Beyond age as a confounder

Beyond age as a confounder Chronological age, biological age, and causality Laurent Gautier∗ September 2025 Abstract In data analysis, age is usually considered a potential confounder and the reflex is to control for it, for example as a covariate in a regression model or as a stratifying factor. Health research focusing on longevity investigates how a healthy state can be maintained or extended as we age. It makes a distinction between chronological age, measuring rotations of the Earth around itself and around the Sun, and biological age, a loosely defined concept with different manifestations – the ability to divide and repair tissues, the production of proteins supporting tissue structure, the ability to eliminate toxins, mitochondrial health, or mutation load. A tenet for healthy aging research is that biological age can be influenced unlike chronological age. For data analysis, statistics, or causal interpretation of machine learning models, this means that the default recommendation to control for age as a potential confounder may no longer apply when biological age is involved. Biological age can also be a mediator, or a collider. When the latter, the variable must not be controlled in the analysis. Time may change me, but I can’t trace time David Bowie, Changes Introduction This article focuses on causal approaches to data analysis when a variable representing a “biological age” is considered. While machine learning is good at finding associations in the data most often by using the most data available, the underlying intent of many data and statistical analysis efforts is to assess or model the causal effect of an exposure on an outcome. In that scenario, the challenge lies in how additional variables besides exposure and outcome are handled in an analysis, as their treatment may greatly affect the quality of that estimate. In some cases, mishandling these variables can create “data mirages” ∗Article published on Substack at https://onlyquestions.substack.com/p/beyond-age-as-aconfounder 1 and lead to misleading conclusions. For example, sign reversal observed in Simpson’s paradox may originate from mediators and colliders, two causal structures described below, incorrectly included in a model. The incorporation of subject matter expertise early in the process, and the help of causal reasoning, can help avoid pitfalls. When looking at patient data, “age” can be one such additional variable and it might be among the most frequently adjusted variables in observational studies. For example, the article “Why and how to control for age in occupational epidemiology”[1], explains that age is viewed as a potential confounder in most studies, and should therefore be controlled. For example, by including it as a covariate in a regression model, or stratifying the analysis (i.e., splitting the data into age groups). However, age can represent two phenomena: • Chronological age is a measure of planetary-scale observations, such as the number of the Earth’s rotations around the sun or on its own axis. • Biological age, that is a measure of biological senescence. This is a loosely defined concept and there are likely different measures for it. For example, the ability to divide and repair tissues, the production of proteins supporting tissue structure, the ability to eliminate toxins, mitochondrial health, or mutation load. Chronological age is considered to be immune to any external influence, which makes the default to control for it a sensible one. On the other hand, biological age does not have that property — Research on longevity and aging actually tries to find ways to influence the biological age. However, the chronological age observed can be causally connected to exposure and outcome studied, creating a selection bias called a colliders bias. The causal decomposition into a Directed Acyclic Graph (DAG) will indicate where caution should be exercised and how chronological and biological age should be used in an analysis. The strength of the relationship between chronological and biological age can be especially important when considering an analytical approach. Exposure, outcome, and age Question: exposure → outcome? A frequent question of interest is: does an exposure, e.g., a specific treatment, diet, or environment factors, causes, or rather contributes to, an outcome of interest? If that is the case, what are the direction and strength of that effect. In health studies, this can be “does treatment X help cure disease Y”, or “does lifestyle X increase the risk of developing health issue Y”. Causal graphs are Directed Acyclic Graphs (DAGs), where the arrow means “causes”, “contributes to”, or “influences”. What we are looking for is to define quantitatively the arrow between exposure and outcome in Figure 1. A path to answer the question with data requires information about each individuals’ exposure and outcome. How to obtain that data, either selecting it from a larger dataset or running a study to acquire it, is out-of-scope for this post but it is ultimately connected to some of the points below about performing an analysis of the data. The data is expected to contain the information 2 Figure 1: Minimimal DAG with Exposure and Outcome. that can answer the question, and possibly indicate the presence of additional associations that are helpful to include in the analysis. In the context of people or patients, age is a frequently collected additional “third variable”. Age decomposition Before proceeding, it is worth asking ourselves what we mean by “age” or intend to measure with it. For example, longevity research is an exciting broad area in health research that invited thinking about healthy aging in contrast to mere age. This brings us to the generic notion of “biological age” as some biological measure of senescence. The biological age does not necessarily have an absolute unit of measure, and could be a fraction of expected lifespan at birth, or some measure of accumulated damage, physiological age, cellular age, or molecular age. There are even arguments for thinking about different biological ages that could be, for example