How to analyze a randomized 1:1, double blind, cross-over clinical trial.

[Matteo Bargagli]

Good morning to everyone.
I would like to start with a big thank you to this forum, because I always had some useful tipps here.

I am writing because I will start soon to anaylse data from a randomized 1:1, double blind, cross-over clinical trial with a certain exposure (drug or placebo).
20 patients were randomized 1:1 to take either placebo or the drug (period 1) and a set of outcome variables were measured (blood parameters) after 2 weeks of treatment.
Afterwards, all patients had a 1-week wash-out period and then they switched to placebo or the drug (period 2), depending on what they have taken in period 1. Again blood parameters were measured after 2 weeks.

Since all patients had 2 different level of exposure (placebo and drug), I would like to ask you which is the correct way to proceed in this dataset.

My objective is to compare: 1. differences in the outcome variables in placebo vs drug patients (inter-individual differences) and 2. changes over time due to the drug, in the same patient (intra-individual).

Thank you in advance!

[Joseph Coveney]

help pkcross

or more generally

help pk

[Matteo Bargagli]

help pkcross

or more generally

help pk

Thank you very much for the fast reply.

In my case, I should have 2 x 2 cross-over study, right? (no outcome measurement during the wash-out period, only 2 treatment exposure and 2 study period).
Which param option is often use in this case, to avoid overparametrization?

Another question if I can: since I collected additional data for these patients (es. previous cardiovascular events). Is there a way to adjust the model to possible confounders?

[Matteo Bargagli]

In addition: I have multiple outcome variables to test, but I have seen that the pkshade code accept a period list for the same variable. How can I include period1 and period2 for multiple variables? (i.e. both glucose and insulin measurements at period1 and period2).

[Joseph Coveney]

In my case, I should have 2 x 2 cross-over study, right?

From your description,yes.

Which param option is often use in this case, to avoid overparametrization?

All four parameterizations have the same model degrees of freedom, but the default parameterization (#3) is the easiest to see what's going on, and conforms to the most commonly made set of assumptions regarding sequence, carryover and period effects.

Another question if I can: since I collected additional data for these patients (es. previous cardiovascular events). Is there a way to adjust the model to possible confounders?

Not for treatment (or period effects), no. You're fitting a mixed-model ANOVA, and the treatment factor is within-subjects, i.e., fixed effects. Time-invariant predictors, such as baseline patient characteristics (confounders), will drop out of the fixed-effect comparisons.

[Joseph Coveney]

In addition: I have multiple outcome variables to test, but I have seen that the pkshade code accept a period list for the same variable. How can I include period1 and period2 for multiple variables? (i.e. both glucose and insulin measurements at period1 and period2).

Switch to MANOVA. Stata's manova estimation command allows for setting up a MANOVA model in a manner analogous to the ANOVA model that pkcross uses behind the scenes.

[Matteo Bargagli]

Thank you very much. I studied the field (https://doi.org/10.4097/kja.21165) and I decided to use a mixed effect linear regression model to test my dataset, including the period (visit1 or visit 2), the treatment sequence (AB or BA) and the treatment effect as fixed effects and the patients as random effect.
So my code would be like this:

xtmixed depvar(blood parameter) i.treatment(placebo or drug) i.period(visit1 or visit2) i.sequence(BA or AB) || patient ID

My question is: should I also include the period by treatment interaction as a fixed effect, to consider also a possible crossover effect?

[Joseph Coveney]

. . . should I also include the period by treatment interaction as a fixed effect, to consider also a possible crossover effect?

In general your statistical model should reflect your study design and include those predictors that are implied by it. In crossover study designs there is often a concern about carryover (hence washout periods) and so-called learning effects, and so are monitored.

[Matteo Bargagli]

Thank you again.
So, since the study design in my case includes a long (4 to 6 weeks) wash-out period, the carryover effect can be omitted and the mixed effect linear regression code that I posted (hence, considering only the period and sequence effects), can be considered correct, right?

[Joseph Coveney]

No.

[Matteo Bargagli]

The problem of this study is that the study design was modified during the course for including other parameters that now I need to analyze.
In addition, 2 patients have incomplete data (only for visit 2 and not visit 1). This is why I dediced to use a mixed model, but I am not an expert.
What code would you use in this case?

