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Obtaining reliable likelihood ratio tests from simulated likelihood functions.

ABSTRACT: MIXED MODELS: Models allowing for continuous heterogeneity by assuming that value of one or more parameters follow a specified distribution have become increasingly popular. This is known as 'mixing' parameters, and it is standard practice by researchers--and the default option in many statistical programs--to base test statistics for mixed models on simulations using asymmetric draws (e.g. Halton draws). PROBLEM 1: INCONSISTENT LR TESTS DUE TO ASYMMETRIC DRAWS: This paper shows that when the estimated likelihood functions depend on standard deviations of mixed parameters this practice is very likely to cause misleading test results for the number of draws usually used today. The paper illustrates that increasing the number of draws is a very inefficient solution strategy requiring very large numbers of draws to ensure against misleading test statistics. The main conclusion of this paper is that the problem can be solved completely by using fully antithetic draws, and that using one dimensionally antithetic draws is not enough to solve the problem. PROBLEM 2: MAINTAINING THE CORRECT DIMENSIONS WHEN REDUCING THE MIXING DISTRIBUTION: A second point of the paper is that even when fully antithetic draws are used, models reducing the dimension of the mixing distribution must replicate the relevant dimensions of the quasi-random draws in the simulation of the restricted likelihood. Again this is not standard in research or statistical programs. The paper therefore recommends using fully antithetic draws replicating the relevant dimensions of the quasi-random draws in the simulation of the restricted likelihood and that this should become the default option in statistical programs. JEL classification: C15; C25.

SUBMITTER: Andersen LM

PROVIDER: S-EPMC4203670 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Obtaining reliable likelihood ratio tests from simulated likelihood functions.

Andersen Laura Mørch LM

PloS one 20141020 10

<h4>Mixed models</h4>Models allowing for continuous heterogeneity by assuming that value of one or more parameters follow a specified distribution have become increasingly popular. This is known as 'mixing' parameters, and it is standard practice by researchers--and the default option in many statistical programs--to base test statistics for mixed models on simulations using asymmetric draws (e.g. Halton draws). PROBLEM 1: INCONSISTENT LR TESTS DUE TO ASYMMETRIC DRAWS: This paper shows that when ...[more]

PMID: 25329712

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Project description:Despite the success of genome-wide association studies in medical genetics, the underlying genetics of many complex diseases remains enigmatic. One plausible reason for this could be the failure to account for the presence of genetic interactions in current analyses. Exhaustive investigations of interactions are typically infeasible because the vast number of possible interactions impose hard statistical and computational challenges. There is, therefore, a need for computationally efficient methods that build on models appropriately capturing interaction. We introduce a new methodology where we augment the interaction hypothesis with a set of simpler hypotheses that are tested, in order of their complexity, against a saturated alternative hypothesis representing interaction. This sequential testing provides an efficient way to reduce the number of non-interacting variant pairs before the final interaction test. We devise two different methods, one that relies on a priori estimated numbers of marginally associated variants to correct for multiple tests, and a second that does this adaptively. We show that our methodology in general has an improved statistical power in comparison to seven other methods, and, using the idea of closed testing, that it controls the family-wise error rate. We apply our methodology to genetic data from the PROCARDIS coronary artery disease case/control cohort and discover three distinct interactions. While analyses on simulated data suggest that the statistical power may suffice for an exhaustive search of all variant pairs in ideal cases, we explore strategies for a priori selecting subsets of variant pairs to test. Our new methodology facilitates identification of new disease-relevant interactions from existing and future genome-wide association data, which may involve genes with previously unknown association to the disease. Moreover, it enables construction of interaction networks that provide a systems biology view of complex diseases, serving as a basis for more comprehensive understanding of disease pathophysiology and its clinical consequences.

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Obtaining reliable likelihood ratio tests from simulated likelihood functions.

Publications

Obtaining reliable likelihood ratio tests from simulated likelihood functions.

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