Confidence Intervals for Binary Responses-R50 & the Logistic Model

Logistic regression is a non-linear method for modeling a binary response variable. For example, y success, failure for blip-scan radar detections. Such responses cannot be modeled using regular linear regression. In our work, many applications of logistic regression present themselves. In the present discussion, models allowing independent slopes and independent intercepts are considered for comparing multiple groups of measures. The question that we consider here is the construction of a confidence interval about the difference in the radar Range 50 R50 values for two logistic curves with each value viz. R1, R0 arising from the separate curve. R50 represents the range at which radar achieves 50 detection probability. This problem is the same as the problem of prediction of the LD50 lethal doseeffective dose 50 value in medical science. We approach the problem analytically using parametric methods. A feature is the use of inverse prediction or calibration methods. Our results are based on the large-sample properties of Maximum Likelihood estimation, and improve on results based on the least-squares model. The application is also given for general RpLp that is, rangedose values not equal to R50. Results for large and small samples are checked against a truth source generated using a Bootstrap program.