Triangular Test And Further Work

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The triangular test has now been used in a wide variety of clinical studies concerned with many therapeutic areas. Examples include trials of corticosteroids for AIDS-induced pneumonia (41), of enoxaparin for prevention of deep vein thrombosis resulting from hip replacement surgery (42), of isradipine for the acute treatment of stroke (43), and of implanted defibrillators in coronary heart disease (44). In pediatric medicine, the triangular design has been used to study the use of surfactant to alleviate respiratory distress in infants (45) and in a trial concerning gastrointestinal reflux (46). An evaluation of the drug Viagra in the treatment of erectile dysfunction after spinal injury also used the method (47), and it has been implemented in animal studies of medical techniques (48). An interesting combination of the triangular test with the play-the-winner rule was applied in a study of spinal anesthesia during cesarean section (49). Within oncology, besides the renal and lung cancer trials mentioned in Sections III and IV, respectively, Storb et al. (50) described a triangular test of immunotherapy as a preparation for bone marrow transplantation in leukemia.

The double triangular test has also found application. Nixon et al. (51)

described such a design in a comparison of pressure sore rates after the use of two types of mattress during cancer surgery, Boden et al. (52) report a trial based on the design in cardiology and Yentis (53) described an application to a trial in elective Caesarian section. Other trials using triangular and related designs are given on the web page: http://www.rdg.ac.uk/mps/mps_home/software/pest4/ practice.htm

The properties of the triangular test are now well understood, and its opti-mality makes it hard to improve. It is not appropriate for every situation, and suitable alternatives exist. The Christmas tree correction could be improved on, but in the case of the triangular test, not by much. An exact version of the triangular test, applicable to a single stream of binary observations, is described by Stallard and Todd (54). There is a range of response types to which the triangular and related designs can be extended; in particular, work is proceeding on survival responses with nonproportional hazards and longitudinal ordinal responses. Methods for analyzing data after sequential trials of this type are also being developed.

In the future, two main challenges remain. One is to use the principles underlying the triangular design to help in the construction of optimal sequential designs for multivariate responses and for multiple treatment comparisons. The other is, quite simply, to spread its usage to all trials that can benefit from its ethical and economic advantages.

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