title: Bias in the estimation of false discovery rate in microarray studies.
abstract: BACKGROUND
  The false discovery rate (FDR) provides a key statistical assessment for microarray studies. Its value depends on the proportion pi(0) of non-differentially expressed (non-DE) genes. In most microarray studies, many genes have small effects not easily separable from non-DE genes. As a result, current methods often overestimate pi(0) and FDR, leading to unnecessary loss of power in the overall analysis.
  
  
  METHODS
  For the common two-sample comparison we derive a natural mixture model of the test statistic and an explicit bias formula in the standard estimation of pi(0). We suggest an improved estimation of pi(0) based on the mixture model and describe a practical likelihood-based procedure for this purpose.
  
  
  RESULTS
  The analysis shows that a large bias occurs when pi(0) is far from 1 and when the non-centrality parameters of the distribution of the test statistic are near zero. The theoretical result also explains substantial discrepancies between non-parametric and model-based estimates of pi(0). Simulation studies indicate mixture-model estimates are less biased than standard estimates. The method is applied to breast cancer and lymphoma data examples.
  
  
  BACKGROUND
  An R-package OCplus containing functions to compute pi(0) based on the mixture model, the resulting FDR and other operating characteristics of microarray data, is freely available at http://www.meb.ki.se/~yudpaw
  
  
  BACKGROUND
  yudi.pawitan@meb.ki.se and alexander.ploner@meb.ki.se.
authors.affiliation: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden. yudi.pawitan@meb.ki.se
authors.forename: Yudi
authors.initials: Y
authors.lastname: Pawitan
authors.forename: Karuturi R Krishna
authors.initials: KR
authors.lastname: Murthy
authors.forename: Stefan
authors.initials: S
authors.lastname: Michiels
authors.forename: Alexander
authors.initials: A
authors.lastname: Ploner
mesh_terms: D003198:Computer Simulation; D005189:False Positive Reactions; D020869:Gene Expression Profiling / Q000379:methods*; D005786:Gene Expression Regulation / Q000235:genetics*; D008957:Models, Genetic; D015233:Models, Statistical; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D015203:Reproducibility of Results; D015983:Selection Bias; D012680:Sensitivity and Specificity