Accounting for Comorbidity in Etiologic Research

Introduction

Over the past decades, etiologic research on human disease has advanced significantly due to improvements in causal inference methodology, availability of health records – including registry-based studies – and establishment of international consortia allowing researchers to gauge the generalizability of results. Throughout, a considerable focus in observational studies has been placed on reducing confounding and other biases.¹ Although numerous publications^2–5 have now addressed various aspects of “adjustment” in design or analyses, many of these works are either theory-based or focused on specific causal structures,^3,4 limiting their wider implementation in applied research. Specifically, the issue of comorbidity, its various causal relationships with the outcome of interest, and downstream analytical recommendations have not been widely discussed. Therefore, addressing the issue of comorbidity in etiologic studies, integrating clinical perspectives and concepts, could help bridge the gap between methodological knowledge and practice.

Comorbidity, first defined by Feinstein (1970),⁶ is the presence (existence or occurrence) of another distinct health condition in an individual with the index disease. However, the definition and interpretation of comorbidity varies.^7,8 A primary point of divergence is its scope; indices like the Charlson Comorbidity Index,^9,10 for example, focus on a specific list of chronic conditions, whereas other study contexts may define comorbidity more broadly to include any co-occurring diagnosis.¹¹ Despite these definitional nuances, studies consistently show that comorbidity is a common phenomenon.¹²

Given the pervasive nature of comorbidity in many disorders,¹³ etiologic studies often consider comorbidity in their design or analyses.^14–19 The motivations for such considerations could include understanding the risk factors for the disease of interest “independent” of its comorbidity,²⁰ control of confounding,²¹ minimizing misclassification,²² or to study effect measure modification by comorbidity.^23,24 Despite these various contexts for considering comorbidity in etiologic research, the underlying motivation is most often to reduce bias or obtain a valid estimate for the parameters of interest. For instance, in pharmacoepidemiologic research, a large observational study assessing the effect of sodium-glucose cotransporter-2 (SGLT2) inhibitors on cardiovascular outcomes adjusted for baseline comorbidities such as obesity and nephropathy to control for potential confounding of the exposure–outcome relationship, yielding a more precise estimate of the drug’s true effect.²⁵

As there is no universally assumed (or universally true) causal structure between comorbidity⁸ and other variables in a study, a one-size-fits-all solution for accounting for comorbidity in etiologic research does not exist. For instance, comorbidity could be a risk factor for the index disease, its consequence, or share a common cause with it. Depending on the causal structure at hand, adjusting for comorbidity can change the effect estimate of the exposure on the outcome, sometimes resulting in attenuation, amplification, or even reversal of the estimated association relative to the comorbidity unadjusted associations.^2–4,26 Understanding the scenarios under which comorbidity adjustment is made and its impact on the main effect of exposure on the index diagnosis is therefore critical.

As the definition of comorbidity does not imply any causal relation or even temporal order between the index disease and the co-occurring comorbid conditions, it is important to be clear about the assumed structure(s) – which often is critical for informing the correct design or analytical strategy. However, a review of the literature reveals that the handling of comorbidity in the design and analysis of etiologic studies often lacks explicit assumptions about their relationship with other variables or may in fact not fully align with the study objectives.^14,19

In this paper, we therefore explore several common causal structures involving an exposure, index disease (outcome) and its comorbidity. For each scenario, we discuss the impact of adjusting for comorbidity on the effect estimates, as well as other potential considerations. We hope this piece can provide guidance for accounting for comorbidity (and potentially other covariates) in epidemiological research and contribute to improved causal inference.

Controlling for comorbidity extends beyond adjustment in the analytical model and can occur by restricting the sample based on comorbidity, stratified sampling or analysis based on comorbidity, or handling differential loss to follow-up or non-random missingness patterns. Henceforth, for ease of reading, we use conditioning and adjusting interchangeably, and unless otherwise specified, the statements about adjustment are applicable to all other conditioning approaches.

