- On 11 Aug 2000 at 14:28:04, "Jack Jenkins" (jack.jenkins.at.Covance.Com) sent the message

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We have a 3-period, 3-sequence cross over design in which we would like

to analyze for food effects. The study design:

Sequence 1: A B C

Sequence 2: B C A

Sequence 3: C A B

where: A is fasted

B is low-fat meal

C is high-fat meal

7 people are assigned to each sequence. For period 1, 12 people (4 per

sequence) will be dosed on day W and 9 people (3 per sequence) will be

dosed on day X. All 21 people will be dosed for period 2 on day Y and

all 21 people will be dosed for period 3 on day Z.

Normally we would use the following model in which period has 3

levels:

y = sequence + subject(sequence) + period + treatment

For the above study, we are considering using the same model in which

period has 4 levels. Do you think this will work or do you have any

other suggestions?

Thank you for your time.

Jack Jenkins - On 12 Aug 2000 at 17:33:02, ml11439.-at-.goodnet.com sent the message

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Dr.Jenkins,

One possible statistical model is repeated-measures analysis

of variance. In this case the sequences would be the different

treatments, and the differences in bioavailability would be the

treatment effects. If the measured treatment effect (F) does not

have a normal distribution, then a nonparametric approach in the

form of a Friedman Statistic could be applied.

Recent statistic books such as Daniel's Biostatistics or Glantz's

Primer of Biostatistics have chapters on repeated-measures analysis

of variance and the use of the Friedman statistic in the nonpara-

metric case.

If there is covariate affecting bioavailability in addition to

the treatment (diet sequence), then an analysis of covariance study

design could be used. This is found in more advanced statistic books

such as Dowdy's Statistics for Research.

Mike Leibold, PharmD, RPh

ML11439.aaa.goodnet.com - On 14 Aug 2000 at 19:49:27, wang.yamei.-at-.kendle.com sent the message

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I think as soon as we have enough wash-out period between day X and day Y

or day W and day Y, we don't need treat that model as 4-level. Otherwise

the whole cross over design and model will be ruined.

Yamei Wang

Statistical Programmer/Biostatistician

Kendle International Inc. - On 16 Aug 2000 at 12:09:29, "Carol Roby" (croby.-at-.stagnes.org) sent the message

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A good site for stats info and online calculator scripts is:

http://member.aol.com/johnp71/javastat.html

Carol A. Roby, PharmD, MS

Clinical Pharmacist

St. Agnes Hospital

900 Caton Avenue

Baltimore, MD 21229

410-368-3109 - On 16 Aug 2000 at 12:11:10, "R.A. Fisher" (ra_fisher.aaa.hotmail.com) sent the message

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Hi Jack/All,

I thought I would hopefully be able give you some guidance regarding

your query. My thoughts are split into two parts. Firstly, some

personal thoughts on why you should look for a period effect in

general, and the second part I hope is the analysis I think you

should undertake.

Why look for period effect

--------------------------

There is often no good reason to suspect a period (or centre) effect

in a PK or biomarker study. These effects shouldn't, in theory,

exist. There is often no true physiological reason for these

differences. Unfortunately, in the real world these differences

frequently exist in the data derived from multi-centre or multiple

period studies, and the magnitude of these effects can be very large.

The obvious suspects are differences in the aquisition, storage,

transfer and analysis of the samples. This potential additional

variability/bias has to be considered. If my biomarker has a CV of

20% based on 50 subjects from a one centre study, will it be 20% if I

had recruited just one subject from each of 50 centres ? In theory,

perhaps yes, in practice, perhaps no.

Analysis

--------

This I hope is a fair re-ordering of your data, which may clarify

some of my comments. I referred to the two occasions for the first

period as w and x, as per your email. The first 12 subjects as

cohort 1, and subjects 13-21 as cohort 2. For simplicity, I have

called the first 4 subjects 1-4, although I know you would have

randomised the subjects within cohorts.

Data per1 per2 per3

Occ w x y z

sub 1-4 a . b c

sub 5-8 b . c a

sub 9-12 c . a b

sub 13-15 . a b c

sub 16-18 . b c a

sub 19-21 . c a b

My opinion is that w and x should be linked under the per 1 banner,

as two levels under per 1. These two levels are intrinsically more

similar to each other than per 2 and per 3 (the first time the

subjects enter the study). This "w versus x" contrast is of interest

in the preliminary analysis.

Some things become more obvious with this layout

i) differences between 'w' and 'x' is a between subject comparison.

ii) differences between sequence is a between subject comparison.

iii) differences between period is a within-subject comparison.

iv) differences between tmt's is a within-subject comparison.

Thus the 'technical' ANOVA (and degrees of freedom) can be written as:

d.f.

w versus x 1 (compare to subject error)

sequence 2 (compare to subject error)

Subject 17

tmt 2 (compare to residual error)

per 2 (compare to residual error)

total 24

Residual (+ everything else(e.g. interactions)) = 2 d.f. for each

within comparison for each subject less 2 for period, less 2 for tmt.

Hence 2 * 21 - 2 - 2 = 38. Hence the good news is the d.f. add up,

and we have N-1 (63-1) total d.f. = 62 (24 from above, and 38

residual).

Our 'weak' between subject contrast of the 'w versus x' to the

subject to subject error, will guide us to the appropriateness of

investigating period effects at the within-subject level. The

sequence effect should (I haven't checked) be orthogonal to the 'w

versus x' comparison.

The reason I wrote 'technical' above the ANOVA table is that I'm not

completely sold on this analysis. The confounding with cohort,

combined with the low power of this contrast, doesn't seem great.

Similarly, I do not like a 'sequence' effect, because I think the

presence or absence of this effect has more to do with whether 7

subjects happen to be giving a higher response than 7 others, rather

than anything to do with the sequence of treatments they actually

received. However, I think your consideration and definition of this

problem was wholly merited.

I hope this helps,

good luck

RA Fisher

p.s.

I would use the reverse williams square for subjects 13-21. That is,

sequences "a c b", "c b a", and "b a c". This ensures that any

potential differencial carry-over is minimised.

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