Factorial Designs

Background Factorial designs are when different treatments are evaluated within the same randomised trial. A factorial design has a number of important advantages.

Advantages Two trials for the price of one. Can test for an ‘interaction’ between treatments – does a treatment work even better in the presence of another therapy?

Disadvantages Can be more complicated to undertake leading to a higher potential for error. Interactions can mean some of the sample is lost, which will reduce power for main comparisons.

Example Waters et al. Examined the use of HRT and antioxidant vitamins for treatment of coronary heart disease. Observational data suggest a benefit of HRT and antioxidant vitamins. Sensible to examine effects of both.

Factorial Design HRT and Placebo Vitamins HRT and Vitamins Placebo HRT VitaminsVitamins + Placebo HRT

Analysis The analysis treats the study as two separate trials. All women who got HRT would be compared with those who did not. Likewise all those given vitamins would be compared with who were not given vitamins.

HRT and Vitamin Trial Over 400 women randomise to the 4 treatment arms. Outcomes included surrogate measures (lipid levels angiograms) plus ‘real’ outcomes – death MIs.

Results Both treatments INCREASED the risk of MI and death. NO interaction with treatments suggesting that the risk of death is additive.

WAVE Trial This trial showed YET AGAIN the harmful effect of HRT AND antioxidant vitamins.

RECORD TRIAL RECORD trial is a factorial trial of calcium with or without vitamin D. Key question is whether vitamin D is effective alone or NEEDS calcium to work. Factorial design is specified to look for an interaction.

Record Trial The interaction is important because there are biologically plausible reasons for both treatments to work better in the presence of each other (I.e a positive interaction). Because vitamin D is so inexpensive it is important to know if this effective on its own.

More complications Basic factorial is 2 X 2 but can be increased by infinite number of factors. UK BEAM trial (backpain) uses a 3 x 2 factorial to test: exercise; GP care; manipulation; exercise plus manipulation. Did include another factor making it a 3 x 2 x 2 design.

BEAM trial Factorial design enabled exercise and manipulation questions to be answered in the same trial. Also enables us to look for interactions between treatments.

Factorial Questionnaire Trial Puffer et al undertook a factorial trial comparing single sided questionnaires vs double with one large questionnaire vs 3 separate questionnaires. Outcome was response rates.

Underuse of Factorial trials Factorial trials could be more widely used as they can answer two questions within the same trial, particularly if there is no reason to suspect an interaction. Factorial trials also enable us to ‘tease’ out the different treatment effects. For example, fall prevention programmes are multifactorial and in standard trial we end up not knowing what produces the main effects.

Systematic Review of Factorial Trials Are interactions common in factorial trials? A review of 44 trials found only 1 trial where an interaction would have given the ‘wrong’ answer and 7 trials where there were indications of an interaction (only 2 were statistically significant). Interactions are relatively unusual and therefore factorial trials are probably an efficient trial approach. McAlister et al. JAMA 2003;289:2545.

Split plot design A split plot design is a special form of factorial design, which mixes cluster and individual randomisation.

SAPPHIRE: example of a split plot design.

Analysis of split plot The same as for a factorial. Will be treated as two separate trials. Again giving us two trials for the price of one.

Summary Factorial trials could and should be more widely used. Caution if there is a chance of a negative interaction one may need to avoid them. Can be administratively more difficult.