[Joseph Coveney]

Sorry, that answer was a bit terse, so much so that I unintentionally reversed the sense intended, which was: No, you don't include a carryover term if your model already has terms for sequence (under which participants are nested), period and treatment. The carryover term is collinear with those in your crossover study, and you have to deal with it as you've done, namely, with a washout period.

So, your specification with -xtmixed- is about all you can do, except that you'd probably want to use the -reml- and -dfmethod()- options unless you have a large sample size.

If patient medical history ("previous cardiac events" etc.) is what you mean by the other parameters that you must now analyze, then as mentioned above their presence won't affect your estimates for within-patient factors—such as period ("learning effects") and treatment—when you have balanced data (suitable for ANOVA). With incomplete data, you'll notice some changes even in the within-patient estimates when you include these baseline patient characteristics (see below for illustration; begin at the "Begin here" comment).

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Logÿrestricted-likelihoodÿ=ÿ-79.812134ÿÿÿÿÿÿÿÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.2631

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.seqÿ|ÿÿÿ.1318568ÿÿÿ.4830677ÿÿÿÿÿ0.27ÿÿÿ0.788ÿÿÿÿ-.8727375ÿÿÿÿ1.136451
ÿÿÿÿÿÿÿ1.perÿ|ÿÿÿ.6609733ÿÿÿ.3047817ÿÿÿÿÿ2.17ÿÿÿ0.041ÿÿÿÿÿ.0288948ÿÿÿÿ1.293052
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿ.1686372ÿÿÿ.3047817ÿÿÿÿÿ0.55ÿÿÿ0.586ÿÿÿÿ-.4634413ÿÿÿÿ.8007158
ÿÿÿÿÿÿÿ1.cveÿ|ÿÿÿ.3783729ÿÿÿ.4989102ÿÿÿÿÿ0.76ÿÿÿ0.457ÿÿÿÿ-.6591677ÿÿÿÿ1.415914
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.8101849ÿÿÿ.4969486ÿÿÿÿ-1.63ÿÿÿ0.113ÿÿÿÿ-1.824663ÿÿÿÿ.2042935
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.8324041ÿÿÿ.4606352ÿÿÿÿÿÿ.2813823ÿÿÿÿ2.462474
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ1.114703ÿÿÿ.3360955ÿÿÿÿÿÿ.6173225ÿÿÿÿ2.012825
------------------------------------------------------------------------------

.ÿcontrastÿseqÿperÿtrt,ÿsmall

Contrastsÿofÿmarginalÿlinearÿpredictions

Margins:ÿasbalanced

-----------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿÿddfÿÿÿÿÿÿÿÿÿÿÿFÿÿÿÿÿÿÿÿP>F
-------------+---------------------------------------------
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-----------------------------------------------------------

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.ÿmixedÿoutÿi.(seqÿperÿtrt)ÿ||ÿpid:ÿ,ÿremlÿdfmethod(kroger)ÿnolrtestÿnolog

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Logÿrestricted-likelihoodÿ=ÿÿ-80.32125ÿÿÿÿÿÿÿÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.1955

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ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.seqÿ|ÿÿÿ.1633879ÿÿÿ.4766058ÿÿÿÿÿ0.34ÿÿÿ0.735ÿÿÿÿÿ-.825032ÿÿÿÿ1.151808
ÿÿÿÿÿÿÿ1.perÿ|ÿÿÿ.6609733ÿÿÿ.3047817ÿÿÿÿÿ2.17ÿÿÿ0.041ÿÿÿÿÿ.0288948ÿÿÿÿ1.293052
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿ.1686372ÿÿÿ.3047817ÿÿÿÿÿ0.55ÿÿÿ0.586ÿÿÿÿ-.4634413ÿÿÿÿ.8007158
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.5894674ÿÿÿ.4000281ÿÿÿÿ-1.47ÿÿÿ0.149ÿÿÿÿ-1.399698ÿÿÿÿ.2207629
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.8055672ÿÿÿ.4439684ÿÿÿÿÿÿ.2735162ÿÿÿÿ2.372578
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ1.114703ÿÿÿ.3360955ÿÿÿÿÿÿ.6173225ÿÿÿÿ2.012825
------------------------------------------------------------------------------