organ specific[2]. Our understanding of biological age gravitates around nine tentative hallmarks of aging[3] (genomic instability, telomere attrition, epigenetic alterations, loss of proteostasis, deregulated nutrient sensing, mitochondrial dysfunction, cellular senescence, stem cell exhaustion, and altered intercellular communication) but the science to fully validate and understand the underlying biology for all of them is needed[4]. For simplicity this article considers one general notion of biological age for simplicity, and in some examples one of the biomarkers for it (DNA methylation). The age recorded in census data, population studies, health registries, administrative health claims, or electronic health records is the “calendar age”, or chronological age. The unit for that number can be expressed in number of rotations the Earth performed around the sun, the number of days and nights, or depending on the latitude the number of season cycles experienced. Figure 2: Minimal DAG with Chronological and Biological Age. Calendar age and biological age have an unequivocal causal dependency: the calendar age will influence the biological age. The reverse is not possible, as it 3 would otherwise imply that biological interventions could have an influence on planetary mechanics or the possibility of time travel. More generally, no causal arrow can point toward chronological age (Figure 2). On the other hand, biological age, or rather markers for it, could be affected by other variables. In causal DAG representations, arrows could point toward them. Other age-related variables such as “age at diagnosis”, “age at initiation of treatment”, or “age at enrollment” could also be pointed to in a causal DAG but, although they further highlight the importance being very specific about what “age” means, this short article will not discuss them. With that distinction between chronological age and biological age in mind, we are ready to review three major causal patterns where age can be a “third variable”, and how to handle it in an analysis. Age as a third variable The last thirty years have witnessed significant progress in the definition of causal effects, and their estimation. Statisticians, econometricians, and epidemiologists have embraced these developments, but the application of causal inference is still working its way through some fields, scientific communities, or curricula about data analysis. Additional possible variables will exist in most situations, although not necessarily measured or available in the dataset, and sometimes the information they contain expose bias in the data. When such variables are present, a priori causal structures derived from subject matter expertise will guide whether they should be incorporated into the analysis to obtain the desired effect estimate and avoid incorrect conclusions. We consider three causal patterns involving an additional variable: the confounder, the mediator, and the collider[5]. Distinguishing chronological age from biological age can help reveal which one is present. The Confounder A confounder is a variable that causally affects the outcome and is also associated with the exposure although not necessarily causal - for example, not randomly distributed between treatment and control groups. The graph for a classic confounder is shown in Figure 3. Figure 3: Minimal graph representation showing a confounder pattern. A DAG would have an arrow from Confounder to Exposure. Studies about the effect of drinking coffee on health can provide examples 4 of confounders[6]. For example, a simple observation of coffee consumption and lung cancer could conclude that it is a risk factor. However, smoking is a confounder as smokers tend to consume more coffee. The negative effect of coffee on lungs disappears as soon as the smoking status is accounted for. Whenever a confounder is present, it MUST be controlled[7]. Example of age as a confounder Age is viewed as a potential confounder by default and should therefore be controlled. If we keep coffee drinking as the exposure of interest, an observational studies investigating the effect of coffee on cause-specific mortality may consider that coffee drinking patterns change with age and the risk of diseases is affected by “age”. This makes “age” a confounder, and controlling for it is then needed. We have not considered the decomposition of age mentioned previously, and if we do the DAG could look like in Figure 4. Figure 4: Age decomposition and confounder. Chronological age has an influence on coffee drinking, while biological age has an effect on the prevalence of diseases, therefore disease-specific mortality. In this case the graph does not radically change how one should handle “age” in an analysis. Chronological age can be used as a confounder, and a measure of biological age could optionally be treated as a modifier and included in the analysis to reduce the variance of the effect estimate. The Mediator A mediator “mediates” the effect by being on a causal path between exposure and outcome. It can be on the unique causal path between exposure and outcome (full mediation), or be in addition to a direct effect of exposure on the outcome. Figure 5 shows a DAG for a mediator when a direct effect of the exposure on outcome: The graph for the pattern is similar to the confounder pattern, with the arrow between exposure and the additional variable, now a mediator, in the other direction. 