Theory and performance of substitution models for estimating relative causal effects in nutritional epidemiology.

BACKGROUND: Estimating relative causal effects (i.e., "substitution effects") is a common aim of nutritional research. In observational data, this is usually attempted using 1 of 2 statistical modeling approaches: the leave-one-out model and the energy partition model. Despite their widespread use, there are concerns that neither approach is well understood in practice. OBJECTIVES: We aimed to explore and illustrate the theory and performance of the leave-one-out and energy partition models for estimating substitution effects in nutritional epidemiology. METHODS: Monte Carlo data simulations were used to illustrate the theory and performance of both the leave-one-out model and energy partition model, by considering 3 broad types of causal effect estimands: 1) direct substitutions of the exposure with a single component, 2) inadvertent substitutions of the exposure with several components, and 3) average relative causal effects of the exposure instead of all other dietary sources. Models containing macronutrients, foods measured in calories, and foods measured in grams were all examined. RESULTS: The leave-one-out and energy partition models both performed equally well when the target estimand involved substituting a single exposure with a single component, provided all variables were measured in the same units. Bias occurred when the substitution involved >1 substituting component. Leave-one-out models that examined foods in mass while adjusting for total energy intake evaluated obscure estimands. CONCLUSIONS: Regardless of the approach, substitution models need to be constructed from clearly defined causal effect estimands. Estimands involving a single exposure and a single substituting component are typically estimated more accurately than estimands involving more complex substitutions. The practice of examining foods measured in grams or portions while adjusting for total energy intake is likely to deliver obscure relative effect estimands with unclear interpretations.

Estimating the effects of lockdown timing on COVID-19 cases and deaths in England: A counterfactual modelling study.

BACKGROUND: During the first wave of the COVID-19 pandemic, the United Kingdom experienced one of the highest per-capita death tolls worldwide. It is debated whether this may partly be explained by the relatively late initiation of voluntary social distancing and mandatory lockdown measures. In this study, we used simulations to estimate the number of cases and deaths that would have occurred in England by 1 June 2020 if these interventions had been implemented one or two weeks earlier, and the impact on the required duration of lockdown. METHODS: Using official reported data on the number of Pillar 1 lab-confirmed cases of COVID-19 and associated deaths occurring in England from 3 March to 1 June, we modelled: the natural (i.e. observed) growth of cases, and the counterfactual (i.e. hypothetical) growth of cases that would have occurred had measures been implemented one or two weeks earlier. Under each counterfactual condition, we estimated the expected number of deaths and the time required to reach the incidence observed under natural growth on 1 June. RESULTS: Introducing measures one week earlier would have reduced by 74% the number of confirmed COVID-19 cases in England by 1 June, resulting in approximately 21,000 fewer hospital deaths and 34,000 fewer total deaths; the required time spent in full lockdown could also have been halved, from 69 to 35 days. Acting two weeks earlier would have reduced cases by 93%, resulting in between 26,000 and 43,000 fewer deaths. CONCLUSIONS: Our modelling supports the claim that the relatively late introduction of social distancing and lockdown measures likely increased the scale, severity, and duration of the first wave of COVID-19 in England. Our results highlight the importance of acting swiftly to minimise the spread of an infectious disease when case numbers are increasing exponentially.

Adjustment for energy intake in nutritional research: a causal inference perspective.

BACKGROUND: Four models are commonly used to adjust for energy intake when estimating the causal effect of a dietary component on an outcome: 1) the "standard model" adjusts for total energy intake, 2) the "energy partition model" adjusts for remaining energy intake, 3) the "nutrient density model" rescales the exposure as a proportion of total energy, and 4) the "residual model" indirectly adjusts for total energy by using a residual. It remains underappreciated that each approach evaluates a different estimand and only partially accounts for confounding by common dietary causes. OBJECTIVES: We aimed to clarify the implied causal estimand and interpretation of each model and evaluate their performance in reducing dietary confounding. METHODS: Semiparametric directed acyclic graphs and Monte Carlo simulations were used to identify the estimands and interpretations implied by each model and explore their performance in the absence or presence of dietary confounding. RESULTS: The "standard model" and the mathematically identical "residual model" estimate the average relative causal effect (i.e., a "substitution" effect) but provide biased estimates even in the absence of confounding. The "energy partition model" estimates the total causal effect but only provides unbiased estimates in the absence of confounding or when all other nutrients have equal effects on the outcome. The "nutrient density model" has an obscure interpretation but attempts to estimate the average relative causal effect rescaled as a proportion of total energy. Accurate estimates of both the total and average relative causal effects may instead be derived by simultaneously adjusting for all dietary components, an approach we term the "all-components model." CONCLUSIONS: Lack of awareness of the estimand differences and accuracy of the 4 modeling approaches may explain some of the apparent heterogeneity among existing nutritional studies. This raises serious questions regarding the validity of meta-analyses where different estimands have been inappropriately pooled.

Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations.

BACKGROUND: Directed acyclic graphs (DAGs) are an increasingly popular approach for identifying confounding variables that require conditioning when estimating causal effects. This review examined the use of DAGs in applied health research to inform recommendations for improving their transparency and utility in future research. METHODS: Original health research articles published during 1999-2017 mentioning 'directed acyclic graphs' (or similar) or citing DAGitty were identified from Scopus, Web of Science, Medline and Embase. Data were extracted on the reporting of: estimands, DAGs and adjustment sets, alongside the characteristics of each article's largest DAG. RESULTS: A total of 234 articles were identified that reported using DAGs. A fifth (n = 48, 21%) reported their target estimand(s) and half (n = 115, 48%) reported the adjustment set(s) implied by their DAG(s). Two-thirds of the articles (n = 144, 62%) made at least one DAG available. DAGs varied in size but averaged 12 nodes [interquartile range (IQR): 9-16, range: 3-28] and 29 arcs (IQR: 19-42, range: 3-99). The median saturation (i.e. percentage of total possible arcs) was 46% (IQR: 31-67, range: 12-100). 37% (n = 53) of the DAGs included unobserved variables, 17% (n = 25) included 'super-nodes' (i.e. nodes containing more than one variable) and 34% (n = 49) were visually arranged so that the constituent arcs flowed in the same direction (e.g. top-to-bottom). CONCLUSION: There is substantial variation in the use and reporting of DAGs in applied health research. Although this partly reflects their flexibility, it also highlights some potential areas for improvement. This review hence offers several recommendations to improve the reporting and use of DAGs in future research.