Validity evaluation of indirect adjustment method for multiple unmeasured confounders: A simulation and empirical study

BACKGROUND

An indirect adjustment method was developed to control for unmeasured confounders in a large administrative cohort study. A previous study that proposed the indirect adjustment method assessed the validity of the method by simulations but did not consider the direction of bias and scenarios with multiple missing confounders. In this study, we evaluated the direction and the magnitude of bias of the indirect adjustment method with multiple correlated unmeasured confounders using simulation and empirical datasets.

METHODS

A simulation study was conducted to compare the bias of the indirect adjustment by varying the number of confounders, magnitude of correlation between confounders, and the number of adjustment variables. An empirical study was conducted by applying the indirect adjustment method to the association between PM₁₀ and mortality using the Korea National Health and Nutrition Examination Survey linked Cause of Death data for 2007-2016.

RESULTS

The simulations of the present study demonstrated that 1) when a confounder is positively associated with both exposure and outcome, indirect adjustment might bias the effect size downward; 2) the magnitude of bias might depend on the correlation between unmeasured confounders; and 3) indirect adjustment for multiple missing confounders at once could result in a higher bias than that for some of the missing confounders. Empirical analyses also showed consistent results, but the bias of indirectly adjusted effect estimates was sometimes larger than that of unadjusted effect estimates.

CONCLUSIONS

The indirect adjustment method is a promising technique to reduce the bias from unmeasured confounding; however, it should be implemented carefully, particularly when there are multiple correlated unmeasured confounders of the same direction.

Evaluation of a method to indirectly adjust for unmeasured covariates in the association between fine particulate matter and mortality

BACKGROUND

Indirect adjustment via partitioned regression is a promising technique to control for unmeasured confounding in large epidemiological studies. The method uses a representative ancillary dataset to estimate the association between variables missing in a primary dataset with the complete set of variables of the ancillary dataset to produce an adjusted risk estimate for the variable in question. The objective of this paper is threefold: 1) evaluate the method for non-linear survival models, 2) formalize an empirical process to evaluate the suitability of the required ancillary matching dataset, and 3) test modifications to the method to incorporate time-varying exposure data, and proportional weighting of datasets.

METHODS

We used the association between fine particle air pollution (PM_2.5) with mortality in the 2001 Canadian Census Health and Environment Cohort (CanCHEC, N = 2.4 million, 10-years follow-up) as our primary dataset, and the 2001 cycle of the Canadian Community Health Survey (CCHS, N = 80,630) as the ancillary matching dataset that contained confounding risk factor information not available in CanCHEC (e.g., smoking). The main evaluation process used a gold-standard approach wherein two variables (education and income) available in both datasets were excluded, indirectly adjusted for, and compared to true models with education and income included to assess the amount of bias correction. An internal validation for objective 1 used only CanCHEC data, whereas an external validation for objective 2 replaced CanCHEC with the CCHS. The two proposed modifications were applied as part of the validation tests, as well as in a final indirect adjustment of four missing risk factor variables (smoking, alcohol use, diet, and exercise) in which adjustment direction and magnitude was compared to models using an equivalent longitudinal cohort with direct adjustment for the same variables.

RESULTS

At baseline (2001) both cohorts had very similar PM_2.5 distributions across population characteristics, although levels for CCHS participants were consistently 1.8-2.0 μg/m³ lower. Applying sample-weighting largely corrected for this discrepancy. The internal validation tests showed minimal downward bias in PM_2.5 mortality hazard ratios of 0.4-0.6% using a static exposure, and 1.7-3% when a time-varying exposure was used. The external validation of the CCHS as the ancillary dataset showed slight upward bias of -0.7 to -1.1% and downward bias of 1.3-2.3% using the static and time-varying approaches respectively.

CONCLUSIONS

The CCHS was found to be fairly well representative of CanCHEC and its use in Canada for indirect adjustment is warranted. Indirect adjustment methods can be used with survival models to correct hazard ratio point estimates and standard errors in models missing key covariates when a representative matching dataset is available. The results of this formal evaluation should encourage other cohorts to assess the suitability of ancillary datasets for the application of the indirect adjustment methodology to address potential residual confounding.

Indirect adjustment of relative risks of an exposure with multiple categories for an unmeasured confounder

PURPOSE

With observational epidemiologic studies, there is often concern that an unmeasured variable might confound an observed association. Investigators can assess the impact from such unmeasured variables on an observed relative risk (RR) by utilizing externally sourced information and applying an indirect adjustment procedure, for example, the "Axelson adjustment." Although simple and easy to use, this approach applies to exposure and confounder variables that are binary. Other approaches eschew specific values and provide only bounds on the potential bias.

METHODS

For both multiplicative and additive RR models, we present formulae for indirect adjustment of observed RRs for unmeasured potential confounding variables when there are multiple categories. In addition, we suggest an alternative strategy to identify the characteristics that the confounder must have to explain fully the observed association.

RESULTS AND CONCLUSIONS

We provide examples involving studies of pediatric computer tomography scanning and leukemia and nuclear radiation workers and smoking to demonstrate that with externally sourced information, an investigator can assess whether confounding from unmeasured factors is likely to occur.

Indirect adjustment for multiple missing variables applicable to environmental epidemiology

OBJECTIVES

Develop statistical methods for survival models to indirectly adjust hazard ratios of environmental exposures for missing risk factors.

METHODS

A partitioned regression approach for linear models is applied to time to event survival analyses of cohort study data. Information on the correlation between observed and missing risk factors is obtained from ancillary data sources such as national health surveys. The relationship between the missing risk factors and survival is obtained from previously published studies. We first evaluated the methodology using simulations, by considering the Weibull survival distribution for a proportional hazards regression model with varied baseline functions, correlations between an adjusted variable and an adjustment variable as well as selected censoring rates. Then we illustrate the method in a large, representative Canadian cohort of the association between concentrations of ambient fine particulate matter and mortality from ischemic heart disease.

RESULTS

Indirect adjustment for cigarette smoking habits and obesity increased the fine particulate matter-ischemic heart disease association by 3%-123%, depending on the number of variables considered in the adjustment model due to the negative correlation between these two risk factors and ambient air pollution concentrations in Canada. The simulations suggested that the method yielded small relative bias (<40%) for most cohort designs encountered in environmental epidemiology.

CONCLUSIONS

This method can accommodate adjustment for multiple missing risk factors simultaneously while accounting for the associations between observed and missing risk factors and between missing risk factors and health endpoints.