5 Figure 5: Minimal DAG showing a mediator pattern. Whether to control for a mediator variable depends on the specific question to be answered. If the total effect of exposure on the outcome is the objective, it should not be controlled. However, if the objective to distinguish between direct and mediated effect of exposure, then one should control for the mediator. Example of age as a mediator When we start considering “age” as composite of calendar and biological age, causal effects into “age” become possible. For example, let’s assume that we want to investigate the effect of alcohol consumption (exposure) as risk factor for developing cognitive diseases (outcome). The general notion of age is reported to influence or be influenced by the following variables: exposure → age: alcohol has a reported effect on markers of cellular aging (DNA methylation[8]) age → exposure: drinking patterns are also reported to evolve with age, and the exact pattern is cohort-specific[9] age → outcome: Cellular aging is reported to have effect on cognition[10] If keeping a general notion of “age”, the graph would get a bidirectional arrow (Figure 6). This is similar to one of the confounder patterns shown earlier, but raises the question of directionality if chronological age is somehow implied. Figure 6: Bi-directional causal arrow between Age and Exposure. Decomposing “age” into chronological age and biological age as we have shown resolves the causal issue (nothing can affect chronological age), and we obtain the updated graph in Figure 7. 6 Figure 7: Decomposition of Age into Chronological Age and Biological resolves the bi-directionality in Figure 6. The general rule would be that if the total effect of exposure on the outcome is wanted, chronological age is a confounder and should therefore be controlled. If a more granular understanding of the causal pathway is needed, for example, to develop a diagnosis test that would utilize DNA methylation-based aging, then a more sophisticated analysis is required to determine direct and indirect effects and quantify the contribution of biological age to the outcome. However, the strength of the coupling between chronological age and biological age, that is how strongly they are correlated, will matter. If the correlation is high, and the confounder (chronological age) is truly a confounder with significant coupling with exposure and outcome, controlling for the counfounder will amount to partially control for the mediator as well, and this affect the quality of our effect estimate. In that case, a clean estimate of the total effect can be difficult to achieve with simple covariate adjustment techniques. More sophisticated methods such as mediation analysis are then necessary. The Collider A collider is close to the causal opposite of a confounder. It is a variable that is affected by both exposure and outcome. This last pattern might be the least intuitive of the three patterns we consider for this article. The DAG looks is shown in Figure 8. In contrast to a confounder, controlling for a collider introduces bias and can distort the measured association between the exposure and outcome. Berkson’s paradox[11] can be a manifestation of this, and this pattern is considered a form of selection bias. The historical example looked at risk factors for diseases among in-patient hospitalized populations: both risk factors increased the odds of being hospitalized (the collider), leading to a spurious negative association between them. Whenever a collider is present, it must NOT be controlled. 7 Figure 8: Minimal DAG with a collider pattern. Chronological and biological ages as confounder and collider Unlike Chronological Age, Biological Age might be influenceable. If it is affected by both the exposure and the outcome it then becomes a collider. We can think of a putative example using again alcohol consumption as the exposure, and DNA Methylation as a measure of Biological Age. Our question is the effect of Alcohol Consumption on Inflammation[12]. We already have the effect of alcohol on DNA methylation, to which we add that Inflammation causes DNA damage and affect methylation[13]. To complete the example, we can add that chronological age has a direct effect, or rather an effect not mediated by DNA Methylation, on inflammation[14]. Figure 9: Age decomposition separates counfounder and collider patterns. The decomposition is shown in Figure 9: we are now in a situation with a confounder that must be controlled and a collider that must not be controlled. Here again, the strength of the correlation between confounder and collider will influence how complex the situation is, and what can be a path forward: • If confounder and collider are not very correlated, information “leakage” about the collider will be limited and the confounder should be simply controlled for. • If the correlation is too high or the leakage unacceptable, look for an another variable than the confounder that is not tangled with the collider 8 • If confounder and collider are highly correlated, bias and variance can distord the estimate. Simple covariate adjustment is then not sufficient and more advanced causal modeling is required. For example, structural equation modeling. Detailing these techniques is well beyond the scope of this article. Otherwise, just as much as the strength of the association between Chronological Age and Biological Age matters, the “strength of the confounder” can influence what is a good course of action. As that strength diminishes the importance of the collider in the system increases. Biological age as a collider We can also find a possible example where Biological Age could be a collider and Chronological Age no longer a confounder, using air pollution for the exposure and asthma for the outcome. The graph is slightly more complex, with the causal effect of Air Pollution on Asthma likely mediated by Inflammation when fine particles and ozone are involved, and Inflammation will affect DNA Methylation. When DNA-binding chemical pollutants such as the ones found in vehicle exhaust are involved, they will have an effect on DNA Methylation patterns. The DAG for this is shown in Figure 10. Figure 10: Example of of Biological Age as a collider. Under the causal assumptions represented by the graphical model above, Chronological Age does not affect exposure or outcome. It is no longer a confounder, and controlling for it can be done but it is an unnecessary step, possibly adding a burden for data collection or missing values handling. However, if Asthma has an effect on DNA Methylation that is not mediated by Inflammation then Biological Age should not be added as a simple covariate or stratification factor when looking at the association between Air Pollution and Asthma. In that case, Biological Age becomes a collider and it must not be controlled. 9