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Estimation of the number of studies with positive trends when studies with negative trends are present
Author(s) -
Crump Kenny S.,
Krewski Daniel
Publication year - 1998
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315723
Subject(s) - estimator , statistics , mathematics , inflection point , point estimation , consistent estimator , econometrics , function (biology) , empirical distribution function , biology , minimum variance unbiased estimator , geometry , evolutionary biology
A two‐point estimator is proposed for the proportion of studies with positive trends among a collection of studies, some of which may demonstrate negative trends. The proposed estimator is the y‐intercept of the secant line joining the points ( a, F̌(a) ) and ( b, F̌(b) ), where F̌(p) is the empirical distribution function of p ‐values from one‐tailed tests for positive trend derived from the individual studies. Although this estimator is negatively biased for any choice of the points 0 ≤ a < b ≤ 1, the bias is less than that of the previously proposed one‐point estimator defined by setting b = 1. The bias of the two‐point estimator is smallest when a and b approach the inflection point of the true distribution function, E [ F̌ ( p )]. The utility of the two‐point estimator is demonstrated by using it to estimate the number of male‐mouse liver carcinogens among carcinogenicity studies conducted by the National Toxicology Program.