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Prediction is an important task in clinical fields. There has been increased interest in using neural networks (NNs) as a potential alternative to multivariate regression models for predicting clinical outcomes. We applied logistic regression and NNs to a real medical data set to estimate the probabilities of nosocomial infection in patients admitted to intensive care units. Their predictive performances were assessed by data-splitting. We described how to deal with medical data to improve the predictive performance of NNs and discussed the advantages and disadvantages of NNs versus logistic regression for predicting clinical outcomes. If we take appropriate measures against the disadvantages of NNs, NNs will probably outperform multivariate regression models. [ABSTRACT FROM AUTHOR]

This article presents information related to notes on applied logistic regression analysis. Although the relationship being modeled often represents a causal relationship in which the single predicted variable is believed to be an effect of the one or more predictor variables, this is not always the case. One can as easily predict a cause from an effect as predict an effect from a cause. Throughout this monograph, the emphasis is on predictive rather than causal relationships, although the language of causal relationships is sometimes employed. Describing a variable as independent or dependent, therefore, or as an outcome or a predictor, does not necessarily imply a causal relationship. Instead, all relationships should be regarded as definitely predictive, but only possibly causal in nature. Data are taken from the National Youth Survey, a national household probability sample of individuals who were adolescents in 1976 and young adults in 1992.

This article presents information related to polytomous logistic regression. Logistic regression analysis may be extended beyond the analysis of dichotomous variables to the analysis of categorical dependent variables with more than two categories. In the literature on logistic regression, the resulting models have been called polytomous or multinomial logistic regression models. Here, the terms dichotomous and polytomous will be used to refer to logistic regression models and the terms binomial and multinomial will be used to refer to logit models from which polytomous logistic regression models may be derived. For polytomous dependent variables, the logistic regression model may be calculated as a special case of the multinomial logit model. Mathematically, th extension of the dichotomous logistic regression model to polytomous dependent variables is straightforward. One value of the dependent variable is designated as the reference category, Y = h0 and the probability of membership in other categories is compared to the probability of membership in the reference category.

This article presents information related to logistic regression diagnostics. When the assumptions of logistic regression analysis are violated, calculation of a logistic regression model may result in one of three problematic effects: biased coefficients, inefficient estimates, or invalid statistical inferences. Bias refers to the existence of a systematic tendency for the estimated logistic regression coefficients to be too high or too low, too far from 0, or too close to 0, compared to the true values of the coefficients. Inefficiency refers to the tendency of the coefficients to have large standard errors relative to the size of the coefficient. This makes it more difficult to reject the null hypothesis even when the null hypothesis is false. Invalid statistical inference refers to the situation in which the calculated statistical significance of the logistic regression coefficients is inaccurate. In addition, high leverage cases, cases with unusually high or low values on the independent variables, or outliers with unusual values on the dependent variable, given the values of the independent variables, may be influential cases that exert a disproportionate influence on the estimated parameters.

This article presents information about interpreting the logistic regression coefficients. In linear regression analysis one evaluates the contribution of each independent variable to the model by testing for its statistical significance and then examining the substantive significance of its effect on the dependent variable. Statistical significance is evaluated using an F or t statistic to produce a probability (p) that one would find this strong a relationship in a sample this large if there really were no relationship between the independent variable and the dependent variable. Substantive significance may be evaluated in one of several ways. One may examine the unstandardized regression coefficient to see whether the change in the dependent variable associated with a given amount of change in the independent variable is large enough to be concerned. One must have an idea beforehand how big a change needs to be before one is concerned with it and equivalently how big a change one is willing to ignore.

This article presents information related to summary statistics for evaluating the logistic regression model. When one evaluates a linear regression model, the evaluation typically has three parts. In linear regression analysis one needs to know (a) whether knowing the values of all of the independent variables put together allows one to predict the dependent variable any better than if one had no information on any of the independent variables and, if so, (b) how well the independent variables as a group explain the dependent variable. For logistic regression, one also may be interested in the frequency of correct as opposed to incorrect predictions of the exact value of the dependent variable, in addition to how well the model minimizes errors of prediction. In linear regression, when the dependent variable is assumed to be measured on an interval or ratio scale, it would be neither alarming nor unusual to find that none of the predicted values of the dependent variable exactly matched the observed value of the dependent variable.

This article presents information related to references to the journal. "Categorical data," analysis by A. Agresti, "Statistical Methods for the Social Sciences," by A. Agresti and B. Finlay. "Logistic Regression Using the SAS system," by P.D. Allison, "Calculation of Polychotomous Logistic Regression Parameters Using Individualized Regressions," by C.B. Begg and R. Grey, "Comparison of Stopping Rules in Forward Regression," by R.B. Bendel and A.A. Afifi, "Understanding Regression Assumptions," by W.D. Berry, " Multiple Regression in Practice,." BY W.D. Berry and S. Feldman, "Statistics for Social Data Analysis," by G.W. Bohrnstedt and D. Knoke, "Structural Equation Models With Latent Variables," by K.A. Bollen, "Principles of Statistics," by M.G. Bulmer, "Statistical Equation Models With Latent Variables," by C.C. Clogg and E.S. Shihadeh, "Criteria for Measures of Association," by H.L. Costner, "The Analysis of Binary Data," by J.G. Cragg and R. Uhler, "The Demand for Automobiles," by J.G. Cragg and R. Uhler, "Loget Modeling," by A. DeMaris.

This article presents information related to appendix probabilities. The probability of an event is estimated by its relative frequency in a population or sample. The joint probability of two independent events is the product of their individual probabilities. For example, the probability that both X and Y are equal to 1, if X and Yare unrelated is P(Y=l and X= 1)=P(Y= 1) x P(X = 1). If X and Y are related (for example, if the probability that Y is equal to 1 depends on the value of X), then P(Y = 1 and X = 1) will not be equal to P(Y = 1)xP(X = 1). Instead, one will want to consider the conditional probability that Y = I when X = 1, or P(Y = 1/ X = 1). The conditional probability that Y = 1 is the probability that Y = 1 for a given value of some other variable. In this context, one may sometimes refer to P(Y = 1), the probability that Y = 1 regardless of the value of any other variable, as the unconditional probability that V =1.