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Hybrid model combines frequentist and Bayesian methods to address scenarios such as calibrating knee implants and determining the optimal surgical treatment for melanoma
A study recently published in the journal The American Statistician describes a new statistical method that combines the Bayesian inference and frequentist inference methods into a hybrid statistical model that works better than either method on its own with small sample sizes.
The method was developed by Gang Han, PhD, professor at the Texas A&M University School of Public Health, along with colleagues from Ohio State University, Rutgers University and Georgetown University Medical Center.
The new method, the Bayesian frequentist hybrid inference, is also known as the hybrid Bayesian inference or simply the hybrid inference. The model was developed for situations in which prior information is available for some parameters but not others. This hybrid approach improves on the frequentist inference by including prior information and on the Bayesian inference by reducing the problem of bias introduced by noninformative priors, where the bias can be substantial if the sample size is relatively small.
The authors developed an expectation-maximization algorithm combined with Monte-Carlo Markov Chain to compute the hybrid estimates. They derived the approximation of the hybrid estimates in their algorithm to reduce the computation time. They showed that the approximation is asymptotically valid and demonstrated in three simulation studies having categorical and continuous data that the proposed method outperformed both frequentist and Bayesian inferences with sample sizes ranging from 20 to 500.
Two real-world applications were used in the paper to illustrate the method. In the first example, the researchers sought to improve a biomechanical engineering knee implant design using calibration and tuning parameters, with priors available for calibration but not tuning. The hybrid inference results were similar to those of another method named simultaneous tuning and calibration. The two methods represent different perspectives and could be used to complement each other to improve the implant.
In a second example, the hybrid inference was applied to study the relationship between tumor location and type and the selected surgical approach for treating acral lentiginous melanoma (ALM), a form of skin cancer that can develop on the soles of feet, palms of hands, or under finger or toenails. Due to the small sample size and the interactions between variables, the results of the frequentist inference were unexpected and not consistent with observations of the relationship. However, when the hybrid inference was applied, the results accurately reflected the significance of the relationship, thus overcoming the issues of small sample size and presence of interactions.
The authors state that future research could be conducted to extend the hybrid inference to incorporate other type of inferences, such as M-estimators.
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