A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

RELATIONSHIP OF ANTISOCIAL PERSONALITY SYNDROME IN BOYS TO PARENTAL ALCOHOL/DRUG DEPENDENCY

The study focused on the relationship between antisocial personality syndrome in boys ages 8-15 and parental alcohol/drug dependency. The population studied was case records of 101 boys coming to a private psychiatrist from 1966 through 1979. The boys were predominantly white and from middle to upper income families.^ A boy was determined to have antisocial personality syndrome if he exhibited antisocial behaviors in four or five major categories, did not exhibit a brain syndrome, and did not exhibit a thought disorder. The five major behavior categories were: (1) self-control (i.e., temper tantrums or hyperactivity), (2) behavior at home (i.e., disobedience or lying), (3) behavior at school (i.e., truancy or cheating), (4) behavior toward peers (i.e., bullying, fighting, or tattling), and (5) behavior against property (i.e., destructiveness or stealing). A boy was determined to be a control if he exhibited antisocial behaviors in two or less behavior categories.^ A parent was determined to have alcohol/drug dependency if s/he exhibited a score above the established threshold (1) for the MacAndrew Alcoholism Scale (28 or above), and (2) for the Holmes Alcoholism Scale (35 or above) which are used with the MMPI. A parent was classified not alcohol/drug dependent if s/he had scores below set thresholds (22 on the MacAndrew Alcoholism Scale and 28 on the Holmes Alcoholism Scale).^ For the final sample (N = 10), there was no reason to believe a relationship exists between antisocial personality syndrome in boys ages 8-15 and parental alcohol/drug dependency (Fisher's Exact Test {FET} P = 1.0). The small sample size primarily occurred as a result of 88.12% of the parents being classified in a questionable category in terms of alcohol/drug dependency.^ The sample was suggestive of a relationship between the fathers' Psychopathic Deviate (Pd) Scale scores as a measure of antisocial tendencies and the boy having antisocial personality syndrome (N = 75; P = .12). There was no evidence of such a relationship for mothers (N = 75; P = .97). ^