Causal Inference
How to check the sequential positivity assumption without propensity scores? Arthur Chatton* Arthur Chatton Robert W Platt Michael Schomaker Miguel Angel Luque-Fernandez Mireille E Schnitzer
The positivity assumption, necessary for considering an association as causal, states that each individual could be theoretically treated or untreated based on their characteristics. A positivity violation occurs when the sample contains a subgroup of individuals with almost no treatment variability. To correctly estimate the causal effect, we must identify such individuals. This identification is complicated in longitudinal settings because positivity must be checked across all time points and generally relies on a large number of propensity score models, unlikely all correctly specified. The Positivity Regression Trees (PoRT) algorithm was recently suggested to check this assumption in cross-sectional settings without requiring assumptions about the modelling nor the data-generating process. It also provides a transparent way to identify the target population. We expand this method to longitudinal settings by considering the whole treatment regimen to identify the individuals and variables yielding a lack of positivity. We demonstrate the potential of this approach by reanalyzing a recent study investigating the effect of HIV antiretroviral therapy among children in South Africa with different levels of smoothing over the treatment histories and times.