Recent high summer temperatures and heat waves, attributed to climate change, have led to increased attention to associations of ambient temperature with morbidity and mortality. Temperature as a cause of mortality has been studied for centuries.1 However, many recent articles on this topic use analytic models and data notably different from those used in the past. Given the availability of large time series data sets, various types of time-based models have been used to characterize associations while controlling confounding and exploring effect measure modification by socioeconomic factors, housing characteristics, and other variables. Many recent epidemiologic analyses of temperature effects have included measures of air pollution as explanatory variables in the analysis, yielding estimates of temperature effects that are adjusted for air pollution.2 In some instances, data and modeling approaches used initially for epidemiologic investigations of air pollution have been subsequently used for investigations of ambient temperature.3
While adjusting for air pollution in studies of temperature has become common, this practice may not always be appropriate. In this commentary, we illustrate potential relationships among temperature, air pollution, and disease on a short-term basis using directed acyclic graphs (DAGs), and we discuss implications of some possible causal structures for estimates of temperature-related health effects.
In time series analyses of air pollution and health effects, temperature is typically considered to be a potential confounder, given its association with mortality and levels of some air pollutants.4 Recent epidemiologic analyses of associations between ambient temperature and health effects have frequently adjusted for air pollution.2 The rationale for such adjustments, although not always explicitly stated, appears to be the same as that for the adjustment for temperature in studies of air pollution: air pollution could be a confounder of ambient temperature-health effect associations.3,5,6 For example, O’Neill et al3 noted that “Unlike in other recent multicity analyses of temperature and mortality associations, we controlled for the effects of PM10 in the models. The level of confounding if particulate pollution is not included can be substantial.” This article followed an earlier article by Zanobetti and Schwartz7 that used a subset of the same data to estimate the association between air pollution and mortality, adjusted for potential confounding by ambient temperature. A recent review and meta-analysis2 reported that 14 of 21 studies of associations between average daily ambient temperature and cardiorespiratory morbidity adjusted for air pollution as a potential confounder of the temperature-morbidity association.
In a causal diagram, confounding refers to an open back-door path between the exposure of interest and outcome. The practice of adjusting for temperature in studies of air pollution and vice versa leads to the question: what causal structures between temperature and air pollution would justify this practice?
CAUSAL RELATIONSHIPS BETWEEN TEMPERATURE AND AIR POLLUTION
We discuss four potential causal structures for the relationships among temperature (T), air pollution (A), and disease (D) using DAGs, which can aid in evaluating causal effects.8 While causal DAG theory may incorporate strong implicit assumptions,9 DAGs are a useful visual tool for evaluating relationships between variables and identifying confounders.10 We use these causal models to clarify the role of air pollution in studies of the total effect of temperature on health. The DAGs presented here are simplified to highlight the associations of interest. In practice, many additional variables may be needed to fully represent complex relationships among temperature, pollution, and weather that influence a given exposure-outcome association.
Temperature Affects Air Pollution
Figure A depicts a causal structure in which T affects both A and D. This figure represents associations posited in air pollution studies where adjustment for T is needed to control for confounding by T of the association between A and D. Note that A is not a confounder of the T-D association because it does not affect T; rather, A is on an intermediate pathway between T and D. If the associations that justify adjustment for daily ambient temperature in analyses of air pollution health effects are correctly depicted by Figure A, then the logic of an analysis of the association between T and D that conditions on A is questionable.
Temperature Is Affected by Air Pollution
In studies of temperature effects on health, the rationale for air pollution adjustment is sometimes described as concern about potential confounding.11Figure B illustrates a causal structure in which A is a confounder of that association. It would be necessary to control for A to obtain a unconfounded estimate of the effect of T on D. Figure A and B both have arrows from T to D and A to D. However, in Figure A, T is a cause of A, while in Figure B, A is a cause of T. While daily air pollution and daily temperature may affect each other over time, standard regression models used in this literature do not incorporate such cyclic relationships.
The direction of the arrow between A and T in Figure B implies that variation in daily air pollution levels causes variation in daily temperature. Such a causal model might seem surprising, given what we know about temperature and air pollution, which tends to suggest that changes in daily ambient temperature influence air pollution levels and not the converse. Consider the relationship between temperature and ozone. We are not aware of evidence that daily variation in ozone has a substantial impact on local daily ambient temperature. However, higher daily ambient temperatures lead to increasing ozone levels through effects on reaction kinetics12; in addition, extreme temperatures may increase energy consumption and consequently lead to changes in local air pollution levels (including changes in chemical composition of particulate matter).13 This is not to suggest that Figure B is necessarily wrong for every air pollutant but rather that investigators need to be explicit about causal assumptions and their plausibility, given the spatial and temporal scales under consideration.
Temperature and Air Pollution Have a Shared Cause
A causal structure that would justify adjustment for temperature in studies of air pollution effects, and for air pollutants in studies of temperature effects, arises if both A and T are affected by a third variable, Z (Figure C). In this DAG, adjustment for either Z or A is sufficient to obtain a unconfounded estimate of the effect of T on D. Potential Z variables include movement of air masses and other weather patterns that may be difficult to measure. If Z is unmeasured—and if we now assume that there is no direct causal effect of T on A (or vice versa)—then adjustment for A in analyses of the effect of T on D would be necessary to block the confounding pathway through Z. Similarly, adjustment for T would control for the pathway through Z in analyses of the effect of A on D. However, the absence of an arrow between A and T is not typically supported by known causal relationships. While we cannot offer a good example in which such a causal structure would be plausible, it serves to illustrate that conditions do arise when adjustment would be appropriate.
