Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Incomplete or partial factorial studiesStudies that evaluate every combination of factors, such as those described above,are sometimes referred to as fully crossed factorial designs. Incomplete or partialfactorial studies exclude some treatment groups for reasons such as suitability,feasibility, or ethics. For example, specific combinations of treatments mightresult in excess toxicity, and it would therefore be unethical to evaluate them in aclinical trial. Alternatively, it might not be feasible or necessary to make certaintreatment comparisons [7]. In such cases, it is possible to economize if cells are leftblank intentionally by not allowing recruitment to those combinations, therebyreducing the total number of groups under comparison and consequently the totalnumber of individuals.For example, in a study that evaluated the effect of different percentage levels ofdietary calcium (Ca) and phosphorus (P) on performance, structural soundness,and bone characteristics of growing pigs at different stages of their development,there were four different available diets with Ca:P ratios of 0.45:0.32, 0.52:0.40,0.65:0.50, and 0.80:0.60. For simplicity, the authors used the weights of the animalsto define their stage of development. A total of 664 pigs were initially fed one ofthree diets with higher Ca:P phosphate content (0.52:0.40, 0.65:0.50, 0.80:0.60)during growth (19–56 kg body weight). This was followed by one of three dietswith lower Ca:P levels (0.45:0.32, 0.52:0.40, 0.65:0.50) until the pigs reached theirmarket weight. This was analyzed as an incomplete 3 × 3 factorial study becausecomparisons for the more extreme Ca:P diets at both ends of the range wereomitted [8].Unbalanced factorial studiesAnother design variation is the unbalanced factorial study, where differentnumbers of individuals are randomized to each cell. These studies commonlyoccur in investigations of combination antihypertensive drugs. Dose combinationsthat are expected to be employed as initial therapy may be given a larger samplesize to ensure there is enough power to detect any additional effect of a thirdtreatment. It is more complicated to analyze an unbalanced factorial study thana balanced design, yet various approaches to dealing with problems related todifferent sample sizes have been suggested [9].Complicated factorial designAn example of a more complicated factorial design, including severalinterventions as well as imbalances between groups, is a study evaluating nauseaand vomiting after elective surgery with general anesthetic [10]. This trial was setup to examine six interventions as a 2 6 (2 × 2 × 2 × 2 × 2 × 2) format; however athird arm, containing 10% of the individuals, was added for the fifth intervention,which resulted in a 2 5 × 3 (2 × 2 × 2 × 2 × 3 × 2) format (see Table 3).109