**Editorial Note**: With this edition of #NephJC, we are introducing a periodic explainer on the stats and epidemiology of the paper we are discussing. Written by Manasi Bapat, with expert input from the methodsman himself, Perry Wilson, we tackle the 2x2 factorial design in this edition. Read, reflect and relish!

Most of us are familiar with standard Randomized Control Trials (RCTs) which have a parallel group design – Intervention/drug vs Placebo control.

So how was the design of the PRESERVE trial different?

PRESERVE trial used a factorial design – this is used when the researchers are interested in studying the effect of two or more interventions applied alone or in combination.

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. An appropriately powered factorial trial is the only design that allows such effects to be investigated.

The simplest factorial design is a 2×2 design which looks at effects of Intervention A (e.g.- Saline or Bicarb) with or without Intervention B (NAC).

These two interventions could have been studied in two separate trials i.e.

**Trial 1- Saline vs Bicarb**

**Trial 2- NAC vs Placebo**

But since the relevant population for both trials is so similar, it makes sense to consider doing them all at once and a factorial design allow us to do exactly that. This design can be an efficient way to conduct two trials in one and hence can also be more economical. Combination of Saline or Bicarb with NAC is of interest particularly because of prior conflicting reports.

### The Catch…

In order to be efficient at evaluating more than one intervention, a factorial trial has to be designed around the degree of certainty one might have in advance, that *there is or isn’t an interaction between two interventions*. If a trial is to have adequate power to detect an interaction, then the sample size will in general need to be increased or the interaction would need to be at least twice as large as the main effects to be detected with the same power. Thus *factorial trials are inherently under powered to detect interactions between two interventions* and such effects are usually investigated as a secondary analysis by introducing appropriate interaction terms.

### Interactions...

Factorial trials allow interpretation of the magnitude of any antagonism or synergism between the interventions, especially if the interaction was the primary effect of interest.

*Interaction goes beyond simple additive effects, it implies synergy*

If intervention A and B combined cause a bigger response than what would be expected with simply adding them (A+B) we can conclude that there is likely a synergistic effect, while if the response is lower when combined they might be causing an antagonistic effect.

Thus the design of a factorial trial should consider whether interactions are possible and appropriately size studies to detect interactions when their existence is unknown.

*Suggested Reading:*

1. Clinical trial structures: Scott R. Evans J Exp Stroke Transl Med. 2010 February 9; 3(1): 8–18. PubMed

2. Hulley et al, Designing Clinical Research, 2nd edition, Lipincott, Williams and Wilkins, 2001

3. Design, analysis and presentation of factorial randomized controlled trials: Montgomery et all BMC Med Res Methodology. 2003; 3: 26.

4. Randomised controlled trials with full factorial designs Sedgwick P, BMJ 2013; 349

5. Factorial Trials: Sedgwick P, BMJ 2010;340