LSM limbo [General Sta­tis­tics]

posted by Helmut Homepage – Vienna, Austria, 2014-07-31 02:54 (2731 d 19:21 ago) – Posting: # 13322
Views: 20,959

Dear Ohlbe,

» How do you calculate the LSM in a full replicate design study (RTRT and TRTR, with some subjects missing here and there) ?

Manually? Never done that. :-D If you are thinking about RSABE (in their FDA and EMA flavors), that’s a strange cup of tea. To quote Patterson & Jones1:

[…] simulation findings support that if a subject is missing both reference ob­ser­vations or the test observation, no bias is introduced.
If one R observation is missing, then MoM estimates of δ and σ²l are biased by period effects if they are present. It should be noted that period effects are known to occur in such designs.
If SABE is applied, subjects with one missing R observation should be eliminated from a MoM analysis until an alternative statistical procedure is available. This is un­precedented in our expe­ri­ence in a regulated bioequivalence setting. Traditionally, one does not exclude data unless there is a scientifically or clinically valid reason to do so. However, with the current draft guidance from FDA for progesterone bio­equi­valence, this appears to be the immediate approach to be applied for SABE. A better statistical alternative is restricted maximum likelihood estimation (to eliminate bias) with the use of the bootstrap for inference.


It’s a complete mess. Subjects with incomplete data are excluded from the estimation of σ²WR, but kept in the calculation of the upper 95% boundary (FDA) or excluded for the calculation of the 90% CI (EMA, all fixed effects. A mixed-effects model is not acceptable for EMA). To be honest, currently there are so many flaws in these methods that I would not bother to calculate anything by hand. Accept what you get from the FDA’s and EMA’s SAS-code (or alternative software) and set this question aside until somebody finds a method to deal with the more important question: How to prevent inflation1,2 of the patient’s risk (according to my latest simulations: EMA up to 9.6% and FDA up to 22.5%). This is a nightmare.


  1. Patterson SD and B Jones
    Viewpoint: observations on scaled average bioequivalence
    Pharm Stat 11(1), 1–7 (2011)
    DOI: 10.1002/pst.498
  2. Wonnemann M, Frömke C, and A Koch
    Inflation of the Type I Error: Investigations on Regulatory Recommendations for Bioequivalence of Highly Variable Drugs
    Pharm Res 31 (preprint published 18 July 2014)
    DOI: 10.1007/s11095-014-1450-z

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