Andrea Rotnitzky

We consider inference about a finite-dimensional parameter integrating samples from independent sources. A recently developed theory considers scenarios where sources align with subsets of the conditional distributions of a single factorization of the joint target distribution. While this theory applies in many settings, it falls short in important data fusion problems, such as two-sample instrumental variable analysis, settings that integrate data from epidemiological studies with diverse designs, and studies with mismeasured variables supplemented by external validation studies. In this paper we derive a comprehensive theory that, in particular, covers these settings by allowing the integration of sources aligned with conditional distributions that do not correspond to a single factorization of the target distribution. We provide a universal characterization of the influence functions of regular and asymptotically linear estimators and the efficient influence function of a target parameter, irrespective of the parameter of interest or the statistical model for the target distribution, thus paving the way for a unified theory for machine-learning debiased, semiparametric efficient estimation.

Background: For infectious diseases, characterizing symptom duration is of clinical and public health importance. Symptom duration may be assessed by surveying infected individuals and querying symptom status at the time of survey response. For example, in a severe acute respiratory syndrome coronavirus 2 testing program at the University of Washington, participants were surveyed at least 28 days after testing positive and asked to report current symptom status. This study design yielded current status data: outcome measurements for each respondent consisted only of the time of survey response and a binary indicator of whether symptoms had resolved by that time. Such study design benefits from limited risk of recall bias, but analyzing the resulting data necessitates tailored statistical tools. Methods: We review methods for current status data and describe a novel application of modern nonparametric techniques to this setting. The proposed approach is valid under weaker assumptions compared with existing methods, allows the use of flexible machine learning tools, and handles potential survey nonresponse. Our method relies on the assumption that the survey response time is conditionally independent of symptom resolution time within strata of measured covariates, and we propose an approach to assess the sensitivity of results to deviations from conditional independence. Results: From the university study, we estimate that 19% of participants experienced ongoing symptoms 30 days after testing positive, decreasing to 7% at 90 days. We found the estimates to be more sensitive to violations of the conditional independence assumption at 30 days compared with 90 days. Female sex, fatigue during acute infection, and higher viral load were associated with slower symptom resolution. Conclusion: The proposed method and accompanying sensitivity analysis procedure provide tools for investigators faced with current status data.

We propose estimators of the mean of a K‐sample U‐statistic when data on the outcomes of interest are missing in some sampled units and auxiliary variables are available in the entire sample. The proposed estimators exploit the information available in the auxiliaries without requiring assumptions about the joint distribution of the auxiliaries and outcomes. The properties of the proposed estimators are derived as a consequence of general results on efficient semiparametric estimation of the mean of a K‐sample U‐statistic with missing at random outcomes, observed auxiliary variables and known missingness probabilities. We illustrate the methods with the estimation of the area under a receiver operating characteristic curve when the biomarker data are observed only in subsamples of the diseased and healthy subjects.

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