Inferring Effect Ordering Without Causal Effect Estimation

Predictive models that estimate outcome probabilities are widely used to guide interventions in applications such as advertising, customer retention, and behavioral nudging. Although these outcome probabilities do not measure causal effects, they are often treated as proxies for identifying individuals with the highest intervention impact. We investigate when and why these predictions (which we refer to as scores) can reliably rank individuals by their causal effects in settings where direct effect estimation is infeasible. The key mechanism underlying this approach is that scores serve as proxies for a latent moderator that drives variation in causal effects. Building on this foundation, we introduce three key conditions -- full latent moderation, full latent mediation, and latent monotonicity -- that determine when scores can recover causal-effect rankings and, in some cases, even outperform direct effect estimation. To support practical applications, we provide guidelines for assessing when scores are viable proxies, particularly in contexts lacking data on new interventions or with delayed outcome measurements. Our findings demonstrate that effect heterogeneity can be leveraged through predictive modeling when the target variable being modeled captures a strong latent moderator, expanding the scope of causal inference beyond traditional effect estimation and, in some cases, reducing the need for large-scale randomized experiments.