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Considerable interest has recently been focused on studying multiplephenotypes simultaneously in both epidemiological and genomic studies, eitherto capture the multidimensionality of complex disorders or to understand sharedetiology of related disorders. We seek to identify {\em multiple regulators} orpredictors that are associated with multiple outcomes when these outcomes maybe measured on very different scales or composed of a mixture of continuous,binary, and not-fully-observed elements. We first propose an estimationtechnique to put all effects on similar scales, and we induce sparsity on theestimated effects. We provide standard asymptotic results for this estimatorand show that resampling can be used to quantify uncertainty in finite samples.We finally provide a multiple testing procedure which can be gearedspecifically to the types of multiple regulators of interest, and we establishthat, under standard regularity conditions, the familywise error rate willapproach 0 as sample size diverges. Simulation results indicate that ourapproach can improve over unregularized methods both in reducing bias inestimation and improving power for testing.

Estimation and testing for multiple regulation of multivariate mixed outcomes