10. Theory-informed statistical & econometric analyses

Statistical analyses describe relationships between a set of variables, with econometric analyses involving the application of economic theory to formulate those relationships. There is a plethora of statistical and econometric methods available and so we do not attempt to cover them all here. Instead, the circumstances when these methods might be useful for incorporating the influences on behaviour into health economic models are described and references to papers discussing the key methods are provided. For any statistical approach chosen, these should be informed by available theory to have more confidence in results and avoid overfitting to the data.

Statistical methods could be used for incorporating the influences on behaviour within health economic models for the following (non-mutually exclusive) reasons:   

1)     To model the relationships between behaviours which influence each other;

2)     To model the long-term impact of interventions upon behaviours;

3)     To model population-level behaviours over time.

Econometric methods for modelling the relationships between behaviours could be considered when behaviours are highly likely to influence each other and the behaviours affect the same outcomes of interest to decision makers, for example, smoking and alcohol consumption (Sullivan, 2014). Behaviours may be complements (decreasing one will decrease the other), substitutes (decreasing one will increase the other) or have no influence on each other. A longitudinal or repeated cross-sectional individual level data set with relevant variables and expertise in econometric analyses would be required to infer causal relationships between behaviours. The econometric analysis should highlight and discuss any necessary assumptions, especially those that cannot be tested.

Statistical analyses could be used to estimate the trajectories of behaviour and the impact of interventions upon a behavioural outcome where it is challenging to directly measure the longer term effects. Bianconcini and Bollent (2018) describe a set of methods which can each be considered special cases of the Latent Variable-Autoregressive Latent Trajectory Model for longitudinal data analysis. Quantification of behavioural theories would be useful within a health economic model if: (i) the intervention aimed to change at least one variable within the theory (e.g., self-efficacy or social influences); or (ii) policy makers would like to explore targeting interventions at individuals with certain levels of a variable within a theory (e.g., level of physical resources or intention to quit). It should be noted that there is little time lag between changes in the mechanisms of action and behaviour, meaning it is not possible to predict future behaviour from current mechanisms of action in the same way that potential future disease can be predicted from current risk factors. In addition, data for the variables (e.g. a measure of motivation) are often not measured or reported within intervention studies. Increasingly, interventions may involve individuals reporting regular psychological, behavioural, health and economic outcomes on mobile phone apps. The use of such devices can provide many data points from individuals receiving an intervention, and could cheaply provide maintenance phase data, which would allow the longer-term impacts of the interventions to be better understood. Economic demand theory can be applied for statistically modelling the relationship between price and consumption where an intervention changes either supply or demand (e.g., implementing a soft drink tax). However, uncertainties around taxation policy impacts and long-term prediction should be highlighted; for example, there may be differences in the size of price changes observed in the data and those used for taxation policy changes. It is also important to consider heterogeneity in these relationships where possible.

Population-level behaviours may change over time because of ageing or external factors that affect the whole population (e.g., economic crisis, shift in social norms). These may affect different age groups differently and there may be cohort effects where behaviour varies according to birth year. Age Period Cohort analysis aims to understand and disentangle these effects using statistical analyses (Bell, 2020). This may be useful where behaviour has been shown to change over time and it is likely that a behaviour is affected by all three effects, for example smoking. The analysis requires a longitudinal or repeat cross-sectional individual level dataset, with the relevant behaviours, age and external factors reported.