Methods

Possible Structure of Associations

Explicitly stating the causal assumptions is critical for the choice of the study design or analytical methods, and clear communication and justification of these decisions. Causal diagrams, specifically Directed Acyclic Graphs (DAGs)²⁷ are a common tool in causal inference for depicting assumptions and assessing bias. A concise and accessible description of the causal diagrams is provided by Greenland et al.²⁸

Here, we use DAGs to depict possible common scenarios underpinning the associations between exposure (X), index condition (outcome; Y) and comorbidity (C):

1. Comorbidity as a common cause of X and Y
2. Comorbidity as a mediator of the effects of X on Y
3. Comorbidity as a collider in the association between X and Y
4. Comorbidity as a consequence of X, but not a risk factor for Y
5. Comorbidity as a risk factor of Y, but independent of X
6. Comorbidity as a consequence of Y, but not directly associated with X

Effect Measures

The impact of adjusting for comorbidity on the estimate of the total effect depends on the choice of effect measures. To extend the applications of our work, for each of the above scenarios presented, we will assess and discuss the effect of conditioning on comorbidity for four different effect measures; 1) risk difference (RD) (linear risk regression), 2) risk ratio (RR) (log binomial regression), 3) odds ratio (OR) (logistic regression), and 4) least squares mean difference (LSMD) (least squares regression).

Simulation Setting

We conducted a simulation study to assess the effect of conditioning on covariate C in each of the causal structures presented in Figure 1. The parameters for the simulations, along with the analytical code, can be accessed at https://github.com/v-k-lab/comorbidity. Briefly, for each of the causal structures presented in Figure 1, we made 5,000 iterations of simulated studies with sample size 10,000. For simplicity, we assumed X and C are both binary variables. For each causal diagram, we simulated 4 sets of outcomes (Y): three binary endpoints (eg, hip fracture) corresponding to the total effect of X on Y on the RD, RR, and OR scales to be 0.2, 2, and 2 respectively; and one normally distributed, continuous endpoint (eg, serum cholesterol level) for which the total effect of X on Y measured by the mean difference was equal to 2.

Figure 1 Depicting causal relation between exposure (X), index disease (Y), and comorbidity (C) in selected common scenarios using Directed Acyclic Graphs (DAGs). (A) DAG 1; (B) DAG 2; (C) DAG 3; (D) DAG 4; (E) DAG 5; (F) DAG 6.

The simulation for the causal structure depicted in Figure 1 panel A included the following steps:

1. Simulate binary covariate, C, with a probability of p_c.
2. Simulate a binary exposure variable, X (0, 1), where the probability of X, p_x, was assumed to be a function of C, P(X = 1|C).
3. Simulate a response Y, where Y was assumed to be a function of X and C.
   1. The response for the linear risk regression estimating RD was simulated by:P(Y = 1|X, C) = 0.2 + 0.2 × x + 0.2 × c
   2. The response for the log binomial model estimating RR was simulated by:P(Y = 1|X, C) = exp(log(0.2) + log(2) × x + log(2) × c)
   3. The response for the logistic regression model estimating OR was simulated by:P(Y = 1|X, C) = 1/(1 + exp(-(log(0.4) + log(2) × x + log(2) × c)))
   4. The response for the linear regression model estimating mean difference was simulated byE(Y|X, C) = N~(2, 2²) + N~(2 × x, 2²) + N~(2 × c, 2²)
4. Run the following models:
   1. Linear risk regression model estimating effect of X on Y, with and without adjusting for C. The effect measure from this model is RD.
   2. log binomial regression model estimating effect of X on Y, with and without adjusting for C. Exponentiate coefficient of X to obtain RR.
   3. logistic regression model estimating effect of X on Y, with and without adjusting for C. Exponentiate coefficient of X to obtain OR.
   4. least squares regression model estimating effect of X on Y, with and without adjusting for C. The effect measure from this model is LSMD.
5. Repeat steps 1–4, 5,000 times.

The point estimate for each effect measure was the median of the estimates from the 5,000 iterations and the lower and upper limits of the 95% CI corresponded to the 2.5th and 97.5th percentile of these 5,000 estimates. Given the true effect estimate for RR, OR, and LSMD was 2, the coefficient of x from each model was evaluated based on the relative bias (estimated effect - 2)/2. For RD, the relative bias was estimated as (estimated effect - 0.2)/0.2

Furthermore, to enhance the real-world applicability of our study, we extended our analyses to scenarios where C is either categorical or continuous, and assessed the impact of misclassification of covariate C on the C adjusted estimated effect.

Results

Anticipated Effect of Conditioning on Comorbidity and Simulation Results

Table 1 presents simulation results. For each of these causal diagrams, the crude and C-adjusted estimated association between X and Y, along with their 95% CI intervals, were summarized for RD, RR, OR, and LSMD effect measures. The relative bias of the point estimate was reported as percentage difference from the unbiased estimate.

