[BioC] ttest or fold change

Stephen P. Baker stephen.baker at umassmed.edu
Tue Dec 16 12:21:14 MET 2003

RE: [BioC] ttest or fold changeOf course investigators don't want false negatives as well as false positives but you can promise neither no false positives nor false negatives except for the trivial case when one either classifies 100% as positive or negative.  The best you can do is to quantify the probabilities, then trade off one for the other, i.e. decreasing the probability of one type of error increases the probability of the other. However, as there is an arbitrary but real defacto standard for type I error of  5% which limits how much the tradeoff can be manipulated.  New approaches such as mixture models offer some promise of improvement and use of the False Discovery Rate can make a very big difference in the number of regulated genes detected. I think this is underutilized.

Fortunately the REAL answer is under the control of the investigator with the help of the statistician.  That is the process of power analysis, i.e. the statistician can help the investigator calculate the number of microarrays that are needed to provide a desired probability of detecting a specified size effect (in fold changes).  There is no effect that is too subtle to detect with enough data.

Of course, there is no such thing as a free lunch and microarrays are still expensive (but getting cheaper),  but then again if one thinks of the cost of any other technology, microarrays are incredibly inexpensive considering the amount of data they produce.  Imagine the cost in materials and labor to do PCR on 10,000 or 20,000 genes!  

The studies we are seeing are getting larger and larger.  Funding agencies are funding well prepared proposals for large studies with many microarrays (i.e. enough to detect meaningful effects) based on small studies of a few microarrays.  These small studies are then pilot studies and pilot studies do not need to be "definitive" to be useful.  They just may not be publishable on their own.  

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Stephen P. Baker, MScPH , PhD(ABD)                      (508) 856-2625
Senior Biostatistician                                                     (775) 254-4885 fax
Academic Computing Services
Lecturer in Biostatistics , Graduate School of Biomedical Sciences
University of Massachusetts Medical School
55 Lake Avenue North                          stephen.baker at umassmed.edu
Worcester, MA 01655  USA

  ----- Original Message ----- 
  From: michael watson (IAH-C) 
  To: Baker, Stephen ; bioconductor at stat.math.ethz.ch 
  Sent: Tuesday, December 16, 2003 4:46 AM
  Subject: RE: [BioC] ttest or fold change

  >This seems small but with a microarray with thousands of genes, this 
  >easily produces a bunch of false positives. I looked at 10 chips from a 
  A truly excellent reply, and one which I will no doubt refer to frequently; I am still 
  very much a novice statistician.  However, and please correct me if I am wrong, but 
  I presume that some scientists are equally afraid of false negatives as false positives? 
  i.e. that if we are so conservative such that we try to ENSURE that there are NO 
  false positives, we may throw away genes as not differentially expressed when in 
  reality they are?  It will be interesting to have a discussion on this - is it possible, 
  using statistics, to guarentee both no false positives and no false negatives?  If not, 
  then surely the investigator must decide which is relevant to the study in question before 
  going on to decide which stats to use. 

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