The test-negative design (TND) is a resource-efficient observational study design that can assess vaccine effectiveness and exposure-proximal immune correlates of disease. The TND enrolls symptomatic individuals seeking diagnostic testing and compares case status by an exposure variable, such as vaccination status or immune marker level, that is measured at testing. While the TND reduces confounding by healthcare-seeking behavior, other sources of confounding may remain. TND studies may also have missing data in the exposure variable due to incomplete records or two-phase sampling designs. We present a targeted maximum likelihood estimation approach involving a semiparametric logistic regression model that targets a causal conditional risk ratio of symptomatic disease in the healthcare-seeking population. Under causal and missing at random assumptions, our method produces an efficient, asymptotically linear estimator that provides flexible, data-driven confounding control and valid causal inference when analyzing TND studies with missing exposure variable data. We evaluate our method's finite sample properties using plasmode simulations of a two-phase TND immune correlates study. We also apply our method to assess COVID-19 vaccine effectiveness and antibody marker correlates of COVID-19 from TND study cohorts derived from the Moderna Coronavirus Efficacy phase 3 trial.

Neural Information Processing Systems http://nips.cc/

We proceed to compute the variances of each estimator. The proof also holds for the non-zero mean case trivially. Causal model details for Section 5.2 In Section 5.2, We include a wide range of machine learning-based causal inference methods to evaluate the performance of causal error estimators. Others configs are kept as default. The others are kept as default.

Neural Information Processing Systems http://nips.cc/

The results of our survey are shown in Table 10.

In practice, building f and g requires the computation for wtiwtj for all i,j. B.2 Classification For the classification task with the logistic regression model, we modify the formula of logistic regression in teaching objectives to make it convenient for derivation. It also indicates that with probability at least p1, the LST teacher can achieve exponential teachability in the iteration t. In order to achieve exponential teachiability in T iterations, the sufficient condition in Eq. (22) must be satisfied in all T iterations. Then, we use a pre-trained DenseNet [65] shown in [53] to generate 1024 dim features and the confidencescoreforeachimage.