sample size single group

[ashar ata]

If I have to estimate the required sample size for an absolute reduction in procedure X1 for diagnosing a disease (by 5%) if instead procedure X2 is instead how should I approach the sample size estimation?

Detail:
Currently procedure X1 is used on everyone but its invasive and also 100% confirmatory (100% sensitivity and 100% specificity).
X2 also has 100% positive predictive value i.e it is confirmatory but very poor sensitivity. If I use procedure X2 before using X1 I will prevent some patients being exposed to procedure X1.

I want this reduction to be at least 5% to justify using X2 before using X1.

how should I approach sample size estimation using any of the stata commands?
Thanks

[Clyde Schechter]

Since X2 has 100% positive predicted value, it, too, must have 100% specificity. So to reduce the number of patient who are subjected to X1, you want X2 to produce 5% fewer positive results than would be the case if we just went to X1. Let's suppose we have 1000 patients. The number of patients who will get X1 if we don't use X2 is 1000. If we use X2, the number who go on to X1 will be sensitivity * prevalence. So the question boils down to determining whether sensitivity * prevalence < 950/1000.

So, you can't go any farther without an estimate of the prevalence of the disease that these tests diagnose. Let's assume you have that. Then the question transforms to determining whether sensitivity of X2 < 950*prevalence/1000 = 0.95*prevalence. So now you need data for the sensitivity of X2. Assuming you will gather data on a random sample of people and test them with both X1 and X2, you will be able to get an estimate of X2's sensitivity from that. So you will be doing a one-sample test of a proportion against a pre-determined value. To pin down a sample size, you will need to specify your type I and type II error probabilities. You can use the -power oneproportion- command for this. Actually, I recommend you do this from the GUI. Select Power and sample-size analysis from the Statistics drop-down menu. Then expand Proportions and select One Sample. From the window that pops up select the Wald test comparing one proportion to a reference value. Fill in the parameters requested, and click Submit, and you'll get your answer.

[ashar ata]

	X1+	X1-
X2+	a	b
X2-	c	d
			n

above is how I see the layout for conducting this study. Everyone gets a X1 and X2. We want to show: a/n>5%. the cell 'b' is essentially 0 given PPV is 100% and Specificity is 100%

If we use X2, the number who go on to X1 will be sensitivity * prevalence

If we use X2 shouldn't the number who go on to get X1 be 1000-(sensitivity * prevalence)?

We are essentially hypothesizing :

1000- (sensitivity * prevalence)>50

the assumed 1000 is the n we need to determine so the above equation becomes:

n-(sensitivity * prevalence)>0.05*n
or
sensitivity*prevalence<0.95*n

So the question boils down to determining whether sensitivity * prevalence < 950/1000.

for n=1000, based on above shouldn't this be: sensitivity * prevalence < 950

Then the question transforms to determining whether sensitivity of X2 < 950*prevalence/1000 = 0.95*prevalence

sensitivity<0.95*prevalence --> sorry this confused me. Could not figure how to conclude this?

So you will be doing a one-sample test of a proportion against a pre-determined value.

Yes I can use power oneproprotion or GUI but to get the sample size but the question remains based on the assumptions above would this provide the required n in the table I show above?
And what is the predetermined value? If I know from preliminary data and existing literature that prevalence is 30% and sensitivity of X2 is about 42%, what is the pre-determined value for which I am doing this one-sample test of proportion? What is the detla I should consider?


power oneproportion 0.05 0.07, test(wald)

.. would this be correct?

[Clyde Schechter]

If we use X2 shouldn't the number who go on to get X1 be 1000-(sensitivity * prevalence)?

Ah, I see. I misunderstood what you were trying to do. You want to use X2 and the only apply X1 to those who come out negative on X2. And you want to be sure that at least 5% of those you test will be in this category. To be X2 positive you must both actually have the disease (since X2 never gives false positives) and get a positive test result, so the probability of that is sensitivity * prevalence, and you want that to exceed 5%.

Now, as with anything based on random sampling, no matter how large your sample size is, you will never have absolute certainty that your result reflects an actual population sensitivity*prevalence of 0.05 or more. You could always have a fluke sample. So you need to decide what probability of getting the wrong answer in either direction is acceptable, with how much margin of error. Those are value judgments based on the utility of getting the answer wrong.