Evaluating health investment: methodological selection and establishing causality

This model aims to inform policy makers and leaders to make healthcare investment more effective by quantifying potential impact and examining alternatives. Often there are limitations to the amount of funding that a country can invest into healthcare. But if existing resources can be allocated more efficiently, it would help to maximize available investments. However, there are some limitations of the existing models seeking to inform these decisions, some of which tend to be short-term in their approach or simply look at the effect of GDP on life expectancy, a measure that is hard to understand in terms of real impact.

We explored qualitative relationships between indicators through a directed acyclic graph (DAG), which simplifies the complex mechanisms between health and wealth by putting various factors and effects into evidence-based groupings, and examining potential relationships between them. To complement the DAG with quantitative analysis, we chose a lasso regression approach. This is beneficial as it assumes uncertainty (ie, that we do not know what the important factors are in determining causality), and it factors in correlation across the different inputs, thereby making it easier to individually select variables across complex systems.

Directed acyclic graph (DAG)

The bidirectional relationship between wealth and health is difficult to measure quantitatively. To support our analysis framework and validate it, we created the directed acyclic graph (DAG, see Technical Report for additional details). A DAG is a visual representation of the hypothesized relationships between variables or a group of variables, capturing potential causality. The groups are created in such a way that that causality flows in one direction. These can include known variables that have been previously identified, and also new ones, including variables that cannot be measured.

The DAG was initially drafted without knowledge of, or reference to the core analysis, and was then developed iteratively with feedback from the wider study team. This approach allowed for greater scrutiny and validation of the assumptions and choices made around the model construction more broadly, such as which Step each variable falls into. By drawing on the underlying theory of the structural causal model, the DAG was used to inform the identification and estimation of many causal effects.

Lasso Regression

Building on the DAG, we developed a two-stage regression based model to link health system attributes and resource allocation with health outcomes, and in turn, macroeconomic activity. This was done with the aim of developing a baseline understanding of the connections across the model. We identified the health system indicators which were most strongly associated with improved health and economic outcomes over time, utilizing multivariate regressions of the panel dataset.

We then implemented a lasso regression, a regularization technique that can be used for variable selection that minimizes multicollinearity across inputs. This technique allows us to identify a minimal selection of health system factors that explain a substantial amount of the variance (eg, bigger range of effects) in our key outcome variables.

After evaluating the relationships between health system investment and health outcomes (Steps 1 and 2), we repeated the analysis to evaluate the predicted Step 2 health outcomes (a function of the Step 1 indicators) as inputs to the Step 3 macroeconomic outcome variables, allowing us to trace the impact of a change in health systems through health outcomes, and ultimately to macroeconomic activity. We considered state and year to be fixed effects for the purpose of this regression, which is called a group lasso approach.

The first step of this analysis gives us a basic understanding of the connections between various health system factors and health outcomes. The second step helps us in understanding more detailed relationships between health and economic outcomes (Steps 2 and 3 of the model).

In addition to identifying the ‘effect sizes’ of the relationship among our independent and dependent variables (the model inputs and outputs), we also used these models to develop three scenarios. These scenarios show how our key outcome variables would change after ‘shocking’ certain input variables, the results of which are shown on the home page. Secondary research was also conducted to further inform the nuance of reporting and interpretation of the results.

Conclusion

Most research that has been done in this field looks at associations between life expectancy and GDP, but our research takes a more holistic approach to understanding these dynamics. The approaches we have chosen, the DAG and lasso regression, have been uniquely combined to give a holistic systems-view of the impact of health investment on socioeconomic outcomes. The application of these analyses can be further explored on a more granular level in the US, or even by extrapolating this methodology to understand these systems in another country.