Abstract
Medical research makes intensive use of statistics in order to support its claims. In this paper we make explicit an epistemological tension between the conduct of clinical trials and their interpretation: statistical evidence is sometimes discarded on the basis of an (often) underlined Bayesian reasoning. We suggest that acknowledging the potentiality of Bayesian statistics might contribute to clarify and improve comprehension of medical research. Nevertheless, despite Bayesianism may provide a better account for scientific inference with respect to the standard frequentist approach, Bayesian statistics is rarely adopted in clinical research. The main reason lies in the supposed subjective elements characterizing this perspective. Hence, we discuss this objection presenting the so-called Reference analysis, a formal method which has been developed in the context of objective Bayesian statistics in order to define priors which have a minimal or null impact on posterior probabilities. Furthermore, according to this method only available data are relevant sources of information, so that it resists the most common criticisms against Bayesianism.
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Notes
While Reference analysis is not the only available proposal with which one may establish objective priors, it is certainly a good case study being it a major approach in this field.
It is useful to emphasize that in the context of Bayesian statistics
probability is always a function of two arguments, the event E whose uncertainty is being measured, and the conditions C under which the measurement takes place; “absolute” probabilities do not exist. In typical applications, one is interested in the probability of some event E given the available data D, the set of assumptions A which one is prepared to make about the mechanism which has generated the data, and the relevant contextual knowledge K which might be available. Thus, Pr(E|D, A, K) is to be interpreted as a measure of (presumably rational) belief in the occurrence of the event E, given data D, assumptions A and any other available knowledge K, as a measure of how “likely” is the occurrence of E in these conditions (Bernardo 2003, p. 4).
The reader may refer also to Douglas (2009), where eight different senses of scientific objectivity have been identified.
These are discussed in detail in Sprenger (2017).
The following discussion is heavily influenced by Bernardo and Ramon (1998). Furthermore, it is important to note that this method is invariant under re-parametrization and avoid by construction the issues affecting the principle of insufficient reason.
Reference analysis is just a specific objective method to minimize the subjective component of Bayesian statistics, and other methodologies are also available, e.g. one should consider Jeffreys (1961), Jaynes (1968). It is important to stress that Jeffreys’ priors and reference priors are equivalent in the case of one-dimensional parameters, while they diverge in the multidimensional case.
The reader should refer to Soofi (1994) for a useful introduction to the technical notion of information applied in statistics.
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Acknowledgements
A. Oldofredi is grateful to the Swiss National Science Foundation for financial support (Grant No. 105212-175971).
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Andreoletti, M., Oldofredi, A. We are All Bayesian, Everyone is Not a Bayesian. Topoi 38, 477–485 (2019). https://doi.org/10.1007/s11245-018-9554-4
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DOI: https://doi.org/10.1007/s11245-018-9554-4