Strategies of Modelling Incident Outcomes Using Cox Regression to Estimate the Population Attributable Risk

When the Cox model is applied, some recommendations about the choice of the time metric and the model's structure are often disregarded along with the proportionality of risk assumption. Moreover, most of the published studies fail to frame the real impact of a risk factor in the target population. Our aim was to show how modelling strategies affected Cox model assumptions. Furthermore, we showed how the Cox modelling strategies affected the population attributable risk (PAR). Our work is based on data collected in the North-West Province, one of the two PURE study centres in South Africa. The Cox model was used to estimate the hazard ratio (HR) of mortality for all causes in relation to smoking, alcohol use, physical inactivity, and hypertension. Firstly, we used a Cox model with time to event as the underlying time variable. Secondly, we used a Cox model with age to event as the underlying time variable. Finally, the second model was implemented with age classes and sex as strata variables. Mutually adjusted models were also investigated. A statistical test to the multiplicative interaction term the exposures and the log transformed time to event metric was used to assess the proportionality of risk assumption. The model's fitting was investigated by means of the Akaike Information Criteria (AIC). Models with age as the underlying time variable with age and sex as strata variables had enhanced validity of the risk proportionality assumption and better fitting. The PAR for a specific modifiable risk factor can be defined more accurately in mutually adjusted models allowing better public health decisions. This is not necessarily true when correlated modifiable risk factors are considered.