Temperature Affects Air Pollution and They Have a Shared Cause
Figure D depicts a causal structure in which Z affects both A and T, and we also allow a causal effect of T on A. Consider again ambient temperature and ozone: sunlight may be a cause of increased ambient temperature and ozone formation, while temperature directly influences reactions that generate ozone.12 These relationships are represented by a causal structure such as Figure D that includes an arrow from T to A. This structure again implies that adjustment for A is inappropriate as it blocks part of the total effect of T on D.
MEDIATION AND MODIFICATION
The DAGs in the Figure are simplified depictions of potentially complex causal relationships among temperature, air pollutants, and mortality. It is worth emphasizing, however, that many more complicated DAGs reinforce the conclusion that adjustment for A, if it has an effect of T, may lead to biased estimates of temperature effects.
A data analyst might accept that temperature affects air pollution and still wish to adjust for air pollution in an analysis of temperature effects. This goal would conform to a modeling approach, as in mediation analysis, where the investigator attempts to block causal paths for temperature effects that operate through air pollution. It is important to recognize that the use of standard analysis methods may produce biased estimates if there is also a unmeasured common cause of A and D.14,15 While mediation analysis is a potential rationale for adjusting temperature effects for air pollution levels, distinctions between estimation of direct versus total effects of temperature on disease are rarely found in this literature. Discussions of the implications of findings typically bear on the total effect of temperature on disease rather than direct effects, and the necessary assumptions for using adjustment to obtain direct effect estimates are not made explicit.
Finally, researchers may be justifiably interested in whether a pollutant, such as ozone, is both an intermediate and an effect measure modifier of the association between ambient temperature and health indicators.16–19 Such effects may be plausible if, for example, temperature effects on a health outcome are exacerbated in settings of high ozone relative to effects observed with low ozone. However, a great deal of care may be needed to define the effect estimated in an analysis that conditions on an air pollutant that is an intermediate and modifier of a temperature-morbidity association. Attention should be given to the potential to induce collider stratification bias in such analyses.
Anderson and Bell20 examined the effect of temperature on risk of mortality in 107 urban US communities during a 14-year period using time series models. Absolute heat and cold effects were calculated as the change in mortality risk at 80°F compared with 60°F and at 40°F compared with 60°F, respectively. To address “confounding from pollutants,”20 the authors conducted sensitivity analyses with models adjusted for ozone. Ozone adjustment had little influence on estimates of the effect of cold on mortality but reduced estimates of the effect of heat on mortality from 5.4% to 4.5%.
Interpreting these findings depends on the underlying causal relationships among temperature, ozone, and mortality. If temperature affects ozone levels (Figure A and D), then adjustment for A blocks part of the total effect of temperature on mortality. We do not find that Figure B or C reasonably represent what is known about how temperature affects ozone. Although it was not the goal of this study, the ozone-adjusted estimate could be interpreted as the direct effect of temperature on mortality if there are no unmeasured shared causes of temperature and ozone and of ozone and mortality. The absence of such factors would be, however, a strong assumption in this study.
Investigators sometimes adjust for variables to determine whether results are robust to changes in the set of adjustment variables. If no change in estimate is observed, as was the case in the analysis by Anderson and Bell20 of the influence of ozone adjustment on estimates of the association between cold temperature and mortality, there may be some assurance that the pollutant is neither a confounder nor a mediator. If there is a change in estimate, however, as was the case in their analysis of the influence of ozone adjustment on estimates of the association between high temperature and mortality, the uncertainty of the underlying causal structure should be acknowledged when interpreting adjusted results.
This exercise illustrates the importance of assumptions that are external to the study data about the causal relationships between measured variables in studies of temperature and health outcomes. Because these depend on the specific pollutants and health outcomes being assessed, the covariates that were measured, and the analysis methods being applied, we do not provide prescriptive guidance, but rather recommend that investigators carefully consider relationships in their studies. Using DAGs to clarify causal structures can help investigators avoid potential biases such as conditioning on an intermediate.
Adjustment for temperature typically is warranted when estimating a unconfounded effect of air pollution on mortality, but not vice versa. This is contrary to the adjustment strategy used in many articles examining the effect of heat on morbidity or mortality.5,11,20–29
Further thinking about estimation of ambient temperature effects in terms of causes that are interventions, as in the potential outcomes framework, merits greater emphasis in this research area. Explicit specification of potential interventions would clarify causal associations implied by the models being fitted. From the policy perspective, describing the quantities being estimated has important implications for how findings can be translated into policy.
We suspect that the situations in which adjustment for air pollution is justified are the exception. In such situations, investigators should provide a clear rationale for their decision to adjust for air pollutants when estimating temperature effects. Clarifying the causal assumptions regarding associations among air pollution, ambient temperature, and disease will help understand just what effects are being estimated.
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