.ÿcontrastÿseqÿperÿtrt,ÿsmall

Contrastsÿofÿmarginalÿlinearÿpredictions

Margins:ÿasbalanced

-----------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿÿddfÿÿÿÿÿÿÿÿÿÿÿFÿÿÿÿÿÿÿÿP>F
-------------+---------------------------------------------
outÿÿÿÿÿÿÿÿÿÿ|
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-----------------------------------------------------------

.ÿ
.ÿ//ÿUnbalanced,ÿfirstÿwithÿandÿthenÿwithoutÿMHx
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ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ1.9
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ2
DFÿmethod:ÿKenward–RogerÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDF:ÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿ20.67
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿ22.96
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿ31.54
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿF(4,ÿÿÿÿ29.56)ÿÿÿÿ=ÿÿÿÿÿÿÿ1.13
Logÿrestricted-likelihoodÿ=ÿ-77.263032ÿÿÿÿÿÿÿÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.3607

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.seqÿ|ÿÿÿ.1472226ÿÿÿ.4881749ÿÿÿÿÿ0.30ÿÿÿ0.766ÿÿÿÿ-.8689765ÿÿÿÿ1.163422
ÿÿÿÿÿÿÿ1.perÿ|ÿÿÿ.6244961ÿÿÿ.3291449ÿÿÿÿÿ1.90ÿÿÿ0.072ÿÿÿÿ-.0601471ÿÿÿÿ1.309139
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿ.1862669ÿÿÿ.3293692ÿÿÿÿÿ0.57ÿÿÿ0.578ÿÿÿÿ-.4988945ÿÿÿÿ.8714282
ÿÿÿÿÿÿÿ1.cveÿ|ÿÿÿ.4055393ÿÿÿ.5052088ÿÿÿÿÿ0.80ÿÿÿ0.431ÿÿÿÿ-.6457666ÿÿÿÿ1.456845
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.8436616ÿÿÿ.5178203ÿÿÿÿ-1.63ÿÿÿ0.113ÿÿÿÿ-1.899031ÿÿÿÿ.2117081
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.7753681ÿÿÿ.4793183ÿÿÿÿÿÿ.2308398ÿÿÿÿ2.604384
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ1.216448ÿÿÿ.3821166ÿÿÿÿÿÿ.6572188ÿÿÿÿ2.251527
------------------------------------------------------------------------------

.ÿcontrastÿseqÿperÿtrt,ÿsmall

Contrastsÿofÿmarginalÿlinearÿpredictions

Margins:ÿasbalanced

-----------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿÿddfÿÿÿÿÿÿÿÿÿÿÿFÿÿÿÿÿÿÿÿP>F
-------------+---------------------------------------------
outÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿseqÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿ20.67ÿÿÿÿÿÿÿÿ0.09ÿÿÿÿÿ0.7660
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿperÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿ20.93ÿÿÿÿÿÿÿÿ3.60ÿÿÿÿÿ0.0717
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿtrtÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿ20.90ÿÿÿÿÿÿÿÿ0.32ÿÿÿÿÿ0.5777
-----------------------------------------------------------

.ÿ
.ÿmixedÿoutÿi.(seqÿperÿtrt)ÿifÿ!ltfuÿ||ÿpid:ÿ,ÿremlÿdfmethod(kroger)ÿnolrtestÿnolog

Mixed-effectsÿREMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿ46
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ24
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ1.9
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ2
DFÿmethod:ÿKenward–RogerÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿDF:ÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿ20.94
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿ25.29
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿ37.49
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿF(3,ÿÿÿÿ27.78)ÿÿÿÿ=ÿÿÿÿÿÿÿ1.32
Logÿrestricted-likelihoodÿ=ÿÿ-77.82013ÿÿÿÿÿÿÿÿÿÿProbÿ>ÿFÿÿÿÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.2888

