Yes, there are several methods to automate the process of finding optimal combinations of biomarkers that can improve diagnostic accuracy while considering cost-effectiveness. One popular method is to use machine learning techniques such as feature selection and ensemble methods.

Feature selection algorithms can automatically identify the most informative subset of biomarkers for a given classification task. These algorithms typically evaluate the relevance and redundancy of each biomarker, and then select the subset of biomarkers that optimize a given performance metric such as accuracy, sensitivity, specificity, or area under the ROC curve (AUC). Some popular feature selection algorithms include recursive feature elimination (RFE), mutual information-based feature selection, and genetic algorithms.

Ensemble methods, on the other hand, combine the predictions of multiple models that are trained on different subsets of biomarkers. This can help reduce the risk of overfitting and improve the generalization performance of the model. Some popular ensemble methods include random forests, gradient boosting, and bagging.

To implement these methods, you can use a variety of machine learning libraries such as scikit-learn in Python or caret in R. These libraries provide a variety of feature selection and ensemble methods that you can use to automate the process of finding optimal biomarker combinations.

It is worth noting that when using machine learning algorithms for feature selection, it is important to use proper cross-validation techniques to ensure that the selected biomarkers generalize well to new data. Additionally, it is important to consider the clinical relevance and cost-effectiveness of the selected biomarkers, as some may be more expensive or difficult to measure than others.

Overall, by using machine learning techniques to automate the process of finding optimal combinations of biomarkers, you can save time and potentially improve the diagnostic accuracy and cost-effectiveness of your study.

In the vein of the above answer you might try something like the attached paper. Best wishes David Booth

Thank you both very much for the answers