Factorial Clinical Trial

A Factorial Clinical Trial is a clinical trial that is a factorial experiment (where two or medical intervention/treatments are administrated simultaneously, patients are assigned randomly to each medical intervention/treatment).

AKA: Fully Crossed Clinical Trial.
Context:
- It can (often) be used to compare the effects of two different medical intervention/treatment.
- It can (sometimes) be used to study the interaction between drugs/treatments.
- It can have advantages, such as:
  - it can study the effect of two or more interventions applied alone or in combination.
  - it is economical as is an efficient way to conduct two trials in one.
- It can have disadvantages, such as:
  - the assumption of no interaction between interventions is often not valid;
  - data monitoring of factorial designs can be complicated;
  - participant recruitment is more complex in factorial trials and can decrease accrual rates.
- …
Example(s):
Counter-Example(s):
See: Washout Period, Clinical Trial Dropout, Group Allocation, Randomization Unit, Clinical Trial Arm, Placebo-Controlled Clinical Trial, Equivalency Clinical Trial, Superiority Clinical Trial, Non-Inferiority Clinical Trial.

References

2022a

(ClinicalTrials.gov, 2021) ⇒ https://clinicaltrials.gov/ct2/about-studies/glossary Retrieved 2022-01-15.
- QUOTE: Factorial assignment: A type of intervention model describing a clinical trial in which groups of participants receive one of several combinations of interventions. For example, two-by-two factorial assignment involves four groups of participants. Each group receives one of the following pairs of interventions: (1) drug A and drug B, (2) drug A and a placebo, (3) a placebo and drug B, or (4) a placebo and a placebo. So during the trial, all possible combinations of the two drugs (A and B) and the placebos are given to different groups of participants.

2022b

(Coursera, 2021) ⇒ "Design and Interpretation of Clinical Trials" (lecture notes).
- QUOTE: In the factorial design, we are testing two or sometimes more experimental interventions simultaneously. So we test treatment A versus the control for treatment A, and we test treatment B versus the control for treatment B. We test the treatments simultaneously, either because it's economical to test the two treatments simultaneously or because, the design can be used to test for interaction between treatments A and B.

**Figure 4: Factorial Design Graph.**

The factorial design can be graphically represented by a two-by-two table. The top row represents participants who were randomized to receive treatment A, and the bottom row represents participants who were randomized to not receive treatment A or to receive the control for treatment A. Similarly, the left column is the people randomized to receive treatment B, and the right column is the people that were randomized to receive the control for treatment B. The cells in the two-by-two table represent the four different combinations that are possible with two treatments, each having its own control group. So on the top left, we have people who are receiving both A and B. In the top right we have people who are receiving A and the control for B. In the bottom left we have people who are receiving B and the control for A, and in the bottom right we have people who are receiving the control for A and the control for B.

To make these comparisons, we use the responses of the people and the margins of the table. In the case where we are interested in the interaction, we have to compare the responses in the cells instead of in the margins. It's important to note that the test for interaction is usually not a powerful test. Unless the sample size is very large, we are likely to have difficulty reliably detecting an interaction between treatments A and B.

To assess the main effect of A, we compare the response of the people in the margin on the far right. That is, the response of those assigned to A, regardless of their assignment to B. We compare that to the response of those assigned to not A, regardless of their assignment to B. We do a similar comparison across the margin at the bottom for those assigned to treatment B versus those assigned to not B. If we are indeed interested in assessing the interaction, we have to compare the effect of A versus not A, and those with B, to the effect of A, versus not A, and those with not B. So we are comparing the cell responses instead of the margin responses.

2022c

(Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/Factorial_experiment Retrieved:2022-1-16.
- In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
  For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2×2 factorial design.
  If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.

2011

(Evans, 2011) ⇒ Scott R. Evans (2011). "Clinical Trial Structures". In: Journal of Experimental Stroke & Translational Medicine, 3(1):8-18.
- QUOTE: Often a research team is interested in studying the effect of two or more interventions applied alone or in combination. In these cases a factorial design can be considered. Factorial designs are attractive when the interventions are regarded as having independent effects or when effects are thought to be complimentary and there is interest in assessing their interaction.
  The simplest factorial design is a 2×2 factorial in which two interventions (factors) are being evaluated, each at two levels (e.g., intervention vs. no intervention). Each study participant is assigned to one level of each of the factors. Four intervention groups are defined based on whether they receive interventions A only, B only, both A and B, or neither A or B. Thus in order to apply the factorial design: (1) you must be able to apply the interventions simultaneously, and (2) it must be ethically acceptable to apply all levels of the interventions (e.g., including placebos if so designed). The factorial design can be viewed as an efficient way to conduct two trials in one. The factorial design is contraindicated when primary interest lies in comparing the two interventions to each other.
  If one can assume that there is no interaction between the two interventions, that is that the effect of one intervention does not depend on whether one receives the other intervention, then a factorial design can be more efficient than a parallel group design. Since factorial designs are economical, they are often employed when sample sizes are expected to be large as in prevention trials. One must first define the scale of measurement and distinguish between additive and multiplicative interaction.
  A limitation of factorial designs is that the assumption of no interaction is often not valid. The effect of one therapy often depends on whether the other therapy is provided(...)
  Interestingly factorial designs are the only way to study interactions when they exist although their efficiency is deminished(...)
  Data monitoring of factorial designs can be complicated. Assigning attribution of the effects during the course of a trial can be difficult(...)
  Participant recruitment is more complex in factorial trials and can decrease accrual rates(...)----