Assess statistical significance of two PPVs

Assess significance of the difference between two PPVs

I recently validated a medical diagnosis in order to compose a study population. To do so, we classified each patient with a diagnosis of interest as probable, possible, or unlikely case, depending on how likely we believed the diagnosis to actually be true.

I then calculated two different PPVs, one probable vs. unlikely and the other possible vs. unlikely, and I would now like to test if the resulting PPVs are statistically significantly different from each other. The numbers are indicated below (++ true positives, +- false positives, -+ false negatives, -- true negatives):

Probable vs unlikely: ++45 +-6 -+0 --11 PPV 0.88 (95% CI 0.79-0.97)

Possible vs unlikely: ++48 +-8 -+0 --11 PPV 0.86 (95% CI 0.77-0.95)

What test do I have to use to see if the difference between the two PPVs is statistically significant?

Thanks for your help. I hope the information above is sufficient.
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Less is more. Stay pure. Stay poor.
First, you may want to reevaluate level of significance value, in that you have multiple comparisons. This is given you have not already done this.
Thank you for your response. Sadly, I do not understand what you mean by 'reevaluate level of significance value, in that you have multiple comparisons'.

On a further note: From the things I have read so far it seems like the Pearson chi-square test might be a possible way to assess the equality of the two PPVs. Is this possible?
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