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Acute infection, if not rapidly and accurately detected, can lead to sepsis, organ failure and even death. Current detection of acute infection as well as assessment of a patient's severity of illness are imperfect. Characterization of a patient's immune response by quantifying expression levels of specific genes from blood represents a potentially more timely and precise means of accomplishing both tasks. Machine learning methods provide a platform to leverage this 'host response' for development of deployment-ready classification models. Prioritization of promising classifiers is dependent, in part, on hyperparameter optimization for which a number of approaches including grid search, random sampling and Bayesian optimization have been shown to be effective. We compare HO approaches for the development of diagnostic classifiers of acute infection and in-hospital mortality from gene expression of 29 diagnostic markers. We take a deployment-centered approach to our comprehensive analysis, accounting for heterogeneity in our multi-study patient cohort with our choices of dataset partitioning and hyperparameter optimization objective as well as assessing selected classifiers in external (as well as internal) validation. We find that classifiers selected by Bayesian optimization for in-hospital mortality can outperform those selected by grid search or random sampling. However, in contrast to previous research: 1) Bayesian optimization is not more efficient in selecting classifiers in all instances compared to grid search or random sampling-based methods and 2) we note marginal gains in classifier performance in only specific circumstances when using a common variant of Bayesian optimization (i.e. automatic relevance determination). Our analysis highlights the need for further practical, deployment-centered benchmarking of HO approaches in the healthcare context.