Table 1 Association Between Exposure (X) and Index Disease (Y) in Crude and Comorbidity (C) Adjusted Models for Different Causal Scenarios

DAG 1: Comorbidity as a Common Cause of X and Y

Real-world example: Obesity (C) in a study of the effects of type 2 diabetes mellitus (X) on ischemic heart disease (Y).

In this scenario, comorbidity is the common cause of exposure and outcome, fulfilling the definition of a confounder. Using DAGs, we observe the open back door path from X to C to Y, resulting in bias. Conditioning on comorbidity is warranted, and failure to condition on comorbidity in this case will result in confounding of the effect estimate of X on Y. The crude estimate was biased for all three models, and the adjusted estimates remained unbiased (Table 1, DAG 1).²¹

Recommended strategy is to adjust for comorbidity.

DAG 2: Comorbidity as a Mediator of the Effects of X on Y

Real-world example: hyperlipidemia (C) in a study of the effects of sedentary lifestyle (X) on ischemic heart disease (Y).

In this case, the path from X to C to Y is causal. C is a mediator on the path reflecting the indirect effect of X to Y. Therefore, conditioning on C resulted in bias in the estimate of the total effect of X on Y, whereas the unconditional effect remained unbiased (Table 1, DAG 2).

Recommended strategy is to not adjust for comorbidity.

DAG 3: Comorbidity as a Collider

Real-world example: injury (C) in a study of the effects of alcohol use (X) on depression (Y).

When the comorbidity is caused by both exposure and index disease, the path connecting exposure and index disease through comorbidity is closed and the comorbidity serves as a collider on that path. Here, the crude estimate provided unbiased effect estimates, and adjusting for C resulted in bias (collider stratification bias) in the estimates.^2,4 This bias is present regardless of the analytical model used, and its magnitude depends on the strength of the association between X and C; and Y and C (Table 1, DAG 3).

Recommended strategy is to not adjust for comorbidity.

DAG 4: Comorbidity as a Consequence of X, but Not a Risk Factor for Y

Real-world example: liver failure (C) in a study of the effects of alcohol use (X) on dementia (Y).

In this case, either conditioning on C or not will not bias the estimate of the effect of X on Y, and both crude and C-adjusted models provided unbiased estimates of RD, RR, OR, and LSMD (Table 1, DAG 4).

Recommended strategy is that both adjusting or not adjusting are fine and will not result in bias.

DAG 5: Comorbidity as a Risk Factor of Y, but Independent of X

Real-world example: alcohol abuse (C) in a study of the effects of air pollution (X) on hepatic cancer (Y).

When comorbidity is a risk factor for the index disease but is not associated with the exposure, adjusting for comorbidity does not introduce bias. RD, RR and LSMD are unbiased in both crude and adjusted models. For the OR, the results for the adjusted and crude models differ due to the non-collapsibility of the OR, representing conditional and marginal effects, respectively. Both estimates are unbiased for their respective target parameters. However, due to the non-collapsibility of nonlinear models (eg, logistic regression), the conditional and marginal effects of X on Y could differ, and the difference in the estimates between the crude and adjusted models reflects the difference in the underlying effects being estimated, and not necessarily possible bias.^3,29–31 The choice of the model should be guided by clear definition of the underlying effect of interest.

Recommended strategy is that both adjusting or not adjusting for comorbidity are analytically sound and will not result in bias.

DAG 6: Comorbidity as a Consequence of Y, but Not Directly Associated with X

Real-world example: opportunistic infection (C) in a study of the effects of syringe service program (X) on risk of HIV infection (Y).

When the disease is a risk factor for comorbidity, the crude estimates are unbiased. However, under the assumption that X has an effect on Y, conditioning on comorbidity in the linear models (eg, RD, RR and LSMD) leads to biased estimates, while the OR from the adjusted model remained unbiased (Table 1, DAG 6). None of the models will be biased by adjusting for C if the effect of X on Y is null.³

Recommended strategy is that both adjusting or not adjusting for comorbidity will not result in bias in OR. It is recommended to not adjust for comorbidity in linear risk, log binomial, and least squares regression models.

