A method for detection of residual confounding in time-series and other observational studies

Abstract

Background: A difficult issue in observational studies is assessment of whether important confounders are omitted or misspecified. In this study, we present a method for assessing whether residual confounding is present. Our method depends on availability of an indicator with 2 key characteristics: first, it is conditionally independent (given measured exposures and covariates) of the outcome in the absence of confounding, misspecification, and measurement errors; second, it is associated with the exposure and, like the exposure, with any unmeasured confounders.

Methods: We demonstrate the method using a time-series study of the effects of ozone on emergency department visits for asthma in Atlanta. We argue that future air pollution may have the characteristics appropriate for an indicator, in part because future ozone cannot have caused yesterday's health events. Using directed acyclic graphs and specific causal relationships, we show that one can identify residual confounding using an indicator with the stated characteristics. We use simulations to assess the discriminatory ability of future ozone as an indicator of residual confounding in the association of ozone with asthma-related emergency department visits. Parameter choices are informed by observed data for ozone, meteorologic factors, and asthma.

Results: In simulations, we found that ozone concentrations 1 day after the emergency department visits had excellent discriminatory ability to detect residual confounding by some factors that were intentionally omitted from the model, but weaker ability for others. Although not the primary goal, the indicator can also signal other forms of modeling errors, including substantial measurement error, and does not distinguish between them.

Conclusions: The simulations illustrate that the indicator based on future air pollution levels can have excellent discriminatory ability for residual confounding, although performance varied by situation. Application of the method should be evaluated by considering causal relationships for the intended application, and should be accompanied by other approaches, including evaluation of a priori knowledge.

Figure 1

Basic Directed Acyclic Graph (DAG); factors B and C affect E. C also affects D.

Figure 2

A, the Unmeasured Factor (U₀) affects air pollution (AP₀) but not disease (D₁): B, indicates the same relationships, but U₀ also affects Disease.

Figure 3

As is Figure 2, but arrow from AP₀ to disease is removed. A, the unmeasured Factor (U₀) affects air pollution (AP₀) but not disease (D₁): B, indicates the same relationships, but U₀ also affects Disease.

Figure 4

A, as in Figure 3A, but also include future value of air pollution (AP₂); B, as in Figure 3B, but also include future value of air pollution (AP₂).

Figure 4

A, as in Figure 3A, but also include future value of air pollution (AP₂); B, as in Figure 3B, but also include future value of air pollution (AP₂).

Figure 5

The Unmeasured Factor (U₀) affects air pollution (AP₀) but not disease (D₁), and the unmeasured factor (U₀*) affects meteorology (M₀), future meteorology (M₂) and disease.

Figure 6

Indicates the association between future air pollution (AP₂) and disease (D₁), due to presence of the unmeasured factor U₀^*. The (other) unmeasured Factor (U₀) affects air pollution (AP₀) but not disease (D₁); U₀* affects meteorology (M₀), future meteorology (M₂) and disease.

Figure 7

Control for the future meteorologic factor (M₂) eliminates the association between future air pollution (AP₂) and disease.

Figure 8

As in Figure 7, U₀ also affects disease (D₁), so confounding is suspect. Control for the future meterologic factor (M₂) no longer eliminates the association between future air pollution (AP₂) and disease.

Figure 9

Measurement error (E₀ and E₁) affects the measured air pollution levels (M₀ and M₁, respectively). The true air pollution level (AP₀), affects disease, but the future level (AP₂) does not have this effect.