Comparing performance of multinomial logistic regression and discriminant analysis for monitoring access to care for acute myocardial infarction.

One way to monitor patient access to emergent health care services is to use patient characteristics to predict arrival time at the hospital after onset of symptoms. This predicted arrival time can then be compared with actual arrival time to allow monitoring of access to services. Predicted arrival time could also be used to estimate potential effects of changes in health care service availability, such as closure of an emergency department or an acute care hospital. Our goal was to determine the best statistical method for prediction of arrival intervals for patients with acute myocardial infarction (AMI) symptoms. We compared the performance of multinomial logistic regression (MLR) and discriminant analysis (DA) models. Models for MLR and DA were developed using a dataset of 3,566 male veterans hospitalized with AMI in 81 VA Medical Centers in 1994-1995 throughout the United States. The dataset was randomly divided into a training set (n = 1,846) and a test set (n = 1,720). Arrival times were grouped into three intervals on the basis of treatment considerations: <6 hours, 6-12 hours, and >12 hours. One model for MLR and two models for DA were developed using the training dataset. One DA model had equal prior probabilities, and one DA model had proportional prior probabilities. Predictive performance of the models was compared using the test (n = 1,720) dataset. Using the test dataset, the proportions of patients in the three arrival time groups were 60.9% for <6 hours, 10.3% for 6-12 hours, and 28.8% for >12 hours after symptom onset. Whereas the overall predictive performance by MLR and DA with proportional priors was higher, the DA models with equal priors performed much better in the smaller groups. Correct classifications were 62.6% by MLR, 62.4% by DA using proportional prior probabilities, and 48.1% using equal prior probabilities of the groups. The misclassifications by MLR for the three groups were 9.5%, 100.0%, 74.2% for each time interval, respectively. Misclassifications by DA models were 9.8%, 100.0%, and 74.4% for the model with proportional priors and 47.6%, 79.5%, and 51.0% for the model with equal priors. The choice of MLR or DA with proportional priors, or DA with equal priors for monitoring time intervals of predicted hospital arrival time for a population should depend on the consequences of misclassification errors.