Dataset Information

Bayesian LASSO, scale space and decision making in association genetics.

ABSTRACT:

Background

LASSO is a penalized regression method that facilitates model fitting in situations where there are as many, or even more explanatory variables than observations, and only a few variables are relevant in explaining the data. We focus on the Bayesian version of LASSO and consider four problems that need special attention: (i) controlling false positives, (ii) multiple comparisons, (iii) collinearity among explanatory variables, and (iv) the choice of the tuning parameter that controls the amount of shrinkage and the sparsity of the estimates. The particular application considered is association genetics, where LASSO regression can be used to find links between chromosome locations and phenotypic traits in a biological organism. However, the proposed techniques are relevant also in other contexts where LASSO is used for variable selection.

Results

We separate the true associations from false positives using the posterior distribution of the effects (regression coefficients) provided by Bayesian LASSO. We propose to solve the multiple comparisons problem by using simultaneous inference based on the joint posterior distribution of the effects. Bayesian LASSO also tends to distribute an effect among collinear variables, making detection of an association difficult. We propose to solve this problem by considering not only individual effects but also their functionals (i.e. sums and differences). Finally, whereas in Bayesian LASSO the tuning parameter is often regarded as a random variable, we adopt a scale space view and consider a whole range of fixed tuning parameters, instead. The effect estimates and the associated inference are considered for all tuning parameters in the selected range and the results are visualized with color maps that provide useful insights into data and the association problem considered. The methods are illustrated using two sets of artificial data and one real data set, all representing typical settings in association genetics.

SUBMITTER: Pasanen L

PROVIDER: S-EPMC4391919 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundStatistical inference based on small datasets, commonly found in precision oncology, is subject to low power and high uncertainty. In these settings, drawing strong conclusions about future research utility is difficult when using standard inferential measures. It is therefore important to better quantify the uncertainty associated with both significant and non-significant results based on small sample sizes.MethodsWe developed a new method, Bayesian Additional Evidence (BAE), that determines (1) how much additional supportive evidence is needed for a non-significant result to reach Bayesian posterior credibility, or (2) how much additional opposing evidence is needed to render a significant result non-credible. Although based in Bayesian analysis, a prior distribution is not needed; instead, the tipping point output is compared to reasonable effect ranges to draw conclusions. We demonstrate our approach in a comparative effectiveness analysis comparing two treatments in a real world biomarker-defined cohort, and provide guidelines for how to apply BAE in practice.ResultsOur initial comparative effectiveness analysis results in a hazard ratio of 0.31 with 95% confidence interval (0.09, 1.1). Applying BAE to this result yields a tipping point of 0.54; thus, an observed hazard ratio of 0.54 or smaller in a replication study would result in posterior credibility for the treatment association. Given that effect sizes in this range are not extreme, and that supportive evidence exists from a similar published study, we conclude that this problem is worthy of further research.ConclusionsOur proposed method provides a useful framework for interpreting analytic results from small datasets. This can assist researchers in deciding how to interpret and continue their investigations based on an initial analysis that has high uncertainty. Although we illustrated its use in estimating parameters based on time-to-event outcomes, BAE easily applies to any normally-distributed estimator, such as those used for analyzing binary or continuous outcomes.

Dataset Information

Bayesian LASSO, scale space and decision making in association genetics.

Background

Results

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