IDENTIFYING EFECTIVE AND SAFE TREATMENTS

P. Bauer, W.Brannath and M.Posch

(Department of Medical Statistics, University of Vienna, Austria)

We consider the situation where *k* treatments and a (zero) control are compared with respect to efficacy and safety. For efficacy the null hypotheses for the many one comparisons in terms of the paramenter of interest are defined as *H*_{oi}^{E}: *µ*_{i} £
*µ*_{0}, *i* = 1, ..., *k*. Here *µ*_{0 }and *µ*_{1}, ..., *µ*_{k} denote the parameter under the control (*µ*_{0}) and the *k* treatments, respectively. For safety the shifted one sided null hypotheses *H*_{oi}^{S}: q
_{i} £
q
_{0} + d
are investigated, where d
is the prefixed safety margin for the corresponding parameter of interest.

A treatment *i* is considered to be effective if *H*_{oi}^{E} is rejected and is considered to be safe if *H*_{oi}^{S} is rejected. If both *H*_{oi}^{E} and *H*_{oi}^{S} are rejected it is considered to be effective and safe.

By considering only the *k* sub-families (*H*_{oi}^{E}, *H*_{oi}^{E} È
*H*_{oi}^{S}), *i *= 1, ..., *k*, the multiple levels applied within the sub-families can be adjusted in a stepwise way. Within the sub-family a hierarchical procedure with a fixed sequence of testing is used. This multiple level- procedure can also be applied to the problem of simultaneously establishing superiority of a treatment to a (zero) control and D
-equivalence to an active control and is more powerful than the procedure by Bauer et al. (1998). If order restrictions are assumed to hold among the parameters of interest a split strategy by applying adjusted multiple levels within the two sub-families (*H*_{oi}^{E}, *i* = 1, ..., *k*) and (*H*_{oi}^{S}, *i* = 1, ..., *k*) can be applied. If all treatments are found to be effective or all treatments are found to be safe this leads to an improvement of the Bonferroni-splitting.

A possible generalization to continuous families with the corresponding confidence intervals is given.

Bauer, P., Röhmel, J., Maurer, W. and Hothorn, L. (1998) Testing strategies in multi-dose experiments including active control. Statist. Med., 17, 2133-46.