in the est imation, i i s num ber of con trol variables, i s the coefficient values of the c ontrol variables, is the err or ter m including other causal factors, and i s t he c onstant. T he c oefficient v alues or indicate the proportional change in cancer mortality rate associated with a one-litre change in weighted per-capita alcohol consumption or a 1 kg change in weighted per capita tobacco consumption � − 1� × 100.
The model fit was evaluated with the aid of the Box-Ljung portmanteau test of the first 10 autocorrelations, Q (10). The model structures used are reported below, alongside the output of the models. All statistical analyses were undertaken via E-views 7.0.

Lag length and lag weight
Geometric lag weight A geometrical lag scheme was used in the estimation with λ=0.7. This approach builds in the lagged effects of alcohol or tobacco consumption, with higher weights placed on more recent years (shown in eFigures 1).

eFigure 1. Geometric Distribution of Lag Effects of Alcohol or Tobacco Consumption on Cancer Mortality in the Past 15 and 20 Years
Skog's lag weight A three parameter lag structure developed by Skog 11 was also used to build lagged alcohol or tobacco consumption on cancer mortality.
Where is the weight of alcohol or tobacco consumption in year t, 1 is the lag parameter for the short-term impact, 2 for long-term impact, and determines their relative imprtance. Based on the previous studies on alcohol consumption and liver cirrhosis mortality, =0.80, 1 =0.50 2 = 0.93 were used in our estimation (shown in eFigures 2).

Unit root test
The ADF unit root test (eTable 1) is employed to test the stationarity of the time series in this study, suggesting that alcohol consumption, tobacco consumption, health expenditure, and all gender-and age-specific cancer mortalities are non-stationary in data at the untransformed level, and become stationary after first differencing at the significance level of 0.05.