Optimal selection of a battery of tests: a multiobjective optimization methodology

Bayesian decision making based on measurements containing errors

The paper presents a Bayesian approach to the construction of diagnostic and prognostic algorithms, based on the use of several diagnostic factors (tests) in combination. With this approach, the simultaneous use of dichotomous, discrete, categoric, and continuous factors is easy and the resulting algorithms are more efficient than those of other known methods. Moreover, each factor value that is available for use is assumed to represent an estimate (the result of an imperfect measurement) of some (unknown) true value. The proposed method of accounting for measurement errors is advantageous as regards efficiency for users of the algorithm (physicians) if the accuracy of the factor-measurement techniques at their disposal differs from that of the constructor of the algorithm (the scientist). The approach is illustrated by an example, and possible error models and methods of collecting statistical data are discussed.

Testing for fetal pulmonary maturity: ROC analysis involving covariates, verification bias, and combination testing

The lecithin/sphingomyelin ratio (L/S) and the measured value of saturated phosphatidylcholine (SPC), amniotic fluid determinations obtained to assess fetal pulmonary maturity, were evaluated with receiver operating characteristic (ROC) curve analysis. The effects of covariates on the ROC curves were analyzed with a regression methodology that took into account all the available data when constructing an ROC curve for each subgroup. To correct for verification bias the authors used a logistic regression analysis to model the probability of verification, thereby permitting correction for verification bias of a fully stratified data set in spite of small cell frequencies. They examined combination testing with prediction rules using prospective logistic modeling, including as variables test results and clinical features. The L/S was found to be significantly better than SPC for assessing fetal pulmonary maturity. For older gestational age the L/S and SPC performed better than for younger gestational age. Contamination of the specimen degraded the ROC curves. Correcting for verification bias did not influence the ROC curves significantly but changed the cutoff value of the test variable for any particular operating point. Prediction rules to evaluate combination testing showed that obtaining the SPC level in addition to the L/S ratio added no significant information compared with the L/S only. Including gestational age in the prediction rule of either test improved the prediction.

Threshold analysis using diagnostic tests with multiple results

Clinical problems represented by decision trees can be analyzed in terms of the probability threshold model, which provides management recommendations based on the prior probability of disease, the test threshold, and the test-treatment threshold. As originally proposed, the threshold model assumes that diagnostic tests provide information about a single event that is relevant to the decision. For some problems, however, a diagnostic test may provide information about more than one such event (e.g., a computed tomography [CT] scan gives information about both mediastinal and hilar metastases in lung cancer). The authors extend the probability threshold model to cases in which a single test provides information about two events that are relevant to the decision. They derive four thresholds that determine the best strategy for any combination of test results. The approach is illustrated for the decision to use a CT scan to stage lung cancer. The analysis reveals that: 1) the range of prior probabilities for which testing is optimal increases; 2) for some prior probabilities only test results about one event are important; 3) for some prior probabilities test results about both events are important; and 4) failure to account fully for information provided by a test can lead to erroneous test and treatment recommendations.