Calibration slope using logistic regression

[spencer keene]

Hello,

The calibration slope is supposed to be estimated by fitting a logistic (logit) regression model in the external data with risk score as the covariate. The binary outcome (e.g. mortality) is the dependent variable and the beta coefficient of the risk score covariate (i.e. independent variable) gives you the calibration slope. So I guess perfect calibration gives you a beta-coefficient of 1.00 on the logit scale (i.e. ln(OR)). Doing this gave me a calibration slope that was too low (0.39).

I then used linear regression with the expected risk and found that it gave a very similar estimate of the calibration slope compared to a lowess graph that I produced (below). But clearly this is not correct as no authors mention this in their publications.



I feel like I am missing something. If someone can walk me through this with codes then that would be amazing.

[Phil Bromiley]

You'll increase your chances of a helpful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. We also don't generally open files.

Assume we are not from your area. Calibration slope probably is discipline specific. It seems you've run a logit of a binary outcome versus one iv. I'm not sure why perfect calibration would give you a coefficient of one - you'll have to work through that. Obviously, that would depend on the scaling of your risk variable. At least with behavioral risk assessments, I'd never expect observers to be properly calibrated. Be sure you're getting the right output (odds ratios or betas vs predicted probabilities). If there is someone you know who does these, check with them. So, you get a lower coefficient than you expect and get a similar result with regression. I might check for outliers on risk but otherwise the results are what they are.