R help - Nov 2008 - Growth rate determination using ANCOVA

I'm a programmer in a biology lab who is starting to use R to automate
some of our statistical analysis of growth rate determination. But I'm
running into some problems as I re-code.

1) Hypotheses concerning Slope similarity/difference:
   I'm using R's anova(lm()) methods to analyse a model which looks
like this:
              growth.metric ~ time * test.tube
   I understand that testing the the interaction between time and tube
(time:test.tube) will tell us if the growth rates (for the last three
test tubes) are significantly different from one another (Ho=slopes
are the same).  The purpose of doing this test is so that we can be
certain our cultures have fully acclimated to the treatment and aren't
going to change much if we stop measuring. This is an important cost
saving practice too as measurements can go on for years.   Yet I'm
worried that our null and alternative hypotheses should be swapped so
that our test is more conservative (Ho=slopes are different ... ie
still acclimating.)

Is there a way to specify my model that flips these hypotheses?
Should I be using a different method?  Is this even appropriate?


2) Growth Rate is confounded with Variance of Growth Rate
   I'm also worried about the fact that rates for cultures with faster
growth are calculated using fewer data points (assuming similar
sampling times between treatments) .  The result is that growth ~ var
(growth).   Not only does this put a wrinkle in my analysis between
treatments, but it also biases the growth acclimation determining
ANCOVA test above.  Faster growing cultures will usually pass the "no
significant difference between slopes test" more easily because there
are fewer points from which to be certain about rejecting Ho.

Is there a way to control for this?
Perhaps I could include the number of points in my model?


3) Statistical validity of using subsets of growth.metric measurements
within a test tube
   There are some lab members who insist that we can throw out the
beginning and end of our log transformed growth.metric measurements
because they are outliers in determining maximum growth.    I've
proposed looping through all possible combinations of 3 or more points
within the growth curve and using the highest or best fitting (best R-
squared) slope.  But this idea has been rejected by our PI as not be a
valid thing to do.

Ideas here?

Thank you.

Dave

dschruth <dschruth <at> gmail.com> writes:

...I am 
>>worried that our null and alternative hypotheses should be swapped so
> that our test is more conservative (Ho=slopes are different ... ie
> still acclimating.)
> 
> Is there a way to specify my model that flips these hypotheses?
No, that not possible because of the "what means different" question.
0.1 ?
0.01? 10?. In medical research, you have to ask the researchers "what is a 
medically relevant improvement? An increase in survival time by 1 month?",
and then formulate "the difference is larger than 1 month with p=0.9".
When you ask the researchers to supply the clinically relevant threshold 
value, most chicken out, and I remember quite a few fights because the 
ethics  committee want it.


Dieter

Hi David,

On Fri, Nov 21, 2008 at 12:01:52PM -0800, dschruth
wrote:
> I'm a programmer in a biology lab who is starting to use R to automate
> some of our statistical analysis of growth rate determination. But I'm
> running into some problems as I re-code.
> 
> 1) Hypotheses concerning Slope similarity/difference:
>    I'm using R's anova(lm()) methods to analyse a model which looks
> like this:
>               growth.metric ~ time * test.tube
>    I understand that testing the the interaction between time and tube
> (time:test.tube) will tell us if the growth rates (for the last three
> test tubes) are significantly different from one another (Ho=slopes
> are the same).  The purpose of doing this test is so that we can be
> certain our cultures have fully acclimated to the treatment and aren't
> going to change much if we stop measuring. This is an important cost
> saving practice too as measurements can go on for years.   Yet I'm
> worried that our null and alternative hypotheses should be swapped so
> that our test is more conservative (Ho=slopes are different ... ie
> still acclimating.)
Good thinking.
> Is there a way to specify my model that flips these hypotheses?
> Should I be using a different method?  Is this even appropriate?
You could think about equivalence tests.  See e.g. references in the
equivalence package. 
 
> 2) Growth Rate is confounded with Variance of Growth Rate
>    I'm also worried about the fact that rates for cultures with faster
> growth are calculated using fewer data points (assuming similar
> sampling times between treatments) .  The result is that growth ~ var
> (growth).   Not only does this put a wrinkle in my analysis between
> treatments, but it also biases the growth acclimation determining
> ANCOVA test above.  Faster growing cultures will usually pass the "no
> significant difference between slopes test" more easily because there
> are fewer points from which to be certain about rejecting Ho.
> 
> Is there a way to control for this?
> Perhaps I could include the number of points in my model?
Depending on the model that you apply, you might be able to explicitly
model the variance to allow for this possibility.  I would guess that
it's not necessarily only the fewer data points contributing to the
greater variation.  Faster-growing cultures might also be inherently
more variable.
 
> 3) Statistical validity of using subsets of growth.metric measurements
> within a test tube
>    There are some lab members who insist that we can throw out the
> beginning and end of our log transformed growth.metric measurements
> because they are outliers in determining maximum growth.    I've
> proposed looping through all possible combinations of 3 or more points
> within the growth curve and using the highest or best fitting (best R-
> squared) slope.  But this idea has been rejected by our PI as not be a
> valid thing to do.
> 
> Ideas here?
I'm feeling very cautious about giving advice on this question as I
don't know enough about the area.  Sorry.

I hope that this helps, otherwise.

Andrew
-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/