Significance tests with Restricted Randomization Design
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Experimental subjects are assigned to one of two treatments sequentially by restricted randomization assignment rules. Significance tests generated from these rules are discussed. Under rather mild conditions on the test scores the asymptotic null permutational distribution of tests based on the urn design (Wei, 1977, 1978a) is shown to be normal.
Mendelian randomization (MR) infers causal effects of exposures on outcomes using genetic variants as instrumental variables, but existing methods remain vulnerable to bias and loss of power when instruments are invalid. We hypothesize that closely related outcome traits share a large overlap in their valid instruments for a given exposure, so that borrowing instruments across such traits can yield more robust MR inference. To operationalize this, we introduce a novel…
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We develop a semiparametric continuous time inferential framework for testing cumulative treatment effects, including both immediate and carryover effects. The latent state process is modeled by an ordinary differential equation (ODE) whose drift depends on state and treatment, while the observed data are noisy measurements of this latent state at irregular, multi resolution time points. We define the average treatment effect (ATE) as the difference of expected cumulative…