Efficient estimation of the attributable fraction when there are monotonicity constraints and interactions

Targeting resources efficiently and justifiably by combining causal machine learning and theory

Introduction

Efficient allocation of limited resources relies on accurate estimates of potential incremental benefits for each candidate. These heterogeneous treatment effects (HTE) can be estimated with properly specified theory-driven models and observational data that contain all confounders. Using causal machine learning to estimate HTE from big data offers higher benefits with limited resources by identifying additional heterogeneity dimensions and fitting arbitrary functional forms and interactions, but decisions based on black-box models are not justifiable.

Methods

Our solution is designed to increase resource allocation efficiency, enhance the understanding of the treatment effects, and increase the acceptance of the resulting decisions with a rationale that is in line with existing theory. The case study identifies the right individuals to incentivize for increasing their physical activity to maximize the population's health benefits due to reduced diabetes and heart disease prevalence. We leverage large-scale data from multi-wave nationally representative health surveys and theory from the published global meta-analysis results. We train causal machine learning ensembles, extract the heterogeneity dimensions of the treatment effect, sign, and monotonicity of its moderators with explainable AI, and incorporate them into the theory-driven model with our generalized linear model with the qualitative constraint (GLM_QC) method.

Results

The results show that the proposed methodology improves the expected health benefits for diabetes by 11% and for heart disease by 9% compared to the traditional approach of using the model specification from the literature and estimating the model with large-scale data. Qualitative constraints not only prevent counter-intuitive effects but also improve achieved benefits by regularizing the model.

Semiparametric estimation of the attributable fraction when there are interactions under monotonicity constraints

BACKGROUND

The population attributable fraction (PAF) is the fraction of disease cases in a sample that can be attributed to an exposure. Estimating the PAF often involves the estimation of the probability of having the disease given the exposure while adjusting for confounders. In many settings, the exposure can interact with confounders. Additionally, the exposure may have a monotone effect on the probability of having the disease, and this effect is not necessarily linear.

METHODS

We develop a semiparametric approach for estimating the probability of having the disease and, consequently, for estimating the PAF, controlling for the interaction between the exposure and a confounder. We use a tensor product of univariate B-splines to model the interaction under the monotonicity constraint. The model fitting procedure is formulated as a quadratic programming problem, and, thus, can be easily solved using standard optimization packages. We conduct simulations to compare the performance of the developed approach with the conventional B-splines approach without the monotonicity constraint, and with the logistic regression approach. To illustrate our method, we estimate the PAF of hopelessness and depression for suicidal ideation among elderly depressed patients.

RESULTS

The proposed estimator exhibited better performance than the other two approaches in the simulation settings we tried. The estimated PAF attributable to hopelessness is 67.99% with 95% confidence interval: 42.10% to 97.42%, and is 22.36% with 95% confidence interval: 12.77% to 56.49% due to depression.

CONCLUSIONS

The developed approach is easy to implement and supports flexible modeling of possible non-linear relationships between a disease and an exposure of interest.

Spatial variation in attributable risks

The attributable risk (AR) measures the contribution of a particular risk factor to a disease, and allows estimation of disease rates specific to that risk. While previous studies consider variability in ARs over demographic categories, this paper considers the extent of spatial variability in ARs estimated from multilevel data with confounders both at individual and geographic levels. A case study considers the AR for diabetes in relation to elevated BMI, and area rates for diabetes attributable to excess weight. Contextual adjustment includes known area variables, and unobserved spatially clustered influences, while spatial heterogeneity (effect modification) is considered in terms of varying effects of elevated BMI by neighbourhood deprivation category. The application is to patient register data in London, with clear evidence of spatial variation in ARs, and in small area diabetes rates attributable to excess weight.