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Hello all,

I was asked to help with a revision of an analysis of a small cross-over trial (2 arms 2 periods). I don't have much experience with these, and I'm having a hard time explaining to them why carry-over effects are important and cannot be dismissed. Does anyone have any tips or resources that explain these concepts to a less statistical audience? Since I'm looking into learning these concepts myself, I'm not providing more information on the trial itself, but please let me know if I should.

Thank you,

Maria

Hi Maria,

I don't know if this is a helpful analogy, but carry over is like having a latte, not rinsing the cup and then using that same cup for a beer. Without washing out the cup, you end up with a latte flavored beer. For something more formal: Understanding controlled trials Crossover trials

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Maria,

Although I like the latte - beer analogy, the classic bools I have: Design and Analysis of Cross-Over Trials by Jones and Kenward and Cross-over Trials in Clinical Research by Senn, have considerable good discussion.  I'm sure more recent references also have good discussion (and perhaps google).

David

I don't know what "bools" are. but I have books.

Maria

An actual example from pharma clinical trial - (a project I worked on) in drug development. 

That  concerns the appropriate length of the wash-out period in PK (pharmacokinetic) trials of a new drug. Washout is the interval of time between two consecutive periods.  The example clinical trial is  sometimes called  an ADME clinical trial "Absorption , Distribution Metabolism and Excretion" trials ( https://www.technologynetworks.com/drug-discovery/articles/what-is-adme-336683 ) .  Many drugs when administered , say by swallowing a pill,  begin dissolving in the gut,  the main molecule (for this example considering small molecule drugs) is the active drug.. As the drug is digested in the gut there may be other "metabolites" , derived from the active molecule that are also active. An important step in drug development is to characterize all metabolites of a drug in humans.  

And A long time ago I worked on a drug with the name of "mycophenolate mofetil" (actually developed in part at a pharma company in Palo Alto with researchers at Stanford). which was the ester of mycophenolic acid "MPA" or shortened to "myco".  when the drug , in pill formulation was digested in the gut and entering the blood stream – there was the active MPA and other active metabolites one of them MPAG ( mycophenolate glucuronide ). Both The MPA the MPAG were both active on the T-cell immune response to the disease (the disease was immunological rejection of a solid organ such as a kidney, heart or liver). Since the drug above was approved a different pharmaceutical company developed the MPA (without the ester) as a drug.

A full description of the "myco" pharmacokinetics here

https://link.springer.com/article/10.2165/00003088-199834060-00002

The washout period has to be long enough for the active drug and all active metabolites to become inactive, sometimes stated  such as " the washout was at least ten half-lives" of the drug and its metabolite.  I forget the length of the washout we used for myco cross over trials (its in the published articles).

 An important operations and budget ($) aspect for the clinical trials is/was 1) how long was patient required to stay in the hospital . 2) and how expensive were the hospital beds and medical care/monitoring.  These are expensive and short washouts were preferred. However, if the washout period was too short, then the active drug and (possibly) several metabolites had an effect on the disease process, and the drug effect in  the subsequent period.  A long standing issue in cross over trials is whether there is some carry over, where drug in period 1, remains in the (say) blood and is active in the subsequent (period 2) for a two period cross over.  

For comparison , for a different  clinical trial than above, when I asked about the half-life (for a different drug /metabolites than above) the half-life was some very large number like 120 hours (about 5 days). In that setting , if a patient was required to stay in the  hospital for five days– the clinical trial and hospital stay with medical attention, MD's, RN's  , other support,  was very expensive ($). 

A slightly more formal description of potential for carry over may be found in so -called TQT (Thorough QT cardiac studies) which are required for new drugs in the early stages of development. Those TQT designs can also be formulated as Latin Squares and there must be adequate washout between all consecutive periods.  Because TQT  are cardiac trials and patient cardiac activity is monitored 24/hours and a dedicated team of (well paid) Cardiologists (often in several time zones) to be available 24/7 . can  be very expensive if a patient has to be in the hospital for several days with round the clock cardiac monitoring There is some limited  discussion of washout in the ICH TQT guidance. I like to mention TQT  when I give talks about drug development to graduate students, that a TQT is nearly a guarantee that the statistician gets summoned to  meet the CEO who (with varyiing degrees of emphasis)  expresses concern about the expense ($) of conducting the TQT  trial and asks some variation on "Do you know how expensive $$$ this trial is for us? Is  there a  way you can figure out a smaller sample size? https://database.ich.org/sites/default/files/E14_Guideline.pdf

I second the Jones and Kenward book as a great reference.

Here's a paper I wrote on this some years back. Carryover should not be ignored in a crossover study but it should  be considered in the design phase with an appropriate washout period.  Once you've done the experiment the statistical power to detect it is small. As an example, imagine that your carryover effect is half of your original treatment effect. Your original study had 80% power based on a within-subject contrast. The carryover effect can only be detected using a between-subject contrast so it will have poor statistical power. 

Putt ME. Power to detect clinically relevant carry-over in a series of cross-over studies. Stat Med. 2006 Aug 15;25(15):2567-86. doi: 10.1002/sim.2275. PMID: 16220475.