The Epistemology of a Positive SARS-CoV-2 Test.

We investigate the epistemological consequences of a positive polymerase chain reaction SARS-CoV test for two relevant hypotheses: (i) V is the hypothesis that an individual has been infected with SARS-CoV-2; (ii) C is the hypothesis that SARS-CoV-2 is the cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, how much confirmation does a positive test lend to each hypothesis? Second, how much evidence does a positive test provide for each hypothesis against its negation? We respond to each question within a formal Bayesian framework. We construe degree of confirmation as the difference between the posterior probability of the hypothesis and its prior, and the strength of evidence for a hypothesis against its alternative in terms of their likelihood ratio. We find that test specificity-and coinfection probabilities when making inferences about C-were key determinants of confirmation and evidence. Tests with < 87% specificity could not provide strong evidence (likelihood ratio > 8) for V against ¬V regardless of sensitivity. Accordingly, low specificity tests could not provide strong evidence in favor of C in all plausible scenarios modeled. We also show how a positive influenza A test disconfirms C and provides weak evidence against C in dependence on the probability that the patient is influenza A infected given that his/her symptoms are not caused by SARS-CoV-2. Our analysis points out some caveats that should be considered when attributing symptoms or death of a positively tested patient to SARS-CoV-2.

Application of Bayesian evidence synthesis to modelling the effect of ketogenic therapy on survival of high grade glioma patients.

BACKGROUND: Ketogenic therapy in the form of ketogenic diets or calorie restriction has been proposed as a metabolic treatment of high grade glioma (HGG) brain tumors based on mechanistic reasoning obtained mainly from animal experiments. Given the paucity of clinical studies of this relatively new approach, our goal is to extrapolate evidence from the greater number of animal studies and synthesize it with the available human data in order to estimate the expected effects of ketogenic therapy on survival in HGG patients. At the same time we are using this analysis as an example for demonstrating how Bayesianism can be applied in the spirit of a circular view of evidence. RESULTS: A Bayesian hierarchical model was developed. Data from three human cohort studies and 17 animal experiments were included to estimate the effects of four ketogenic interventions (calorie restriction/ketogenic diets as monotherapy/combination therapy) on the restricted mean survival time ratio in humans using various assumptions for the relationships between humans, rats and mice. The impact of different biological assumptions about the relevance of animal data for humans as well as external information based on mechanistic reasoning or case studies was evaluated by specifying appropriate priors. We provide statistical and philosophical arguments for why our approach is an improvement over existing (frequentist) methods for evidence synthesis as it is able to utilize evidence from a variety of sources. Depending on the prior assumptions, a 30-70% restricted mean survival time prolongation in HGG patients was predicted by the models. The highest probability of a benefit (> 90%) for all four ketogenic interventions was obtained when adopting an enthusiastic prior based on previous case reports together with assuming synergism between ketogenic therapies with other forms of treatment. Combinations with other treatments were generally found more effective than ketogenic monotherapy. CONCLUSIONS: Combining evidence from both human and animal studies is statistically possible using a Bayesian approach. We found an overall survival-prolonging effect of ketogenic therapy in HGG patients. Our approach is best compatible with a circular instead of hierarchical view of evidence and easy to update once more data become available.