Small-sample estimation of negative binomial dispersion, with applications to SAGE data

Biostatistics. 2008 Apr;9(2):321-32. doi: 10.1093/biostatistics/kxm030. Epub 2007 Aug 29.


We derive a quantile-adjusted conditional maximum likelihood estimator for the dispersion parameter of the negative binomial distribution and compare its performance, in terms of bias, to various other methods. Our estimation scheme outperforms all other methods in very small samples, typical of those from serial analysis of gene expression studies, the motivating data for this study. The impact of dispersion estimation on hypothesis testing is studied. We derive an "exact" test that outperforms the standard approximate asymptotic tests.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Bias
  • Binomial Distribution*
  • Biometry / methods
  • Expressed Sequence Tags
  • Gene Expression Profiling / methods*
  • Gene Expression Profiling / statistics & numerical data
  • Gene Library
  • Humans
  • Information Storage and Retrieval / methods
  • Information Storage and Retrieval / statistics & numerical data
  • Likelihood Functions
  • RNA, Messenger / analysis*
  • Regression Analysis
  • Research Design / statistics & numerical data
  • Sample Size
  • Stochastic Processes
  • Weights and Measures*


  • RNA, Messenger