Michael Dewey wrote: > At 17:12 09/04/06, Ramón Casero Cañas wrote: > > I am not sure what the problem you really want to solve is but it seems > that > a) abnormality is rare > b) the logistic regression predicts it to be rare. > If you want a prediction system why not try different cut-offs (other > than 0.5 on the probability scale) and perhaps plot sensitivity and > specificity to help to choose a cut-off?
Thanks for your suggestions, Michael. It took me some time to figure out how to do this in R (as trivial as it may be for others). Some comments about what I've done follow, in case anyone is interested. The problem is a) abnormality is rare (Prevalence=14%) and b) there is not much difference in the independent variable between abnormal and normal. So the logistic regression model predicts that P(abnormal) <= 0.4. I got confused with this, as I expected a cut-off point of P=0.5 to decide between normal/abnormal. But you are right, in that another cut-off point can be chosen. For a cut-off of e.g. P(abnormal)=0.15, Sensitivity=65% and Specificity=52%. They are pretty bad, although for clinical purposes I would say that Positive/Negative Predictive Values are more interesting. But then PPV=19% and NPV=90%, which isn't great. As an overall test of how good the model is for classification I have computed the area under the ROC, from your suggestion of using Sensitivity and Specificity. I couldn't find how to do this directly with R, so I implemented it myself (it's not difficult but I'm new here). I tried with package ROCR, but apparently it doesn't cover binary outcomes. The area under the ROC is 0.64, so I would say that even though the model seems to fit the data, it just doesn't allow acceptable discrimination, not matter what the cut-off point. I have also studied the effect of low prevalence. For this, I used option ran.gen in the boot function (package boot) to define a function that resamples the data so that it balances abnormal and normal cases. A logistic regression model is fitted to each replicate, to a parametric bootstrap, and thus compute the bias of the estimates of the model coefficients, beta0 and beta1. This shows very small bias for beta1, but a rather large bias for beta0. So I would say that prevalence has an effect on beta0, but not beta1. This is good, because a common measure like the odds ratio depends only on beta1. Cheers, -- Ramón Casero Cañas http://www.robots.ox.ac.uk/~rcasero/wiki http://www.robots.ox.ac.uk/~rcasero/blog ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
