# Does an interim sample size re-estimation increase type 1 error if based on the overall event rate?

Suppose that a sample size is to be calculated for a trial: a presumed effect size summarizes the effect of intervention (relative risk RR $$\exp(\theta_1)$$), and background gives the rate of events in the control arm (say a risk R $$\exp(\theta_0)$$).

It's found that $$N$$ patients would need to be recruited over some years, over which an expected $$n events are expected to occur: $$\exp(\theta_0) N/2$$ as per the control-arm incidence and $$\exp(\theta_0 + \theta_1) N/2$$ in the treatment to have 85% power.

If during the course of the trial, investigators inspect the distribution of events in a blinded fashion and find it is some value $$m < n$$, is it reasonable to re-estimate $$\theta_0$$ to fit the event rate and increase enrollment to increase chances of statistically significant findings?

My thought is that if the intervention is highly effective, you would conclude that the frequency of outcome was much lower than expected and recruit more people to the study when you could do with recruiting less.

Is there a way to reliably update sample size/power without unblinding a study using an interim analysis?

## 1 Answer

There's an extensive literature on this you can find easily e.g. via Google scholar. It seems that simulations indicate that sample size reestimation on blinded event rates is fine (see this paper or this one or this one).

• I agree that if sample re-estimation is conducted before unblinding type I error is not inflated. Mar 9, 2019 at 11:22
• Promising links. Paywalled though, and I think site rules ask for not link-only answer. The Friede paper seems to be right on track, but I am curious what they say about the importance of correctly guessing the effect size at re-estimation. Mar 18, 2019 at 13:59