The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Bayesian Method to Semiparametric Hierarchical Selection Models

준모수적 계층적 선택모형에 대한 베이지안 방법

  • 정윤식 (부산대학교 자연과학대학 통계학과) ;
  • 장정훈 (부산대학교 자연과학대학 통계학과)
  • Published : 2001.03.01
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Abstract

Meta-analysis refers to quantitative methods for combining results from independent studies in order to draw overall conclusions. Hierarchical models including selection models are introduced and shown to be useful in such Bayesian meta-analysis. Semiparametric hierarchical models are proposed using the Dirichlet process prior. These rich class of models combine the information of independent studies, allowing investigation of variability both between and within studies, and weight function. Here we investigate sensitivity of results to unobserved studies by considering a hierachical selection model with including unknown weight function and use Markov chain Monte Carlo methods to develop inference for the parameters of interest. Using Bayesian method, this model is used on a meta-analysis of twelve studies comparing the effectiveness of two different types of flouride, in preventing cavities. Clinical informative prior is assumed. Summaries and plots of model parameters are analyzed to address questions of interest.

메타분석(Meta-analysis)은 서로 독립적으로 연구되어진 결과들을 전체적인 하나의 결과로 도출하기 위해 사용되어지는 통계적 방법이다. 이러한 통계적 방법을 설명할 모형으로는 선택모형(selection model)을 포함한 계층적 모형(hierarchical model)을 사용하며, 이러한 모형들은 베이지안 메타분석에 유용한 것으로 알려져 있다. 그러나, 메타분석의 자료들은 일반적으로 출판편의(publication bias)를 갖고 있으므로 이를 극복하고자 가중함수(weight function)를 이용하여 분포함수를 새롭게 정의하여 사용한다. 최근에 Silliman(1997)은 계층적 모형(hierarchical model)에 가중함수를 첨부한 계층적 선택모형(hierarchical selection model)을 정의하고 모수적 베이지안 방법을 제시하였다. 본 연구에서는 미관측된 연구효과에 디리슈레 과정 사전분포(Dirichlet process prior)를 적용한 준모수적 계층적 선택모형(semiparametric hierarchical selection models)을 소개한다. 여기서 제시된 준모수적 계층적 선택모형을 베이지안 방법으로 추정하기 위하여 마코프 연쇄 몬테칼로(Markov chain Monte Carlo)방법을 이용한다. 제시된 방법을 적용하기 위하여 실제 자료(Johnson, 1993)인 충치를 예방하기 위한 두 가지의 예방약의 효과에 대한 차이를 비교하기 위해 얻어진 12개의 연구를 이용하여 메타분석을 한다.

Keywords

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