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Vol. 71, No. 1, 2011
Issue release date: April 2011
Section title: Commentary
Free Access
Hum Hered 2011;71:59–66
(DOI:10.1159/000324838)

Where’s the Evidence?

Vieland V.J.
Battelle Center for Mathematical Medicine, The Research Institute at Nationwide Children’s Hospital, Columbus, Ohio, USA
email Corresponding Author

Abstract

Science is in large part the art of careful measurement, and a fixed measurement scale is the sine qua non of this art. It is obvious to us that measurement devices lacking fixed units and constancy of scale across applications are problematic, yet we seem oddly laissez faire in our approach to measurement of one critically important quantity: statistical evidence. Here I reconsider problems with reliance on p values or maximum LOD scores as measures of evidence, from a measure-theoretic perspective. I argue that the lack of an absolute scale for evidence measurement is every bit as problematic for modern biological research as was lack of an absolute thermal scale in pre-thermodynamic physics. Indeed, the difficulty of establishing properly calibrated evidence measures is strikingly similar to the problem 19th century physicists faced in deriving an absolute scale for the measurement of temperature. I propose that the formal relationship between the two problems might enable us to apply the mathematical foundations of thermodynamics to establish an absolute scale for the measurement of evidence, in statistical applications and possibly other areas of mathematical modeling as well. Here I begin to sketch out what such an endeavor might look like.

© 2011 S. Karger AG, Basel


  

Key Words

  • Calibration
  • Evidence
  • Likelihood ratios
  • p values
  • Statistical inference
  • Thermodynamics
  • Thermometry

References

  1. Siegfried T: Odds are, it’s wrong. Sci News 2010;177:26.

    External Resources

  2. Vieland VJ: Thermometers: something for statistical geneticists to think about. Hum Hered 2006;61:144–156.
  3. Hodge SE, Vieland VJ: Expected monotonicity – a desirable property for evidence measures? Hum Hered 2010;70:151–166.
  4. Vieland VJ: The replication requirement. Nat Genet 2001;29:244–245.
  5. Gorroochurn P, Hodge SE, Heiman GA, Durner M, Greenberg DA: Non-replication of association studies: ‘pseudo-failures’ to replicate? Genet Med 2007;9:325–331.
  6. Edwards A: Likelihood. Baltimore, Johns Hopkins University Press, 1992.
  7. Royall R: Statistical Evidence: A Likelihood Paradigm. London, Chapman & Hall, 1997.
  8. Goodman SN: Toward evidence-based medical statistics. 1. The p value fallacy. Ann Intern Med 1999;130:995–1004.
  9. Goodman SN: Toward evidence-based medical statistics. 2. The Bayes factor. Ann Intern Med 1999;130:1005–1013.
  10. Lehrer J: The truth wears off. The New Yorker 2010;13:52.
  11. Ioannidis JPA: Why most published research findings are false. PLoS Med 2005;2:e124.
  12. Chang H: Inventing Temperature: Measurement and Scientific Progress. New York, Oxford University Press, 2004.
  13. Cox RT: The Algebra of Probable Inference. Baltimore, Johns Hopkins University Press, 1961.
  14. Jaynes ET: Probability Theory: The Logic of Science. New York, Cambridge University Press, 2003.
  15. Shannon CE: A Mathematical theory of communication. Bell System Tech J 1948;27:379–423, 623–656.

    External Resources

  16. Callen HB: Thermodynamics and an Introduction to Thermostatistics, ed 2. New York, Wiley, 1985.
  17. Pippard AB: The Elements of Classical Thermodynamics. London, Cambridge University Press, 1960.
  18. Fermi E: Thermodynamics. New York, Dover Publications, 1956.

  

Author Contacts

Veronica J. Vieland
Battelle Center for Mathematical Medicine
The Research Institute at Nationwide Children’s Hospital
700 Children’s Drive, Columbus, OH 43205 (USA)
Tel. +1 614 722 2688, E-Mail Veronica.Vieland@NationwideChildrens.org

  

Article Information

Received: January 6, 2011
Accepted after revision: February 2, 2011
Published online: March 22, 2011
Number of Print Pages : 8
Number of Figures : 0, Number of Tables : 0, Number of References : 18

  

Publication Details

Human Heredity (International Journal of Human and Medical Genetics)

Vol. 71, No. 1, Year 2011 (Cover Date: April 2011)

Journal Editor: Devoto M. (Philadelphia, Pa./Rome)
ISSN: 0001-5652 (Print), eISSN: 1423-0062 (Online)

