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In the first stage of a two-stage study, the researcher uses a statistical model to impute the unobserved exposures. In the second stage, imputed exposures serve as covariates in epidemiological models. Imputation error in the first stage operate as measurement errors in the second stage, and thus bias exposure effect estimates. This study aims to improve the estimation of exposure effects by sharing information between the first and second stage. At the heart of our estimator is the observation that not all second-stage observations are equally important to impute. We thus borrow ideas from the optimal-experimental-design theory, to identify individuals of higher importance. We then improve the imputation of these individuals using ideas from the machine-learning literature of domain-adaptation. Our simulations confirm that the exposure effect estimates are more accurate than the current best practice. An empirical demonstration yields smaller estimates of PM effect on hyperglycemia risk, with tighter confidence bands. Sharing information between environmental scientist and epidemiologist improves health effect estimates. Our estimator is a principled approach for harnessing this information exchange, and may be applied to any two stage study.

The estimated accuracy of a classifier is a random quantity with variability. A common practice in supervised machine learning, is thus to test if the estimated accuracy is significantly better than chance level. This method of signal detection is particularly popular in neuroimaging and genetics. We provide evidence that using a classifier's accuracy as a test statistic can be an underpowered strategy for finding differences between populations, compared to a bona-fide statistical test. It is also computationally more demanding than a statistical test. Via simulation, we compare test statistics that are based on classification accuracy, to others based on multivariate test statistics. We find that probability of detecting differences between two distributions is lower for accuracy based statistics. We examine several candidate causes for the low power of accuracy tests. These causes include: the discrete nature of the accuracy test statistic, the type of signal accuracy tests are designed to detect, their inefficient use of the data, and their regularization. When the purposes of the analysis is not signal detection, but rather, the evaluation of a particular classifier, we suggest several improvements to increase power. In particular, to replace V-fold cross validation with the Leave-One-Out Bootstrap.

Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in order to be significant, an activation has to be larger than the inter-subject variability. Indeed, detected regions are smaller when using random effect analysis versus fixed effects. The statistical assumptions behind the classic random effects model are that the effect in each location is normally distributed over subjects, and "activation" refers to a non-null mean effect. We argue this model is unrealistic compared to the true population variability, where, due to functional plasticity and registration anomalies, at each brain location some of the subjects are active and some are not. We propose a finite-Gaussian--mixture--random-effect. A model that amortizes between-subject spatial disagreement and quantifies it using the "prevalence" of activation at each location. This measure has several desirable properties: (a) It is more informative than the typical active/inactive paradigm. (b) In contrast to the hypothesis testing approach (thus t-maps) which are trivially rejected for large sample sizes, the larger the sample size, the more informative the prevalence statistic becomes. In this work we present a formal definition and an estimation procedure of this prevalence. The end result of the proposed analysis is a map of the prevalence at locations with significant activation, highlighting activations regions that are common over many brains.