Sample size calculation with wrong zalpha?

[patrickEinz]

I tried to reproduce the sample size calculations in Table 4 of the Obuchowski paper (2004) for a single ROC curve. For a significance level of 0.05, an expected AUC of 0.7, a desired power of 0.9 and kappa = 1, the sample size calculation should result in 33 patients for each of the two groups.

However,
power.roc.test(auc=0.7, sig.level=0.05, power=0.9, kappa=1.0)
gives ncases = ncontrols = 40.21369 as a result.

Maybe the problem is that inside the function, the z-value for the significance level is calculated by
zalpha <- qnorm(sig.level),
which gives the lower alpha percentile (-1.64 instead of 1.64), not the upper one. I think it should be:
zalpha <- qnorm(sig.level, lower.tail = F) or, of course
zalpha <- qnorm(1 - sig.level)

Thank you very much for your work and for maintaining this great package!

[xrobin]

Thanks for your report!

The Obuchowski (2004) paper describes one-sided tests, in which case pROC returns the expected results:

> power.roc.test(auc=0.7, sig.level=0.05, power=0.9, kappa=1.0, alternative="one.sided")

     One ROC curve power calculation 

         ncases = 32.65397
      ncontrols = 32.65397
            auc = 0.7
      sig.level = 0.05
          power = 0.9

However you are right this is looking weird. I will look into it.

[xrobin]

This is now fixed for the one ROC curve case. Note that resulting values are unchanged and were correct already.

I still need to look into it for the two ROC curves case, where the same mistake apparently occurs.

[xrobin]

Fixed in the 2 ROC curves and list of parameters cases too. It was a good occasion to cleanup the code at the same time.

Again, no difference in the output. But clearer, and more appropriate use of the distributions.

Thanks again for reporting this inconsistency and helping make pROC better.