Sample size and loss of subjects in an experiment

[Gerónimo Maldonado]

Hi Experts:

From theory I know that any sample size calculation is based on the total number of subjects who are needed in a particular study. In practice, eligible subjects will not always be willing to take part on the study and it will be necessary to approach more subjects than are needed in the first instance. My question is: How can I account for those subjects who refuse to participate? Is there any method or equation to account for something that is called "loss factor"?.  In example... A sample size calculation told me that I need 400 subjects (200 men / 200 female) to reject the null hypothesis of certain experiment... but I want to adjust that sample size in case I loss some of the subjects of any stratum. How can I do that?... A thought...

Thanks in advance!

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[Art Kendall]

Sample size estimates tell you the _achieved_ sample size you need.

How to guess the refusal rate has depends on the discipline's experience in similar studies, how you recruit subjects, whether you run subjects one at a time or as a single group,etc., etc.

You need to make an educated guess on the refusal proportion.
to get a good guess of how many to try to recruit divide the desired sample size by (1-refusal proportion).

I presume your study is focused on comparing men and women, they may not refuse at the same rate.

In calculating sample size I strongly recommend leaving alpha and beta at conventional levels, and let the effect size that would make a practice/policy/theoretical difference be the major determinant.


On 12/7/2011 1:00 PM, Gerónimo Maldonado wrote:

Hi Experts:

From theory I know that any sample size calculation is based on the total number of subjects who are needed in a particular study. In practice, eligible subjects will not always be willing to take part on the study and it will be necessary to approach more subjects than are needed in the first instance. My question is: How can I account for those subjects who refuse to participate? Is there any method or equation to account for something that is called "loss factor"?.  In example... A sample size calculation told me that I need 400 subjects (200 men / 200 female) to reject the null hypothesis of certain experiment... but I want to adjust that sample size in case I loss some of the subjects of any stratum. How can I do that?... A thought...

Thanks in advance!

--

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[Rich Ulrich]

DESIGN QUESTION.  NOT an SPSS question.

I read your problem a little differently than Art does, maybe because of
different research backgrounds.

In the clinical studies in psychiatry, the number of subjects *approached*
(as compared to the number recruited) is irrelevant to the formal power.
You have to estimate both, in order to show that you have enough subjects
available in the designated time frame.  Also, excessive refusals may raise
doubts about practicality or how well you can generalize at the end.  But
the number approached is not relevant to the power calculation.  That power
calculation tells you how many must be randomized to the treatments.

The "loss factor" of real concern starts after randomization.  How many
subjects drop out?  How many drop out, say, "before any effective treatment"?
How do you account for these subjects?  But that does not *directly*  affect
computed power, either...  what it does, is, it screws up the expected Effect Size.

 - The Sound Research Rule is, "Randomize, then Analyze."   In other words,
those "lost" people must remain in the analysis - you have to treat them as
some sort of non-success, for your primary tests of outcome.... unless you have
some *very*  good argument otherwise.  Possibly valid:  Parents of minor (patient)
move out of treatment region.  Horrible mistake:  Patient dies, wrongly presumed
to be unrelated to treatment.
 
So, when you are figuring your "possible outcomes", you have to
incorporate your "loss factor"  as weighing against the desired outcomes.
- In your sample size calculation, it told you that you need 400 subjects
to "reject the null, assuming and effect size of [such and so] while testing
with [a certain test] using [a certain alpha level]."    The *most* conservative
way to incorporate a "loss factor"  is to assume that all the untreated+lost
would have been successes, and all the treated+lost  would have been
failures.  That certainly changes the appearance of the effect size if there
are many losses to speak of, since 10% loss in each group gives you a
20% bias *against*  your proposed treatment...  if you know nothing more
than "lost to treatment".

 - And that is why it is very important to document *exactly* how and
why subjects were lost -- If there is any chance at all to weigh these in
as less-than-complete-failures, you certainly want to. 

--
Rich Ulrich

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Date: Wed, 7 Dec 2011 14:00:48 -0400
From: [hidden email]
Subject: Sample size and loss of subjects in an experiment
To: [hidden email]

Hi Experts:

From theory I know that any sample size calculation is based on the total number of subjects who are needed in a particular study. In practice, eligible subjects will not always be willing to take part on the study and it will be necessary to approach more subjects than are needed in the first instance. My question is: How can I account for those subjects who refuse to participate? Is there any method or equation to account for something that is called "loss factor"?.  In example... A sample size calculation told me that I need 400 subjects (200 men / 200 female) to reject the null hypothesis of certain experiment... but I want to adjust that sample size in case I loss some of the subjects of any stratum. How can I do that?... A thought...

Thanks in advance!

--