In cases in which the outcome variable is binary (e.g., success/no success) or a count variable (e.g, number of depressive symptoms), the effect of a treatment or intervention is often expressed as ratio (e.g., risk ratio, odds ratio). While it is relatively straightforward to estimate some kind of ratio effect based on a logistic regression or Poisson regression, it is a non-trivial question whether ratio effect measures should be considered and if yes, how they can be interpreted and which assumptions need to be fulfilled in order for them to have a causal interpretation. For example, it is somewhat counter-intuitive in the context of ratio effects that an effect measure based on group averages does not necessarily resemble an average over individual effect measures, not even in randomized controlled trials. This phenomenon is known as (non-)collapsibility and has received quite a lot of attention in the biostatistics and epidemiology literature. In this talk, we use the stochastic theory of causal effects for defining different types of ratio effects and for clarifying the necessary assumptions for their identification. We briefly introduce the core aspects of the stochastic theory of causal effects before showing how to define ratio effects either as individual ratio effects or as average ratio effects. The different types of effects require different causality assumptions and have a different meaning, which only becomes clear when building on theories of causal effects.

Randomized controlled trials (RCTs) are the gold standard for estimating causal treatment effects. In the context of binary outcomes, difference- and ratio-based specifications of an average treatment effect (ATE) can be estimated from logistic regression models. Using the Delta method, symmetric confidence intervals for a given ATE specification can be constructed. However, since treatment effects build on individual outcome probabilities, the range of ATE estimates is naturally restricted. Symmetric intervals can therefore exceed the admissible range of values when effect sizes or estimation uncertainty are large. Moreover, especially with highly nonlinear ratio effects, symmetric confidence intervals may represent uncertainty on either side of the point estimate very differently than asymmetric intervals would. In this work, we examine two ways of obtaining asymmetric confidence intervals which adapt to valid boundaries and which may better accommodate effect nonlinearities. For logistic regression models incorporating fixed covariates, a transformation approach is employed that maps effect estimates to a space where symmetric intervals are admissible and then transforms interval boundaries back. For models with stochastic covariates, a bootstrap approach is used that estimates asymmetric quantiles of the ATE distribution by resampling. We present a simulation study that compares inference using symmetric and asymmetric confidence intervals for ATEs under difference- and ratio-based effect specifications and different levels of effect size and heterogeneity. Preliminary results indicate that, while symmetric intervals perform well overall, asymmetric intervals not only adhere to the admissible range of estimates but can also help improve inference with large and highly heterogenous ratio-based effects.

Although the typically reported average treatment effect may be positive suggesting that the treatment is effective, at the level of individual participants the treatment effect may be zero or even negative-- the treatment may even harm some individuals. For making decisions on whether a specific person should take the treatment, information on the probability of benefitting or being harmed by the treatment for a single person is necessary. In this talk, we introduce Pearl’s (2009) concept of causal attribution for personalized treatment selection. While precise statements about the causal effect of a treatment for an individual are only possible to a limited extent, bounds may be estimated in which the probability of benefit or harm lay. These bounds can be calculated using data at the group level, which can come from randomized-controlled trials (RCTs), observational studies (OBS), or both. The bounds may be narrowed by incorporating effect moderators. In a simulated toy example, we illustrate the properties of the approach. In an empirical example we show how the combination of RCT and OBS data as well as the inclusion of covariates helps to narrow down the interval of the individual treatment effect.

One reason for non-replicability of study results is that study characteristics, such as population, setting, or outcome measure, vary across primary and replication study. So far, effect heterogeneity across studies has only been described, but there has been hardly any effort to explaining it, in the sense of identifying causal moderators. This may be due to the fact that in current replication studies many study characteristics vary at once, making it extremely difficult to infer causes for non-replicability. Causal inference is even more challenged by the fact that these characteristics not only vary between studies, but also within studies and that they are related to each other.

In this work, we show how causal decomposition may be used for identifying sources of effect heterogeneity across replication studies. Instead of investigating the causal effect of certain study characteristics on the treatment effect, causal decomposition decomposes initial effect heterogeneity between studies in effect heterogeneity reduction due to intervening on a target variable and remaining effect heterogeneity. Making use of Directed Acyclic Graphs, we consider different possible scenarios, in which the target variable is either a baseline covariate or a mediator of the impact of the study-variable on the individual treatment effect. We delineate under which assumptions reduction and remaining effect heterogeneity can be identified. The approach is illustrated on an example from investigating the imagined intergroup contact effect in social psychology.

Causal graphs provide a rigorous framework for encoding assumptions about causal relationships, yet their integration with multilevel models remains limited. Despite their popularity in the applied sciences existing path diagram conventions of multilevel models do not adhere to formal graph-theoretic principles. We review common path diagram conventions in multilevel modeling and demonstrate—using a bivariate regression example—that they primarily serve as statistical model visualizations rather than causal graphs. We formalize multilevel models as parametric Structural Causal Models with equations linear in the parameters and Gaussian error terms, and introduce a principled approach for translating them into Acyclic Directed Mixed Graphs. This translation captures both the structural equations and the dependence among latent exogenous components implied by varying parameters, aligning multilevel models with contemporary graph-based causal inference methods. We illustrate this framework using a well-known empirical example—the High School and Beyond study—and extend it to dynamic models with varying parameters. Our conference contribution provides a systematic bridge between parametric multilevel models and modern causal graph theory, clarifying key assumptions, enabling graphical identification, and supporting transparent causal interpretation in multilevel data structures.