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  • 1.  ANOVA for repeated AUC

    Posted 01-31-2018 09:32
    Here is the scenario, can we come up with proper stat test? 

    The study has 30 subjects, each person receive 5 different treatments & 1 placebo on different parts of body. Each time point, including baseline, the test areas are treated and measured. The endpoint is Area Under Curve (AUC) of a marker.  

    What would be the best way to analyze?

    The easiest is a one-way ANOVA of AUC at the very last time point. In this  each subject will have 6 readings from 6 treatments. Total of 30*6=180 data points. The records from the same subject have to be assumed independent samples which are not really. 

    Idea 2: a repeated measurement ANOVA. Site is the measuring sites on each subject's body.
    Proposed SAS code: proc mixed; model AUC = treat visit site treat*visit / ddfm=kr ; repeated visit / subject=pid*site ;

    If repeated measurement model works, should AUC up to the time point be used (total AUC), or AUC from precious time point to this measuring point (AUC fragment) should be used?

    Are there better ways to construct the stat model?

    Please advise. 

    Thank you.

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    Brian Lin

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  • 2.  RE: ANOVA for repeated AUC

    Posted 02-01-2018 11:30
    ​This sounds like a crossover design with 5 treatment periods.  Was each subject randomized to a sequence of treatments (locations), or was the order always the same for all subjects (single sequence)? 

    The AUC measure is just a mathematical way to consolidate the repeated measurements within each treatment period.  Depending on the purpose of the repeated measurements this could be a standard practice (e.g., sampling blood levels of a drug). If you are analyzing AUC, you do not need to keep track of the time points within each treatment period (baseline, time 1, time 2, etc).  The next level of repeated time becomes the treatment periods. But these are not true repeated measures either since each period is at a different location.  It is important to know if there is a random component to the order of treatments or not.  If so, then a standard crossover model will work.  If not, the site and period become somewhat confounded and there is no way to separate a carryover effect from previous treatment periods.

    It would be helpful to know specifically the study design.  Howe were subjects allocated to the 5 sites and 5 periods?

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    Susan Spruill
    Statistical Consultant
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    Original Message


  • 3.  RE: ANOVA for repeated AUC

    Posted 02-02-2018 09:27
    Susan and Eric, thanks for the answers.

    The design is that each subject's back (or arm) were drawn with 6 equal size squares (or circle).  Each square / circle / site receives one treatment assignment. All subjects receive all 5+1 treatments in different sequences.

    At the beginning of the trial, a marker is applied to all sites once, and the availability of the marker is measured at every time point. AUC is measured as a numeric value. Topical treatments were applied by clinical staff on subject's sites accordingly, once every day in the clinic after the readings were taken. 

    The sequence is randomized but every subjects will have 6 squares (5 treatment plus a placebo site / area) . The upper back of Subject 1 may be on treatment A, and Subject 2 may be on treatment B.

    Time is not evenly space. It is like Day 1 (baseline), Day 1 (2 / 12 hours), Day 2, 3, 5, 7.

    Thanks again.

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    Brian Lin

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    Original Message


  • 4.  RE: ANOVA for repeated AUC

    Posted 02-02-2018 15:11

    Susan and Eric are right on the target: one can't provide a meaningful analysis without knowing the study objective(s) and design. Is there any application of placebo/treatment at the baseline (I'd assume not)? Are the placebo and 5 treatments applied simultaneously to each subject at each subsequent time point; or are they applied sequentially in which case is an application time coincide with "Each time point"? Not only is there longitudinal dependence, there is also cross-treatment dependence introduced by each subject receiving placebo and 5 treatments. The latter is sort of similar to a cross-over experiment, but reading Brian's description it does not appear to me a cross-over experiment. The (partial) AUCs (from baseline to a time point) are not repeated measures; especially, if the marker values are positive then the partial AUCs increase monotonically along time, and they behave more or less like a time series with a monotone location drift if the time points are equally spaced.

     

    We don't fully know the study objective, but I wonder if a simpler, more elegant design can address it (even more effectively).

     

    I guess it would be safe to analyze the total AUC (at the very last time point) with a proper mixed-effect linear model that adequately address the cross-treatment (now confounded with within-subject) dependency, but not sure how useful the result is in addressing the study objective.

     

    BTW is this yet another example that the Statistician was called after the fact?

     

    Cheng Cheng, Ph.D.

    Member

    Department of Biostatistics

    St. Jude Childen's Research Hospital

    262 Danny Thomas Place, MS 768

    Memphs, TN 38105

    Tel. 901-595-2935; FAX 901-595-8843

    Email disclaimer: http://www.stjude.org/emaildisclaimer

     




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  • 5.  RE: ANOVA for repeated AUC

    Posted 02-01-2018 22:51

    Area under what kind of curve? What quantity does the vertical axis represent? Does the quantity have units of measurement?

    Are the time points equally spaced? Or do they grow in length at later times?

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