Factorial Clinical Trial

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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).



References

2022a

2022b

2022 FactorialDesign Fig4.png
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