For 7/52 #MEstimatorMonday let's talk about correcting measurement error Here, I am going to think about correcting for measurement error using external data for sensitivity and specificity - ThreadSky

pausalz.bsky.social • 9 days ago

For 7/52 #MEstimatorMonday let's talk about correcting measurement error

Here, I am going to think about correcting for measurement error using external data for sensitivity and specificity

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pausalz.bsky.social•9 days ago

An easy to apply method is the Rogan-Gladen Estimator (no relation to Joe Rogan). The estimator is given by the following, where Y is the gold-standard and Y* is the mismeasured

pausalz.bsky.social•9 days ago

The previous expression indicates that we know sensitivity and specificity perfectly, but this is almost never the case. Instead, we might have some external data available

So, we instead *estimate* sensitivity and specificity. As a result, our variance estimator should include that variability

pausalz.bsky.social•9 days ago

As should be the obvious theme by now, we can use M-estimators and the sandwich variance estimator to incorporate the variability from all the sources

So let's get out stack of estimating equations. For simplicity we will assume that our sensitivity and specificity are transportable across contexts

pausalz.bsky.social•9 days ago

Sensitivity and specificity are then simply conditional means (or proportions). Here R=0 indicates the external observations we are using to estimate sensitivity and specificity

pausalz.bsky.social•9 days ago

To this, we can add the estimating function for the mean of the mismeasured variable in our main data. Below is this conditional probability added to the column vector

pausalz.bsky.social•9 days ago

Finally, we can translate the Rogan-Gladen estimator into an estimating function using a little algebra (left as an exercise for the reader, to be mildly annoying)

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