Logistic regression in medical decision making and epidemiology

In his recent textbook "Primer of Biostatistics", S, A, Glantz refers to the nowadays growing pressure on clinicians for more effective use of medical resources. He asserts that clinicians should be able to make better informed judgements about claims of medical efficacy. They can participate then more intelligently in the debate on how to allocate medical resources. These better informed judgements are the objective of "medical decision making", where the choices to be made in diagnostic and therapeutic strategies are studied Medical decision making is to be based for a great part on statistical reasoning. A statistical approach which has proven to be valuable in this field is a technique known as logistic regression analysis. The assessment of the performance of this logistic model is the subject of this thesis. Applications in medical decision making are considered, mainly with respect to medical diagnosis. Logistic regression analysis may be viewed as a sophisticated diagnostic aid. Multiple test outcomes and patient characteristics are incorporated into a logistic model for the probability that a patient belongs to a certain disease class. Performance of the logistic model in etiologic-epidemiological studies is another area of study. In this context logistic regression is used for the detection of risk factors, ad jus ted for confounding in order to obtain unbiased assessments. This thesis includes ten chapters, consisting of papers which have either been published or which were recently submitted for publication by the author, many of them in cooperation with various colleagues. The chapters have been grouped into three parts. Part 1 (chapter 1) presents a review of developments in logistic regression from 1970 up to 1986. It outlines statistical aspects of the model such as estimation. hypothesis testing and model selection. Part 2 (chapters 2 - 7) deals with logistic discriminant analysis in medical diagnosis. An extensive evaluation of a logistic model for the diagnosis of Crohn's disease by agglutination reactions is presented in chapter 2. Actually, this chapter results from our evolving insights since the first application of logistic discriminant analysis for the diagnosis of Crohn's disease (chapter 3). Comparison of logistic discrimination with some other discriminant analysis methods is studied in chapter 4 through application to real data from clinical practice, and in chapters 5 and 6 through the use of simulated data. This comparative evaluation was performed on datasets consisting of mixtures of continuous and discrete data. The underlying distribution in the first simulation study (chapter 5) is a fourdimensional normal from which discrete variables were obtained by discretizing the continuous variables. The simulation study in chapter 6 is based on a location model. Within each outcome combination of the discrete variables a multivariate normal distribution is assumed. The next chapter concerns the evaluation oflogistic discriminant analysis for modelling QSAR's, quantitative structure- activity relationships (chapter 7). It is used there as a technique for detecting which chemical compounds will be useful for the development of new drugs. The third and final part of this thesis (chapters 8- 10) is concerned with the application and evaluation of the logistic model in etiologic-epidemiological studies, particularly in case-control studies. In chapter 8 the first epidemiologic application of the logistic model in TheN etherlands, which uses estimates of the model parameters based on conditional likelihood, is presented. Risk factors for stroke are investigated in a case-control study conducted some years ago in Tilburg. In chapter 9 the (multiplicative) logistic model is compared with an (additive) linear model for case-control studies with one continuous exposure factor and without consideration of confounding variables. Some aspects concerning variables selection in epidemiologic studies, also relevant for logistic regression, are discussed in chapter 10. The thesis is concluded with a summary. 12