Diagnostic testing: Model estimation and decision support using graphical models

Many agricultural decision problems can be treated within the framework of diagnostic testing. Observations are made sequentially in to order to classify a production unit as normal/unnormal, diseased/healthy etc. The decision problem is to find the optimal classification depending on the observations. The framework is well established and optimal use of such diagnostic testing schemes require considerations concerning the test precision, the cost involved, as well as the potential benefit. Recent developments within graphical modeling ensures that estimation of model parameters as well as the optimisation of decisions can be treated within a coherent framework. The present paper will demonstrate the use of this approach, based on an example from animal production. The problem is to classify a sow as pregnant/non-pregnant. Similar considerations may be made concerning other agricultural production units. Diagnostic tests are usually performed within a sequence of observations with varying precision and costs. Thus, the tests are seldom perfect (gold) indicators of the underlying state. In the pregnancy testing case, the typical sequence is visual heat detection, followed by one or two pregnancy testings using a dedicated electronic measuring device. Hormonal testing is an option as well but is not considered in the paper. The test characteristic is often described using a so called Receiver Operating Characteristic curve (or a ROC curve), showing the relationship between sensitivity and specificity of the test. A major part of the problem is the estimation of parameters describing this curve. The curve depends on the magnitude of different error sources. These error sources can be described using a graphical model, and the model parameters may be estimated using e.g. the Markov Chain Model Carlo method. This estimation is presented in the paper, based on experimental data comparing different devices for pregnancy testing. A small extension of the graphical model leads to an Influence Diagram which in turn leads to the solution of the decision problem. Part of the decision problem is to find the optimal tradeoff between sensitivity and specificity for the testing scheme. The tradeoff can be thought of as the selection of a threshold value. Thus the decision problem is a sequence of decisions concerning threshold values and decisions depending on the test outcome for the individual animals. As illustrated in the paper we need to take the full sequence into account when making optimal decisions both concerning the threshold values