# 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?