Statistical Inference and the Plethora of Probability Paradigms: A Principled Pluralism

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability

The epistemology of the SARS-CoV-2 test

We investigate the epistemological consequences of a positive SARS-CoV-2 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 sole cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, given a positive SARS-CoV-2 test, what should we believe about the hypothesis and to what degree? Second, how much evidence does a positive test provide for a 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 for realistic assumptions about the base rate of infected individuals, P(V)≲20%, positive tests having low specificity (75%) would not raise the posterior probability for V to more than 50%. Furthermore, if the test specificity is less than 88.1%, even a positive test having 95% sensitivity would only yield weak to moderate evidence for V against ¬V. We also find that in plausible scenarios, positive tests would only provide weak to moderate evidence for C unless the tests have a high specificity. One has thus to be careful in ascribing the symptoms or death of a positively tested patient to SARS-CoV-2, if the possibility exists that the disease has been caused by another pathogen

Emergence and evidence: a close look at Bunge’s philosophy of medicine

In his book “Medical Philosophy: Conceptual issues in Medicine“, Mario Bunge provides a unique account of medical philosophy that is deeply rooted in a realist ontology he calls “systemism”. According to systemism, the world consists of systems and their parts, and systems possess emergent properties that their parts lack. Events within systems may form causes and effects that are constantly conjoined via particular mechanisms. Bunge supports the views of the evidence-based medicine movement that randomized controlled trials (RCTs) provide the best evidence to establish the truth of causal hypothesis; in fact, he argues that only RCTs have this ability. Here we argue that Bunge neglects the important feature of patients being open systems which are in steady interaction with their environment. We show that accepting this feature leads to counter-intuitive consequences for his account of medical hypothesis testing. In particular, we point out that (i) the confirmation of hypotheses is inherently stochastic and affords a probabilistic account of both confirmation and evidence which we provide here; (ii) RCTs are neither necessary nor sufficient to establish the truth of a causal claim; (iii) testing of causal hypotheses requires taking into account background knowledge and the context within which an intervention is applied. We conclude that there is no “best” research methodology in medicine, but that different methodologies should co-exist in a complementary fashion

The epistemology of the SARS-CoV-2 test

We investigate the epistemological consequences of a positive SARS-CoV-2 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 sole cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, given a positive SARS-CoV-2 test, what should we believe about the hypothesis and to what degree? Second, how much evidence does a positive test provide for a 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 for realistic assumptions about the base rate of infected individuals, P(V)≲20%, positive tests having low specificity (75%) would not raise the posterior probability for V to more than 50%. Furthermore, if the test specificity is less than 88.1%, even a positive test having 95% sensitivity would only yield weak to moderate evidence for V against ¬V. We also find that in plausible scenarios, positive tests would only provide weak to moderate evidence for C unless the tests have a high specificity. One has thus to be careful in ascribing the symptoms or death of a positively tested patient to SARS-CoV-2, if the possibility exists that the disease has been caused by another pathogen

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 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 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

Emergence and evidence: a close look at Bunge’s philosophy of medicine

In his book “Medical Philosophy: Conceptual issues in Medicine”, Mario Bunge provides a unique account of medical philosophy that is deeply rooted in a realist ontology he calls “systemism”. According to systemism, the world consists of systems and their parts, and systems possess emergent properties that their parts lack. