A Treatment-Anchored Proxy Diagnostic for Hidden Confounding

Can indirect measurements of hidden factors help detect confounding between a treatment and an outcome? AO-CES measures how much these proxies change the predicted treatment. It then tests whether that change predicts the outcome after accounting for treatment and recorded covariates. We characterize misleading proxy mixtures in linear Gaussian models and correct the leading estimation bias under explicit learning conditions. In a controlled Gaussian study with 3,200 observations, correction reduces false positives from 90% to 5.5% while retaining 100% detection. Across 21 benchmark conditions, full-proxy prediction is competitive with five feature-learning variants, including variational autoencoders. As an application after Fast Causal Inference, AO-CES detects 93-100% of confounded pairs in structured graphs. These results show how proxy measurements can strengthen the assessment of hidden-confounding risks and guide closer causal scrutiny of observational findings.