Factorial Designs

1
Factorial Designs
2
Background

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

3
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?

4
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.

5
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.

6
Factorial Design
HRT and Placebo Vitamins HRT and Vitamins
Placebo HRT Vitamins Vitamins Placebo HRT
7
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.

8
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.

9
Results

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

10
WAVE Trial

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

11
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.

12
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.

13
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.

14
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.

15
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.

16
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.

17
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 20032892545.
18
Split plot design

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

19
SAPPHIRE example of a split plot design.
20
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.

21
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.