Identification of causal effects in case-control studies

Background Case-control designs are an important yet commonly misunderstood tool in the epidemiologist’s arsenal for causal inference. We reconsider classical concepts, assumptions and principles and explore when the results of case-control studies can be endowed a causal interpretation. Results We establish how, and under which conditions, various causal estimands relating to intention-to-treat or per-protocol effects can be identified based on the data that are collected under popular sampling schemes (case-base, survivor, and risk-set sampling, with or without matching). We present a concise summary of our identification results that link the estimands to the (distribution of the) available data and articulate under which conditions these links hold. Conclusion The modern epidemiologist’s arsenal for causal inference is well-suited to make transparent for case-control designs what assumptions are necessary or sufficient to endow the respective study results with a causal interpretation and, in turn, help resolve or prevent misunderstanding. Our approach may inform future research on different estimands, other variations of the case-control design or settings with additional complexities.

The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables

Empirical researchers often combine multiple instrumental variables (IVs) for a single treatment using two-stage least squares (2SLS). When treatment effects are heterogeneous, a common justification for including multiple IVs is that the 2SLS estimand can be given a causal interpretation as a positively weighted average of local average treatment effects (LATEs). This justification requires the well-known monotonicity condition. However, we show that with more than one instrument, this condition can only be satisfied if choice behavior is effectively homogeneous. Based on this finding, we consider the use of multiple IVs under a weaker, partial monotonicity condition. We characterize empirically verifiable sufficient and necessary conditions for the 2SLS estimand to be a positively weighted average of LATEs under partial monotonicity. We apply these results to an empirical analysis of the returns to college with multiple instruments. We show that the standard monotonicity condition is at odds with the data. Nevertheless, our empirical checks reveal that the 2SLS estimate retains a causal interpretation as a positively weighted average of the effects of college attendance among complier groups. (JEL C26, I23, I26, J24, J31, R23)

Causality and the Cox Regression Model

This article surveys results concerning the interpretation of the Cox hazard ratio in connection to causality in a randomized study with a time-to-event response. The Cox model is assumed to be correctly specified, and we investigate whether the typical end product of such an analysis, the estimated hazard ratio, has a causal interpretation as a hazard ratio. It has been pointed out that this is not possible due to selection. We provide more insight into the interpretation of hazard ratios and differences, investigating what can be learned about a treatment effect from the hazard ratio approaching unity after a certain period of time. The conclusion is that the Cox hazard ratio is not causally interpretable as a hazard ratio unless there is no treatment effect or an untestable and unrealistic assumption holds. We give a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

(Successful) Democracies Breed Their Own Support

Using large-scale survey data covering more than 110 countries and exploiting within country variation across cohorts and surveys, we show that individuals with longer exposure to democracy display stronger support for democratic institutions. We bolster these baseline fi?ndings using an instrumental-variables strategy exploiting regional democratization waves and focusing on immigrants' exposure to democracy before migration. In all cases, the timing and nature of the effects are consistent with a causal interpretation. We also establish that democracies breed their own support only when they are successful: all of the effects we estimate work through exposure to democracies that are successful in providing economic growth, peace and political stability, and public goods.

Mathematical Explanations in Evolutionary Biology or Naturalism? A Challenge for the Statisticalist

This article presents a challenge that those philosophers who deny the causal interpretation of explanations provided by population genetics might have to address. Indeed, some philosophers, known as statisticalists, claim that the concept of natural selection is statistical in character and cannot be construed in causal terms. On the contrary, other philosophers, known as causalists, argue against the statistical view and support the causal interpretation of natural selection. The problem I am concerned with here arises for the statisticalists because the debate on the nature of natural selection intersects the debate on whether mathematical explanations of empirical facts are genuine scientific explanations. I argue that if the explanations provided by population genetics are regarded by the statisticalists as non-causal explanations of that kind, then statisticalism risks being incompatible with a naturalist stance. The statisticalist faces a dilemma: either she maintains statisticalism but has to renounce naturalism; or she maintains naturalism but has to content herself with an account of the explanations provided by population genetics that she deems unsatisfactory. This challenge is relevant to the statisticalists because many of them see themselves as naturalists.

Robustness and bias of European excess death estimates in 2020 under varying model specifications

Various procedures are in use to calculate excess deaths during the ongoing COVID-19 pandemic. Using weekly death counts from 20 European countries, we evaluate the robustness of excess death estimates to the choice of model for expected deaths and perform a cross-validation analysis to assess the error and bias in each model's predicted death counts. We find that the different models produce very similar patterns of weekly excess deaths but disagree substantially on the level of excess. While the exact country ranking along percent excess death in 2020 is sensitive to the choice of model the top and bottom ranks are robustly identified. On the country level, the 5-year average death rate model tends to produce the lowest excess death estimates, whereas high excess deaths are produced by the popular 5-year average death count and Euromomo-style Serfling models. Cross-validation revealed these estimates to be biased under a causal interpretation of "expected deaths had COVID-19 not happened."

The Causal Interpretation of “Overall Vaccine Effectiveness” in Test-Negative Studies

Test-negative studies are commonly used to estimate influenza vaccine effectiveness (VE). In a typical study, an “overall VE” estimate may be reported based on data from the entire sample. However, there may be heterogeneity in VE, particularly by age. We therefore discuss the potential for a weighted average of age-specific VE estimates to provide a more meaningful measure of overall VE. We illustrate this perspective first using simulations to evaluate how overall VE would be biased when certain age groups are over-represented. We found unweighted overall VE estimates tended to be higher than weighted VE when children were over-represented and lower when elderly were over-represented. Then we extracted published estimates from the US Flu VE network, in which children are overrepresented, and some discrepancy between unweighted and weighted overall VE was observed. Differences in weighted versus unweighted overall VE could translate to substantial differences in the interpretation of individual risk reduction in vaccinated persons, and the total averted disease burden at the population level. Weighting overall estimates should be considered in VE studies in future.