Causal inference methods for treatment effect estimation usually assume independent experimental units. However, this assumption is often questionable because experimental units may interact. We develop augmented inverse probability weighting (AIPW) for estimation and inference of causal treatment effects on dependent observational data. Our framework covers very general cases of spillover effects induced by units interacting in networks. We use plugin machine learning to estimate infinite-dimensional nuisance components leading to a consistent treatment effect estimator that converges at the parametric rate and asymptotically follows a Gaussian distribution.

Metastatic non-small cell lung cancer (NSCLC) patients treated with immune checkpoint inhibitors (ICIs) may suffer from heavy side effects and not all patients benefit from the treatment. We conducted a comprehensive statistical analysis to identify promising (bio-)markers for treatment response. We analyzed retrospective data from NSCLC patients treated with ICIs in first- or further-line therapy settings at the University Hospital Zurich. We investigated 16 possible prognostic markers with respect to overall survival, tumor size reduction, and the development of an immune-related adverse event (irAE) and assessed the robustness of our results. For the further-line patient group, the most significant result was that increased basophil counts were associated with increased odds of tumor size reduction within three months and with the development of an irAE. For the first-line patient group, the most significant results were that increased lymphocyte counts, the histology of adenocarcinoma, and the intake of non-steroidal anti-rheumatic drugs (NSAR) were associated with decreased hazards of dying. Our study yielded new hypotheses for predictive (bio-)markers for response to ICIs in NSCLC patients. The possibly beneficial role of high basophil counts is a particularly interesting finding. Our results should be tested on independent data in a prospective fashion.

We develop a fully non-parametric, fast, easy-to-use, and powerful test for the missing completely at random (MCAR) assumption on the missingness mechanism of a data set. The test compares distributions of different missing patterns on random projections in the variable space of the data. The distributional differences are measured with the Kullback-Leibler Divergence, using probability Random Forests (Malley et al., 2011). We thus refer to it as "Projected Kullback-Leibler MCAR" (PKLM) test. The use of random projections makes it applicable even if very little or no fully observed observations are available or if the number of dimensions is large. An efficient permutation approach guarantees the level for any finite sample size, resolving a major shortcoming of most other available tests. Moreover, the test can be used on both discrete and continuous data. We show empirically on a range of simulated data distributions and real data sets that our test has consistently high power and is able to avoid inflated type I errors. Finally, we provide an R-package PKLMtest with an implementation of our test. * Authors with equal contribution. † We are grateful to Jun Li for providing us with parts of their code.

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