**Non-inferiority clinical trials: a multivariate test for multivariate PD**

Laffont C. M.(1), Fink M(2) and Concordet D(1)

(1) INRA, UMR 1331, Toxalim, F-31027 Toulouse, France. Université de Toulouse, INPT, ENVT, UPS, EIP, F-31076 Toulouse, France; (2) Novartis Pharma AG, Basel, Switzerland

**Objectives**: Composite PD endpoints are a common feature of clinical trials. This multiplicity poses a challenge for the statistical comparison of two treatments, generally the non-inferiority of a drug to a reference. Several strategies are possible. One is to test each endpoint separately but the risk is to have different conclusions and to fail to demonstrate non-inferiority because we have to correct for the multiplicity of the tests (loss of power). A second strategy is to derive a single variable from the multiple endpoints (either binary: responder/non-responder, or linear combination) and perform a single test. In that case, we lose part of the information. We have seen in previous works^{1,2,3} that it is possible to model all endpoints simultaneously. In that context, we propose a multidimensional statistical test which exploits all the information and is *a priori* more powerful.

**Methods**: We assume that a multivariate population model is available where treatment differences are coded as ratio parameters on the PD parameters of interest. We define the statistical hypotheses of the test in a multidimensional framework. As previously discussed^{4}, several definitions are possible based on intersection/union principles. We propose a decision rule which can be interpreted geometrically as follows: the null hypothesis H_{0} is rejected when the confidence region of the vector of ratio parameter estimates has no common point with H_{0}. Based on several simulation studies, we explore the advantages of this test over separate univariate tests. We then apply the test to real clinical data where the efficacy of NSAIDs on chronic osteoarthritis is evaluated using four ordinal responses.

**Results**: We found that there is a balance between the dimension (the number of endpoints), the correlation between estimates, and the size of the dataset. When applied to real clinical data, non-inferiority was demonstrated with the multivariate test. When no correction was applied to account for the multiplicity of the tests, it was also demonstrated on each response separately. In contrast, when the multiplicity of the tests was accounted for as it should, non-inferiority could not be demonstrated for any response.

**Conclusion**: Multivariate testing definitely raises some challenges for the scientists and regulatory authorities (definition of null hypothesis, non-inferiority margin) but needs to be explored as it can be a powerful tool to increase power and thus reduce clinical costs.

**References**:

[1] Laffont CM and Concordet D. How to analyse multiple ordinal scores in a clinical trial? Multivariate vs. univariate analysis. PAGE 20 (2011) Abstr 2157.

[2] Laffont CM, Fink M, Gruet P, King JN, Seewald W and Concordet D. Application of a new method for multivariate analysis of longitudinal ordinal data testing robenacoxib in canine osteoarthritis. PAGE 21 (2012) Abstr 2548.

[3] Ueckert S, Plan EL, Ito K, Karlsson MO, Corrigan B and Hooker AC. Application of Item Response Theory to ADAS-cog Scores Modelling in Alzheimer's Disease. PAGE 21 (2012) Abstr 2318.

[4] Hasler M and Hothorn LA. Simultaneous confidence intervals on multivariate non‐inferiority. Statistics in Medicine, 2012 online.