abstract: Understanding how adherence affects outcomes is crucial when developing and assigning interventions. However, interventions are often evaluated by conducting randomized experiments and estimating intent-to-treat effects, which ignore actual treatment received. Dose-response effects can supplement intent-to-treat effects when participants are offered the full dose but many only receive a partial dose due to nonadherence. Using these data, we can estimate the magnitude of the treatment effect at different levels of adherence, which serve as a proxy for different levels of treatment. In this dissertation, I conducted Monte Carlo simulations to evaluate when linear dose-response effects can be accurately and precisely estimated in randomized experiments comparing a no-treatment control condition to a treatment condition with partial adherence. Specifically, I evaluated the performance of confounder adjustment and instrumental variable methods when their assumptions were met (Study 1) and when their assumptions were violated (Study 2). In Study 1, the confounder adjustment and instrumental variable methods provided unbiased estimates of the dose-response effect across sample sizes (200, 500, 2,000) and adherence distributions (uniform, right skewed, left skewed). The adherence distribution affected power for the instrumental variable method. In Study 2, the confounder adjustment method provided unbiased or minimally biased estimates of the dose-response effect under no or weak (but not moderate or strong) unobserved confounding. The instrumental variable method provided extremely biased estimates of the dose-response effect under violations of the exclusion restriction (no direct effect of treatment assignment on the outcome), though less severe violations of the exclusion restriction should be investigated. / Dissertation/Thesis / Doctoral Dissertation Psychology 2018

This thesis studies inference to the complier treatment effect denoted LATE. The standard approach is to base the inference on the two-stage least squares (2SLS) estimator and asymptotic Neyman inference, i.e., the t-test. The paper suggests a Fisher Randomization Test based on the t-test statistic as an alternative to the Neyman inference. Based on the setup with a randomized experiment with noncompliance, for which one can identify the LATE, I compare the two approaches in a Monte Carlo (MC) simulations. The results from the MC simulation is that the Fisher randomization test is not a valid alternative to the Neyman’s test as it has too low power.

This thesis develops a general strategy for factorial linear model analysis for experimental and observational studies. It satisfactorily deals with a number of issues that have previously caused problems in such analyses. The strategy developed here is an iterative, four-stage, model comparison procedure as described in Brien (1989); it is a generalization of the approach of Nelder (1965a,b). The approach is applicable to studies characterized as being structure-balanced, multitiered and based on Tjur structures unless the structure involves variation factors when it must be a regular Tjur structure. It covers a wide range of experiments including multiple-error, change-over, two-phase, superimposed and unbalanced experiments. Examples illustrating this are presented. Inference from the approach is based on linear expectation and variation models and employs an analysis of variance. The sources included in the analysis of variance table is based on the division of the factors, on the basis of the randomization employed in the study, into sets called tiers. The factors are also subdivided into expectation factors and variation factors. From this subdivision models appropriate to the study can be formulated and the expected mean squares based on these models obtained. The terms in the expectation model may be nonorthogonal and the terms in the variation model may exhibit a certain kind of nonorthogonal variation structure. Rules are derived for obtaining the sums of squares, degrees of freedom and expected mean squares for the class of studies covered. The models used in the approach make it clear that the expected mean squares depend on the subdivision into expectation and variation factors. The approach clarifes the appropriate mean square comparisons for model selection. The analysis of variance table produced with the approach has the advantage that it will reflect all the relevant physical features of the study. A consequence of this is that studies, in which the randomization is such that their confounding patterns differ, will have different analysis of variance tables. / Thesis (Ph.D.)--Department of Plant Science, 1992.