For additional information: http://www.karger.com/HHE


Copyright / Drug Dosage / Disclaimer

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

Abstract

Science is in large part the art of careful measurement, and a fixed measurement scale is the sine qua non of this art. It is obvious to us that measurement devices lacking fixed units and constancy of scale across applications are problematic, yet we seem oddly laissez faire in our approach to measurement of one critically important quantity: statistical evidence. Here I reconsider problems with reliance on p values or maximum LOD scores as measures of evidence, from a measure-theoretic perspective. I argue that the lack of an absolute scale for evidence measurement is every bit as problematic for modern biological research as was lack of an absolute thermal scale in pre-thermodynamic physics. Indeed, the difficulty of establishing properly calibrated evidence measures is strikingly similar to the problem 19th century physicists faced in deriving an absolute scale for the measurement of temperature. I propose that the formal relationship between the two problems might enable us to apply the mathematical foundations of thermodynamics to establish an absolute scale for the measurement of evidence, in statistical applications and possibly other areas of mathematical modeling as well. Here I begin to sketch out what such an endeavor might look like.

© 2011 S. Karger AG, Basel


  

Author Contacts

Veronica J. Vieland
Battelle Center for Mathematical Medicine
The Research Institute at Nationwide Children’s Hospital
700 Children’s Drive, Columbus, OH 43205 (USA)
Tel. +1 614 722 2688, E-Mail Veronica.Vieland@NationwideChildrens.org

  

Article Information

Received: January 6, 2011
Accepted after revision: February 2, 2011
Published online: March 22, 2011
Number of Print Pages : 8
Number of Figures : 0, Number of Tables : 0, Number of References : 18

  

Publication Details

Human Heredity (International Journal of Human and Medical Genetics)

Vol. 71, No. 1, Year 2011 (Cover Date: April 2011)

Journal Editor: Devoto M. (Philadelphia, Pa./Rome)
ISSN: 0001-5652 (Print), eISSN: 1423-0062 (Online)

For additional information: http://www.karger.com/HHE


Article / Publication Details

First-Page Preview
Abstract of Commentary

Received: 1/6/2011
Accepted: 2/2/2011
Published online: 3/22/2011
Issue release date: April 2011

Number of Print Pages: 8
Number of Figures: 0
Number of Tables: 0

ISSN: 0001-5652 (Print)
eISSN: 1423-0062 (Online)

For additional information: http://www.karger.com/HHE


Copyright / Drug Dosage

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

References

  1. Siegfried T: Odds are, it’s wrong. Sci News 2010;177:26.

    External Resources

  2. Vieland VJ: Thermometers: something for statistical geneticists to think about. Hum Hered 2006;61:144–156.
  3. Hodge SE, Vieland VJ: Expected monotonicity – a desirable property for evidence measures? Hum Hered 2010;70:151–166.
  4. Vieland VJ: The replication requirement. Nat Genet 2001;29:244–245.
  5. Gorroochurn P, Hodge SE, Heiman GA, Durner M, Greenberg DA: Non-replication of association studies: ‘pseudo-failures’ to replicate? Genet Med 2007;9:325–331.
  6. Edwards A: Likelihood. Baltimore, Johns Hopkins University Press, 1992.
  7. Royall R: Statistical Evidence: A Likelihood Paradigm. London, Chapman & Hall, 1997.
  8. Goodman SN: Toward evidence-based medical statistics. 1. The p value fallacy. Ann Intern Med 1999;130:995–1004.
  9. Goodman SN: Toward evidence-based medical statistics. 2. The Bayes factor. Ann Intern Med 1999;130:1005–1013.
  10. Lehrer J: The truth wears off. The New Yorker 2010;13:52.
  11. Ioannidis JPA: Why most published research findings are false. PLoS Med 2005;2:e124.
  12. Chang H: Inventing Temperature: Measurement and Scientific Progress. New York, Oxford University Press, 2004.
  13. Cox RT: The Algebra of Probable Inference. Baltimore, Johns Hopkins University Press, 1961.
  14. Jaynes ET: Probability Theory: The Logic of Science. New York, Cambridge University Press, 2003.
  15. Shannon CE: A Mathematical theory of communication. Bell System Tech J 1948;27:379–423, 623–656.

    External Resources

  16. Callen HB: Thermodynamics and an Introduction to Thermostatistics, ed 2. New York, Wiley, 1985.
  17. Pippard AB: The Elements of Classical Thermodynamics. London, Cambridge University Press, 1960.
  18. Fermi E: Thermodynamics. New York, Dover Publications, 1956.