Date:         Sat, 7 May 2005 20:33:14 +0200
Reply-To:     David.Carr@gmx.de
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David Carr <David.Carr@GMX.DE>
Subject:      Re: Appropriate statistical analysis on percentage chang
Content-type: text/plain; charset=US-ASCII

Madan.Kundu@RANBAXY.COM wrote:
>Can you tell me what will be the appropriate statistical analysis on
>percentage change data?
>
>Let me explain....
>
>Consider a clinical trial. Here we have baseline values and also
> final values on the variable X. so our dataset will contain three >
variable:
>
>1. Patient ID
>
>2. Baseline value
>
>3. Final value
>
>Now we can compute two new variables as:
>
>1. Change = Final value - Baseline value
>
>2. Percentage change = (Final value -Baseline value)*100/Base line

> value
>
> Now my query is what will be the appropriate statistical analyses
> on this percentage change data?

Dear Madan,

The are two further literature sources that I could highly recommend
for your query on percentage change:

1. Peter L. Bonate (2000)
"Analysis of Pretest-Posttest Designs".
Boca Ration: Chapman & Hall/CRC.

Bonate covers several different relative change scores of which
percentage change is one. In his summary of relative change
functions, he mentions the following:

a. Relative change scores are commonly found in the literature, both
as descriptive statistics and is use in hypothesis testing.

b. Relative change functions convert prestest and postest scores into
a single summary measure which can be used with any of the
statistical tests for difference scores.

c. All the problems seen with difference scores are seen with
realtive change scores. In addition
  i. The average percent of average population change score is a
biased estimator of the population change.
  ii. The degree of bias is dependent on many variables including the
correlation between pretest and poststest scorews and the initial
pretest score. It should be pointed out, however, that if the average
prestest score is large, the degree of bias may be small.

d. Converpretest and posttest scores into a relative change score may
result in a highly skewed or asymmetrical distribution which violates
the assumptions of most parametric statistical tests.

e. Change scores are still subject to the influence of regression
towards the mean.

f. It is the opinion of the author that percent change scores should
be avoided. If their use cannot be avoided, check to make sure the
scores do not violate the assumptions of the statistical test being
used.

g. Use of log-ratio scores appear to be a viable alternative to
traditional change scores because they are not as asymmetrical as
percent change scores.

h. The distribution of percent change scores tends to be not normally
distributed with increasing departure form normality as the sample
size increases and with decreasing departure from normality as the
test-rtetest correlation increases. Both log-ratio scores and
modified perecent change scores may have better symmetry properties
than percent change scores and they tend to be normally distributed
more often than percent change scores.

2. Donald A. Berry (1990)
Basic principles in designing and analysing clinical studies.
In "Statistical Methodology in the Pharmaceutical Sciences", Ed.
Donal A. Berry, New York: Marcell Dekker, Inc. pp.1-55.

Berry mentions
"For the purpose of data analysis, I prefer replacing perecent change
with "symmetrized percent change"..."

Symmetrized percent change (SPC) is defined as follows
(Y-X)*100/(Y+X),
where Y=post-test, and X=pre-test.

Berry mentions further:
"This number is no further from 0 than is percent change, and it is
typically closer. SPC is bouded between -100 and +100. So the effect
of subjects with small baselines is lessened......

A disadvantage of symmetrized percent change is that researchers and
consumers are conditioned to thinking about percent change. To
overcome this, one can analyze the data in the transformed scale SPC
and then report averages in the PC scale. This gives a"robust percent
suppression":
RPC = (200 * SPC) / (100 - SPC).

I want to stress that while analysis in the SPC scale is better than
in the PC (perecent change) scale, absolute change from baseline or
other transformations may be preferred to both. One way to decide is
to plot the data (or the residuals in ANOVA) and choose the
transformation for which the data are most nearly normal. (see Berry,
1987, Logarithmic transformation in ANOVA, Biometrics, 43, 439-456)."

Yours,

David Carr
X-act Cologne Clinical Research GmbH