The additional analyses, using either a categorical or continuous specification of the covariate C, yielded results consistent with the main findings (Supplemental Table S1). Furthermore, models incorporating misclassified measures of comorbidity—whether differentially or non-differentially misclassified with respect to exposure—produced effect estimates that fell between those from the crude model and those adjusted for correctly measured C (Supplemental Table S2) for causal structures depicted in DAGs 1–4 and DAG 6. This pattern was also true when adjusting for non-differentially misclassified C in the causal structure depicted in DAG 5. Nevertheless, when adjusting for differentially misclassified C in the causal structure depicted in DAG 5, estimates could fall outside the range defined by those from the crude models and those adjusted for correctly measured C.

Additional analyses yielded a consistent pattern across varying levels of misclassification in scenarios with binary exposure and binary outcome: regardless of whether comorbidity acted as a confounder or a mediator, the effect estimates fell between those from the crude model and those adjusted for correctly measured C (Supplemental Figure S1).

Discussion

This study provides a detailed exploration of the potential roles of comorbidity in the association between exposure and index disease, highlighting the diverse causal relationships that can exist between these variables. Accounting for the correct causal structure has extensive implications for causal inference in etiologic research. By systematically examining common causal structures and their effects on bias, this work addresses a critical but underexplored issue: the appropriate handling of comorbidity in causal research.

Our findings confirm that the role of comorbidity in the exposure–outcome relationship determines the impact of conditioning. When comorbidity acts as a confounder, conditioning effectively mitigates confounding bias across all the effect measures (eg, risk difference [RD], risk ratio [RR], odds ratio [OR], and least-squares mean difference [LSMD]). Conversely, when comorbidity serves as a mediator or collider, conditioning introduces bias into the total effect estimate of the exposure on the outcome. This highlights the critical need to avoid inappropriate adjustments.

When comorbidity is either a cause or consequence of the exposure but has no direct connection to the outcome (except through the exposure), adjusting for comorbidity does not affect the estimated effect. However, if comorbidity is a consequence of the outcome, rather than exposure, adjustment introduces bias in log-binomial and linear regression models, but not in logistic regression models. If comorbidity is a cause of the outcome, adjusting for it does not result in bias. However, in nonlinear models like logistic regression, the distinction between marginal and conditional effects due to the non-collapsibility of effect measures emphasizes the importance of aligning analytical strategies with study objectives, which extends beyond merely minimizing bias. For example, marginal effects provide insight into the exposure’s effect on the outcome at the population level, whereas, the conditional effect could be more relevant for inference on an individual level.

Although our results demonstrate that inappropriate handling of comorbidity in the analyses could lead to bias, it is important to note that the direction and magnitude of such bias depend on the distribution and prevalence of the exposure, outcome, comorbidity, and the nature of the associations among these variables. While our primary focus was on comorbidity expressed as a binary measure (presence/absence of a co-occurring condition), additional analyses using categorical and continuous expressions of comorbidity showed that our approach extends to other variable types.

Furthermore, although our examples focused on a single comorbidity at a time, in practice, multiple comorbid conditions may be associated with the index disease. The relation of these comorbidities with the study exposure and the index disease could be different, and each should be considered according to underlying assumptions and their causal relations.

We also illustrated the effects of differential and non-differential misclassification of comorbidity in scenarios with binary exposure and comorbidity. While in our main analyses we assumed no measurement error, no selection bias, and no model misspecification, in real-life settings, and in the presence of one or more of these issues, the impact of adjusting for comorbidity on the overall bias might change.

We focus on comorbidity as a tangible, interpretable example to emphasize the importance of causal reasoning in etiologic research. However, the principles extend far beyond this context. The analytical challenges and strategies we explored reflect the well-established concepts in causal inference,^1–3,27 which provide a principled framework for evaluating covariates—whether demographic factors, co-medications, or clinical markers—and are instrumental for valid inference across a wide range of research setting.

In conclusion, this study corroborated the results from the simulations and theoretical insights, illustrating how the causal role of comorbidity influences bias under various analytical strategies. Our results emphasize the importance of explicit causal assumptions and appropriate model selection to ensure valid inferences. By examining several common causal structures between exposure, index disease and its comorbidity, this study provides practical guidance for refining study design and analytical methods. While no universal approach exists for handling comorbidity, integrating methodological rigor with clinical insight – essential to decide which of the causal structures is most applicable in the study setting – will enhance the validity and applicability of etiologic research.