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I have a database of $P$ patients' hospital encounters over a period of $T$ years. Patient $p \in \{1, 2, \ldots P\}$ visited the clinic $N_p$ times. If patient $p$ was diagnosed with condition C ($C_p = 1$), we record the timestamp of the diagnosis. If no diagnosis was made after the censoring time of $T$ years, we treat them as not having condition C ($C_p = 0$). The prevalence of condition C is small, on the order of 1-3%, and it is possible that some patients may not have been diagnosed, despite having the condition (Type II error). Without having a physician re-examine each $C=0$ patient's charts, notes, etc. (which would involve a lot of manual labor), is there any way to estimate the population type II error rate of the diagnoses? (If it simplifies things, you can assume the type I error rate is 0, but ideally, I would like this to be a free variable.)

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