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Is there anybody who can tell me or explain to me about finding the Type 1 error for a Bayesian clinical trial. Of a 100 patients I need 59 successful patients to exceed my posterior threshold. I have been able to work this through R but now am stuck trying to find the probability Type 1 error for these 59 successes. I know the value should be ~ 0.044, but has to how to find this value I am unsure. Any help please.

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  • $\begingroup$ To compute type I error you need to fully describe the sample space, including the schedule of intended looks at the data even if these looks are never taken, and including any indeterminism in the sample size. $\endgroup$ Commented Jun 26, 2013 at 16:06
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    $\begingroup$ On a more philosophical note -- formally, type I errors are defined within the Pearson-Neyman decision / hypothesis testing framework, which is not compatible with the Bayesian approach. $\endgroup$
    – January
    Commented Jun 26, 2013 at 16:40
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    $\begingroup$ @January, "not compatible" is too strong. Bayesian Adaptive Methods for Clinical Trials has a lot of information about computing Type I errors under Bayesian adaptive designs. $\endgroup$
    – Cyan
    Commented Jul 1, 2013 at 3:45

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Formulate a sampling model (or preferably, a bunch) in which the null hypothesis is true. Try the model used in the Bayesian adaptive part, plus different dependence structures, missing covariates, anything that breaks model assumptions in plausible ways -- especially ways that might inflate the "success" rate under the Bayesian model.

Simulate the trial under each of these different models a large number of times, say 10,000 or 100,000. The relative frequency with which the trial gets >59 successful patients is a Monte Carlo estimate of the Type I error rate under the assumed model.

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