Modeling causes of death: an integrated approach using CODEm

Abstract

Background: Data on causes of death by age and sex are a critical input into health decision-making. Priority setting in public health should be informed not only by the current magnitude of health problems but by trends in them. However, cause of death data are often not available or are subject to substantial problems of comparability. We propose five general principles for cause of death model development, validation, and reporting.

Methods: We detail a specific implementation of these principles that is embodied in an analytical tool - the Cause of Death Ensemble model (CODEm) - which explores a large variety of possible models to estimate trends in causes of death. Possible models are identified using a covariate selection algorithm that yields many plausible combinations of covariates, which are then run through four model classes. The model classes include mixed effects linear models and spatial-temporal Gaussian Process Regression models for cause fractions and death rates. All models for each cause of death are then assessed using out-of-sample predictive validity and combined into an ensemble with optimal out-of-sample predictive performance.

Results: Ensemble models for cause of death estimation outperform any single component model in tests of root mean square error, frequency of predicting correct temporal trends, and achieving 95% coverage of the prediction interval. We present detailed results for CODEm applied to maternal mortality and summary results for several other causes of death, including cardiovascular disease and several cancers.

Conclusions: CODEm produces better estimates of cause of death trends than previous methods and is less susceptible to bias in model specification. We demonstrate the utility of CODEm for the estimation of several major causes of death.

Figure 1

Examples of missingness patterns observed in data for a single country and cause of death. Green represents available data and red represents missing.

Figure 2

Example weighting schemes for 100 component models at different values of ψ.

Figure 3

Heatmap of stability in maternal mortality component model rankings. Each row represents a component model, and each column corresponds to how many hold-outs are used when ranking. Rows are sorted by rankings using all 25 hold-outs. Cells are colored based on their ranking, with the green models being the best and red the worst. The last column displays in-sample ranks. The figure shows that rankings stabilize as hold-outs increase, and that in-sample ranking does not correlate well with out-of-sample.

Figure 4

In-sample, test 1, and test 2 performance on RMSE and trend test for maternal mortality component models.

Figure 5

Correlation between test 1 and test 2 rankings of maternal mortality component models.

Figure 6

Correlation in maternal mortality component model rankings by number of hold-outs performed.