Dataset Information

Bayesian posteriors for arbitrarily rare events.

ABSTRACT: We study how much data a Bayesian observer needs to correctly infer the relative likelihoods of two events when both events are arbitrarily rare. Each period, either a blue die or a red die is tossed. The two dice land on side [Formula: see text] with unknown probabilities [Formula: see text] and [Formula: see text], which can be arbitrarily low. Given a data-generating process where [Formula: see text], we are interested in how much data are required to guarantee that with high probability the observer's Bayesian posterior mean for [Formula: see text] exceeds [Formula: see text] times that for [Formula: see text] If the prior densities for the two dice are positive on the interior of the parameter space and behave like power functions at the boundary, then for every [Formula: see text] there exists a finite [Formula: see text] so that the observer obtains such an inference after [Formula: see text] periods with probability at least [Formula: see text] whenever [Formula: see text] The condition on [Formula: see text] and [Formula: see text] is the best possible. The result can fail if one of the prior densities converges to zero exponentially fast at the boundary.

SUBMITTER: Fudenberg D

PROVIDER: S-EPMC5441737 | biostudies-literature | 2017 May

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Bayesian posteriors for arbitrarily rare events.

Fudenberg Drew D He Kevin K Imhof Lorens A LA

Proceedings of the National Academy of Sciences of the United States of America 20170425 19

We study how much data a Bayesian observer needs to correctly infer the relative likelihoods of two events when both events are arbitrarily rare. Each period, either a blue die or a red die is tossed. The two dice land on side [Formula: see text] with unknown probabilities [Formula: see text] and [Formula: see text], which can be arbitrarily low. Given a data-generating process where [Formula: see text], we are interested in how much data are required to guarantee that with high probability the ...[more]

PMID: 28442566

Similar Datasets

Project description:Background/aimsRegulatory approval of a drug or device involves an assessment of not only the benefits but also the risks of adverse events associated with the therapeutic agent. Although randomized controlled trials (RCTs) are the gold standard for evaluating effectiveness, the number of treated patients in a single RCT may not be enough to detect a rare but serious side effect of the treatment. Meta-analysis plays an important role in the evaluation of the safety of medical products and has advantage over analyzing a single RCT when estimating the rate of adverse events.MethodsIn this article, we compare 15 widely used meta-analysis models under both Bayesian and frequentist frameworks when outcomes are extremely infrequent or rare. We present extensive simulation study results and then apply these methods to a real meta-analysis that considers RCTs investigating the effect of rosiglitazone on the risks of myocardial infarction and of death from cardiovascular causes.ResultsOur simulation studies suggest that the beta hyperprior method modeling treatment group-specific parameters and accounting for heterogeneity performs the best. Most models ignoring between-study heterogeneity give poor coverage probability when such heterogeneity exists. In the data analysis, different methods provide a wide range of log odds ratio estimates between rosiglitazone and control treatments with a mixed conclusion on their statistical significance based on 95% confidence (or credible) intervals.ConclusionIn the rare event setting, treatment effect estimates obtained from traditional meta-analytic methods may be biased and provide poor coverage probability. This trend worsens when the data have large between-study heterogeneity. In general, we recommend methods that first estimate the summaries of treatment-specific risks across studies and then relative treatment effects based on the summaries when appropriate. Furthermore, we recommend fitting various methods, comparing the results and model performance, and investigating any significant discrepancies among them.

Dataset Information

Bayesian posteriors for arbitrarily rare events.

Publications

Bayesian posteriors for arbitrarily rare events.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets