Analysis of change in liver histology

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Munyaradzi Dimairo

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Jul 14, 2011, 9:18:39 AM7/14/11
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Hi Stats Masters, ha!

i'm currently designing a pilot trial to test an intervention in
hypogonadal men with non-alcoholic steatohepatitis (NASH). the primary
outcome is the change in histological grade of liver steatosis at 12
months. this is measured on a histology index score of 0 to 4 which
translate to a change score of -4 to 4 (9 point scale). negative
change is related to positive outcomes and vice versa.

here is my question;

what is the most efficient statistical method to analyse this outcome
which is on a 9 point scale (-4 to 4) ?.
of course minimising baseline imbalances in critical here. patients in
lower liver grades can only experience restrictive negative change;
e.g grade one patients can only experience a change of -1. similarly,
grade 4 can only experience negative change or stay the same.

the analysis method will definitely affect the sample size calculation
(in future definitive trial) and information required for this pilot
proposal

your help will be greatly appreciated forks.


with thanks in advance

Munya

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Thompson,Paul

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Jul 14, 2011, 12:45:16 PM7/14/11
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This is a very difficult question to answer, since an "index" ordinal score such as the one you discuss is based on other measures. In some cases, the other measures are very impervious to change, in other cases they are volatile. What are the UNDERLYING actual measurements that the index is summarizing?
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Frank Harrell

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Jul 14, 2011, 4:06:22 PM7/14/11
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The difference between two ordinal variables is no longer ordinal.
There is every reason to consider the final measurement as the
dependent variable, and to covariate adjust for the initial one
(nonlinearly). I'd recommend a proportional odds model.

Frank

On Jul 14, 11:45 am, "Thompson,Paul" <Paul.Thomp...@SanfordHealth.org>
wrote:

Munyaradzi Dimairo

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Jul 15, 2011, 10:36:34 AM7/15/11
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thanks Paul;

from the best of my medical knowledge,histological grade of liver
steatosis is assessed through liver biopsy. i don't have a lot medical
details on how they interpret the biopsy and classify into 5
categories (0=absence of fibrosis, stage 1=perisinusoidal or
portal, stage 2=perisinusoidal and portal/periportal, stage 3=septal
or bridging fibrosis, and stage 4=cirrhosis.) i'll try to dig out more
on the classification process.

with many thanks

Munya

Munyaradzi Dimairo

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Jul 15, 2011, 10:53:00 AM7/15/11
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Hi Frank;

my initial though was re-classification of the difference into
(deteriotating(>=1 change), no change, moderate improvement (-1),
marked improvement(>=-2)). it seems it's unlikely to expect a change
of at least -3 points within a year. of course a deterioration of at
least 2 points could be expected. i could even combine the last two
categories depending on the proportion expected to have at least 2
point improvement. i'm aware about issues of losing information by
categorisation but i thought this is a scenario where you're stuck
between the walls. in essence, i won't be losing a lot of information
if a positive change of at least 3 points is "unlikely".

i would then use ordinal regression (proportional odds or something else).

is this attractive?


with thanks

Munya

MartinHolt

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Jul 15, 2011, 12:07:02 PM7/15/11
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Hi Munya,

I've found that a very good reference for the use of scales is "Health
Measurement Scales, A Practical Guide To Their Development and Use" by
Streiner D.L. and Norman G.R.. Chapter 11 (18pp) is "Measuring Change"
which starts with, "The measurement of change has been a topic of
considerable confusion in the medical literature." echoing Paul
Thompson's initial reply. (This text was printed in 1999.) So I
hesitate to say more, and note that you said, " patients in lower
liver grades can only experience restrictive negative change; e.g
grade one patients can only experience a change of -1. similarly,
grade 4 can only experience negative change or stay the same." I think
this complicates things.

In case you cannot find the text, the following paragraph (p172) I
think addresses this concern:
"The solution to this problem for assessing individual change
recommended by Cronbach and Furby (1970) is the use of residualized
gain scores. Instead of subtracting pre-test from post-test, we first
fit the line relating the pre-test and post-test scores using
regression analysis. We then estimate the post-test score of each
patient from the regression equation. The residualized gain score is
the difference between between the actual post-test score and the
score which was predicted from the the regression equation. In other
words, the residualized gain score removes from consideration that
portion of the gain score which was linearly predicted from the pre-
test score. What remains is an indication of those individuals who
changed more or less than was expected."

HTH,

Martin Holt
Medical Statistician

On Jul 15, 3:53 pm, Munyaradzi Dimairo <mdima...@gmail.com> wrote:
> Hi Frank;
>
> my initial though was re-classification of the difference into
> (deteriotating(>=1 change), no change, moderate improvement (-1),
> marked improvement(>=-2)). it seems it's unlikely to expect a change
> of at least -3 points within a year. of course a deterioration of at
> least 2 points could be expected. i could even combine the last two
> categories depending on the proportion expected to have at least 2
> point improvement.  i'm aware about issues of losing information by
> categorisation but i thought this is a scenario where you're stuck
> between the walls. in essence, i won't be losing a lot of information
> if a positive change of at least 3 points is "unlikely".
>
> i would then use ordinal regression (proportional odds or something else).
>
> is this attractive?
>
> with thanks
>
> Munya
>
> --- Hide quoted text -
>
> - Show quoted text -

MartinHolt

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Jul 15, 2011, 12:19:45 PM7/15/11
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The Cronbach and Furby 1970 paper referred to in my posting just now
is,
"Cronbach, L.J. and Furby, L.(1970). How should we measure 'change'-
or should we? Psychological Bulletin, 74, 68-80."
I couldn't find a free full-text link but maybe someone will......

Martin
> > - Show quoted text -- Hide quoted text -

Frank Harrell

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Jul 15, 2011, 2:09:33 PM7/15/11
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No, I think that approach is very problematic. You have the
"difference in two ordinals is not ordinal" problem, floor effects,
ceiling effects, and covered-up heterogeneity which reduces power. My
earlier suggestion solves all these problem, I believe.
Frank

On Jul 15, 9:53 am, Munyaradzi Dimairo <mdima...@gmail.com> wrote:
> Hi Frank;
>
> my initial though was re-classification of the difference into
> (deteriotating(>=1 change), no change, moderate improvement (-1),
> marked improvement(>=-2)). it seems it's unlikely to expect a change
> of at least -3 points within a year. of course a deterioration of at
> least 2 points could be expected. i could even combine the last two
> categories depending on the proportion expected to have at least 2
> point improvement.  i'm aware about issues of losing information by
> categorisation but i thought this is a scenario where you're stuck
> between the walls. in essence, i won't be losing a lot of information
> if a positive change of at least 3 points is "unlikely".
>
> i would then use ordinal regression (proportional odds or something else).
>
> is this attractive?
>
> with thanks
>
> Munya
>

John Sorkin

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Jul 15, 2011, 2:28:36 PM7/15/11
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Prof Harrell
What did you mean by . . . and to covariate adjust for the initial one (nonlinearly). In particular, in this context what did you mean by nonlinearly?
John

>>> Frank Harrell <f.ha...@vanderbilt.edu> 7/15/2011 2:09:33 PM >>>

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mdim...@gmail.com

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Jul 15, 2011, 2:33:27 PM7/15/11
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I agree on the ceiling and floor effect as I said on earlier email. For instance, those in grade 1 could only experience an improvement of 1 unit. Yes, there reduction in power is an issue but if I power the study assuming that scenario it won't a problem except an increase in sample size. What a trade off.

I also agree that your suggestion was great! It's only that I'm concerned with the proportions in the extreme categories. That is below -2 and above 2. If these proportions are unlikely as it seems, then a reduction in power will be great under the proportional odds model of all the difference. I might be wrong here.

Many thanks Frank for the great idea!

Regards

Munya


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mdim...@gmail.com

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Jul 15, 2011, 2:40:33 PM7/15/11
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Thanks Martin, I will look at the paper closely. Yes, it complicates things about the ceiling and floor effects.

Your suggestion is an interesting idea that I've never thought off. I will dig in on this idea.

Many thanks Martin!

Munya
Sent using BlackBerry® from Orange

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Sender: meds...@googlegroups.com
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Thompson,Paul

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Jul 15, 2011, 2:58:11 PM7/15/11
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About cirhossis: is that an absorbing state (once you are cirrhotic, can you ever go back from that state)?

Frank Harrell

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Jul 15, 2011, 5:53:02 PM7/15/11
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What I was referring to is that when using the proportional odds model
one sometimes needs the baseline version of the follow-up response to
be modeled without assuming a linear effect on the log odds. The
baseline scale could be modeled as a quadratic, or using dummy
variables, for example.

Frank

On Jul 15, 1:28 pm, "John Sorkin" <jsor...@grecc.umaryland.edu> wrote:
> Prof Harrell
> What did you mean by . . . and to covariate adjust for the initial one (nonlinearly). In particular, in this context what  did you mean by nonlinearly?
> John
>
> >>> Frank Harrell <f.harr...@vanderbilt.edu> 7/15/2011 2:09:33 PM >>>

Frank Harrell

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Jul 15, 2011, 5:55:26 PM7/15/11
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Increasing the sample size so that you can use a less efficient
analysis is probably an ethics issue, i.e., in general it may require
more subjects to be studied to obtain the same level of evidence as
that provided by a more efficient method.

The proportional odds model is not adversely affected by having cells
containing only one subject. You can even use the PO model to
efficiently analyze continuous Y when there are no ties.

Frank

MartinHolt

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Jul 17, 2011, 8:43:58 AM7/17/11
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Just to clarify, I wasn't suggesting not to follow your approach,
Frank. Where I said "using regression analysis" I wondered if that
could be the proportional odds method you'd recommended. Sorry if I
confused things,

Martin

Frank Harrell

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Jul 17, 2011, 2:07:43 PM7/17/11
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No problem. Yes I think I was referring to the proportional odds
model. Other choices include GAMs, and if lucky regarding
transformation of Y, ordinary regression.

Frank

Bruce Weaver

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Jul 18, 2011, 9:35:27 AM7/18/11
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On Friday, 15 July 2011 17:55:26 UTC-4, Frank Harrell wrote:

--- snip ---
 
The proportional odds model is not adversely affected by having cells
containing only one subject.  You can even use the PO model to
efficiently analyze continuous Y when there are no ties.

Frank


Frank, do you say that in your book somewhere, or in an article?  I can well imagine being asked for a reference if/when I tell that to my boss, or someone I'm advising.

Thanks,
Bruce

-- 
Bruce Weaver
bwe...@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/Home
"When all else fails, RTFM."

Frank Harrell

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Jul 18, 2011, 11:07:14 AM7/18/11
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Probably in the reference below. A few example fits (quartiles ->
deciles -> 100-tiles -> no binning) will demonstrate this.
Frank

@ARTICLE{pet90par,
author = {Peterson, Bercedis and Harrell, Frank E.},
year = 1990,
title = {Partial proportional odds models for ordinal response
variables},
journal = Applied Statistics,
volume = 39,
pages = {205-217}
}


On Jul 18, 8:35 am, Bruce Weaver <bwea...@lakeheadu.ca> wrote:
> On Friday, 15 July 2011 17:55:26 UTC-4, Frank Harrell wrote:
>
> > --- snip ---
>
> > The proportional odds model is not adversely affected by having cells
> > containing only one subject.  You can even use the PO model to
> > efficiently analyze continuous Y when there are no ties.
>
> > Frank
>
> Frank, do you say that in your book somewhere, or in an article?  I can well
> imagine being asked for a reference if/when I tell that to my boss, or
> someone I'm advising.
>
> Thanks,
> Bruce
>
> --
> Bruce Weaver
> bwea...@lakeheadu.cahttp://sites.google.com/a/lakeheadu.ca/bweaver/Home

Bruce Weaver

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Jul 18, 2011, 11:29:19 AM7/18/11
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Thanks Frank.  Here's the link for those who have JSTOR access:

   http://www.jstor.org/stable/2347760

Bruce
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