Kellyn F. Arnold

Introduction: Multiple myeloma (MM) prognosis worsens once patients become triple‐class exposed (TCE) to at least one treatment in each class: immunomodulators, proteasome inhibitors, and anti‐CD38 monoclonal antibodies.Methods: We conducted a retrospective study using the Cancer Analysis System database to assess characteristics, treatment patterns, and clinical outcomes for adults diagnosed with MM between 2014 and 2020. The main cohort included patients ≥18 years‐old diagnosed with incident MM (including TCE patients) who had at least one record of systemic anticancer therapy treatment within 30 days prior to, on, or any time after their diagnosis.Results: The main cohort comprised 14,990 patients, predominantly white and male, with a median age at diagnosis of 71 years. Of these, 848 (5.6%) became TCE. In the main cohort (n = 14,990), 57.2% of patients received only one line of therapy, and >50% of all first‐line regimens included bortezomib. Median overall survival (OS) from diagnosis was 51.5 months. After becoming TCE (n = 848), median OS was 13.2 months and median time to next treatment or death was 5.7 months.Conclusions: This study provides current evidence on real‐world OS and management for patients with MM in England, including those who become TCE.

Understanding causality, over mere association, is vital for researchers wishing to inform policy and decision making – for example, when seeking to improve population health outcomes. Yet, contemporary causal inference methods have not fully tackled the complexity of data hierarchies, such as the clustering of people within households, neighbourhoods, cities, or regions. However, complex data hierarchies are the rule rather than the exception. Gaining an understanding of these hierarchies is important for complex population outcomes, such as non-communicable disease, which is impacted by various social determinants at different levels of the data hierarchy. The alternative of analysing aggregated data could introduce well-known biases, such as the ecological fallacy or the modifiable areal unit problem. We devise a hierarchical causal diagram that encodes the multilevel data generating mechanism anticipated when evaluating non-communicable diseases in a population. The causal diagram informs data simulation. We also provide a flexible tool to generate synthetic population data that captures all multilevel causal structures, including a cross-level effect due to cluster size. For the very first time, we can then quantify the ecological fallacy within a formal causal framework to show that individual-level data are essential to assess causal relationships that affect the individual. This study also illustrates the importance of causally structured synthetic data for use with other methods, such as Agent Based Modelling or Microsimulation Modelling. Many methodological challenges remain for robust causal evaluation of multilevel data, but this study provides a foundation to investigate these.

Deterministic variables are variables that are functionally determined by one or more parent variables. They commonly arise when a variable has been functionally created from one or more parent variables, as with derived variables, and in compositional data, where the “whole” variable is determined from its “parts.” This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving derived variables and/or compositional data. We propose a 2-step approach in which all variables are initially considered, and a choice is made as to whether to focus on the deterministic variable or its determining parents. Depicting deterministic variables within DAGs brings several benefits. It is easier to identify and avoid misinterpreting tautological associations, that is, self-fulfilling associations between deterministic variables and their parents, or between sibling variables with shared parents. In compositional data, it is easier to understand the consequences of conditioning on the “whole” variable and to correctly identify total and relative causal effects. For derived variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions. DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving derived variables and/or compositional data.

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.

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. We aimed to clarify the implied causal estimand and interpretation of each model and evaluate their performance in reducing dietary confounding. 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. 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.” 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.

Background: In longitudinal data, it is common to create ‘change scores’ by subtracting measurements taken at baseline from those taken at follow-up, and then to analyse the resulting ‘change’ as the outcome variable. In observational data, this approach can produce misleading causal-effect estimates. The present article uses directed acyclic graphs (DAGs) and simple simulations to provide an accessible explanation for why change scores do not estimate causal effects in observational data. Methods: Data were simulated to match three general scenarios in which the outcome variable at baseline was a (i) ‘competing exposure’ (i.e. a cause of the outcome that is neither caused by nor causes the exposure), (ii) confounder or (iii) mediator for the total causal effect of the exposure variable at baseline on the outcome variable at follow-up. Regression coefficients were compared between change-score analyses and the appropriate estimator(s) for the total and/or direct causal effect(s). Results: Change-score analyses do not provide meaningful causal-effect estimates unless the baseline outcome variable is a ‘competing exposure’ for the effect of the exposure on the outcome at follow-up. Where the baseline outcome is a confounder or mediator, change-score analyses evaluate obscure estimands, which may diverge substantially in magnitude and direction from the total and direct causal effects. Conclusion: Future observational studies that seek causal-effect estimates should avoid analysing change scores and adopt alternative analytical strategies.

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 proxy confounding by common dietary causes. Objective: To clarify the implied causal estimand and interpretation of each model and evaluate their performance in reducing dietary confounding. Design: Semi-parametric 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 intake. Accurate estimates of both the total and average relative causal effects may instead be estimated by simultaneously adjusting for all dietary components, an approach we term the ‘all-components model’. Conclusion: Lack of awareness of the estimand differences and accuracy of the four modelling approaches may explain some of the apparent heterogeneity among existing nutritional studies and raise serious questions regarding the validity of meta-analyses where different estimands have been inappropriately pooled.

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. 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. 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). 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.