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.seqÿ|ÿÿÿ.1707821ÿÿÿÿ.484662ÿÿÿÿÿ0.35ÿÿÿ0.728ÿÿÿÿ-.8349542ÿÿÿÿ1.176518
ÿÿÿÿÿÿÿ1.perÿ|ÿÿÿ.6270732ÿÿÿ.3281812ÿÿÿÿÿ1.91ÿÿÿ0.070ÿÿÿÿ-.0555312ÿÿÿÿ1.309678
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿ.1760314ÿÿÿ.3281812ÿÿÿÿÿ0.54ÿÿÿ0.597ÿÿÿÿÿ-.506573ÿÿÿÿ.8586359
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.5968616ÿÿÿ.4138842ÿÿÿÿ-1.44ÿÿÿ0.158ÿÿÿÿ-1.435099ÿÿÿÿ.2413763
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿparametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿerr.ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-----------------------------+------------------------------------------------
pid:ÿIdentityÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.7631662ÿÿÿÿ.462171ÿÿÿÿÿÿ.2328811ÿÿÿÿ2.500944
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ1.209737ÿÿÿ.3784369ÿÿÿÿÿÿ.6552595ÿÿÿÿ2.233412
------------------------------------------------------------------------------

.ÿcontrastÿseqÿperÿtrt,ÿsmall

Contrastsÿofÿmarginalÿlinearÿpredictions

Margins:ÿasbalanced

-----------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿÿddfÿÿÿÿÿÿÿÿÿÿÿFÿÿÿÿÿÿÿÿP>F
-------------+---------------------------------------------
outÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿseqÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿ21.77ÿÿÿÿÿÿÿÿ0.12ÿÿÿÿÿ0.7279
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿperÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿ20.94ÿÿÿÿÿÿÿÿ3.65ÿÿÿÿÿ0.0698
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿtrtÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿ20.94ÿÿÿÿÿÿÿÿ0.29ÿÿÿÿÿ0.5973
-----------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

Interpretation can get involved here.

[Matteo Bargagli]

Thank you very much for the detailed information. Now I understand and since I have a sufficiently long washout period (3x more time than the treatment) the carryover effect should be controlled.
I have just the last question, if I could:
If I run the analysis and I have significance for both the treatment and the sequence, what should I conclude? That the changes in the outcome variable might be due to a period by treatment interaction and not only by the effect of the treatment vs placebo?

[Joseph Coveney]

Now I understand and since I have a sufficiently long washout period (3x more time than the treatment) the carryover effect should be controlled.

Possibly.

In the past, a common use of the two-treatment, two-period crossover study design was in an industrial setting involving bioequivalence testing of a generic drug product against the so-caled innovator's original. There, the required duration of a washout period could be judged in advance, inasmuch (i) as the outcome variable (parent drug and metabolite concentrations in the bloodstream) could be measured at baseline of the second period, confirming the absence of any carryover drug levels, (ii) the drug substance (active pharmaceutical ingredient) was well characterized (biological half life, liability for enzyme induction etc.), and (iii) the formulation (immediate- versus extended-release) and route of administration could be taken into consideration when deciding the length of the washout period.

I don't know whether any of the those pertains to your situation. And if your outcome is pharmacodynamic (blood-glucose and serum-insulin time courses after a glucose load?), then absence of residual drug levels wouldn't necessarily be assurance of absence of carryover effects: it's possible that a prior exposure to the drug (versus placebo) has a long-lasting or even permanent physiological or biochemical change in participants. If so, then you could see a differential carryover effect among those who were assigned to the initially exposed group.

That is, you'd need to rule out the possibility of a carryover effect on other grounds than just the duration of the washout period (two to three weeks) relative to the drug-exposure period (one week).

If . . . I have significance for both the treatment and the sequence, what should I conclude? That the changes in the outcome variable might be due to a period by treatment interaction and not only by the effect of the treatment vs placebo?

To quote from here (itself quoting an authoritative source), "For a standard 2X2 crossover design, the sequence effect is confounded with the carryover effect and the formulation-by-period interaction. Therefore, a statistically significant sequence effect could indicate that a) there is a true sequence effect b) there is a true carryover effect c) true formulation by period interaction or, d) there is a failure of randomization (Chow and Liu, 2000)."

In the conventional bioequivalence testing context described above, given the extensive background knowledge of the drug and its formulation, a sequence effect was often discounted as a Type I error and its statistical testing as a precondition for testing the (within-subjects) treatment effect of interest was discouraged. In your case, you might need to resort to testing the first period results only (at much reduced power) in order to get at an unconfounded assessment of a drug-versus-placebo difference.

[Matteo Bargagli]

Thank you very much. Now I have everything clear!!!