Fuzzy approach to meta-analysis

نویسندگان

  • Paulo Alfonso Bracarense Costa
  • Rogério Cid Bastos
  • Abraham Kandel
چکیده

Meta-analysis is a statistical procedure to do syntheses of evidences. In the production of scientific knowledge, in spite of paradigmatic skips of quality, the rising of the accumulation of acquired knowledge (based in camed studies) is, in the general, the way as science moves forward to accomplish new discoveries and to confirm other already obtained. The methods developed for the attainment of the meta-analysis, analysis of analyses previously accomplished, have been developed during this century. More recently, starting from works of the half of the 70th, there was a great impulse in the meta-analytical methods, for have been extended to a great variety of areas of the knowledge, notably in the Education, Psychology and Medicine. Substituting the revision of narrative literature for more scientific forms of synthesis with the use of statistical instrumental of significance. There are a little number of works published in meta-analysis. The main area of application is in medical research, and with sporadic applications of intelligent techniques in that field, if any. A concise discussion was done by MANTON ET AL.(1994), and more as suggestion of possibility of the use of their GoM (Grade of Membership) technique than as a consistent development in the area. The main meta-analytic methods were presented in the Panel on Statistics Issues and Opportunities for Research in the Combination of Information supported by the National Research Council of USA directed by J.R.Gaver, whose results were published by the National Academic Press. (GAVER ET AL., 1992). One of the most important book in the field was written by HEDGES AND OLKIN (1985). This book deals with statistical methods for meta-analysis. In the last year, a link between meta-analysis and analysis of sensibility was done by PETIT (2000), but without utilization of intelligent techniques. Following the strong trend of paradigmatic change in the treatment with the ignorance and the uncertainty, the present work proposes a methodology for the metaanalysis accomplishment, incorporating to the random component of the uncertainty, another component that search uncertainties whose nature is not random. It is considered, then, the vagueness, the imprecision and the ambiguity in the statistical modeling of the meta-analysis, through the incorporation of concepts of Fuzzy Set Theory. Basically the probabilistic-fuzzy model for a random sample is the product of multinomial model with cells of probability given by For each question or measure j for the individual i yijl is the response represented by a set of Lj binary random variables. Then yijl is the empirical realizations of the random variable Yijl.The variable gik is used to represent the grade of membership to the i-th individual for the k-th extreme profile in a fuzzy pa'rtition of the sample space. See WOODBURY (1974) for more details. hkjl is the probability of a response "1" for the j-th question by the individual with the k-th extreme profile. The traditional meta-analysis, as much in its classic approach as bayesian, is carried through pooling the significance levels or of the so called "effect size", of the original studies that are considered as sample units. The effect size is a measure of difference between statistics obtained by different treatments, standardized, in general, by a joint variance. Its necessity elapses of the fact that studies with close purposes, supply different measures of effect, what would disable the construction of a common measure for the several studies. Based on the Manton model (MANTON ET AL. 1994) for diagnoses in the medical research, this work considers a probabilistic-fuzzy model, which has as independent variables the significance level, the sample size and the effect size of each study. As response the "relevance" of each study is looked for, based on those information, through the calculation of the probability of a study to be "relevant" or not. The variable relevance has a very clear meaning in clinical research, as much in the diagnosis as prognostic study. It is by nature a variable with linguistic values, which translates the human reasoning in the decision making. The deal with that variable can only be given in terms of mathematical tools that can represent it. Fuzzy Set Theory supplies those tools. The suggested model intends to calculate the probability of relevance of the studies that compose the meta-analysis. And from those values search a joint value of those probabilities, that summarizes the findings in the particular studies. The model is intermediate between the analysis of the individual of the regular medical procedure and the analysis of set of individuals of the statistical methods. It builds, finally, a bridge between the "unique" and the "typical". These fuzzy sets are define as linguistic variables. Considering the discutions around the p-value CASSELA ET AL. (1996), GIBBONS AND PRATT (1975), HUNG ET AL (1 997), and SCHERVISH (1 996) one stabilishes three sets: Highly significant, Significant and Non-significant. In the same way, based on COHEN(1988) and ALGINA(1995) one can define the fuzzy sets for effect size: Effect size large, Effect size medium and Effect size small. The two sets, Big sample size and Short sample size, was defined based on COCHRAN (1 983), GOODMAN (1 989) And OAKES(1993). These three fuzzy sets define eigtheen extreme profiles. The probability of the elements (studies in meta-analysis) in each extreme profile were given in the figure below. The elicitation and assessment of these probability are given by the method of preferences, or subjective probabilities of DEGROOT (1 970) modified. Extreme 1 Large Sample 1 Small Sample I Small ES 17 0.50 18 0.48 19 0.25 1 16 0.25 1 17 0.23 1 18 0.06 1 Profile

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تاریخ انتشار 2001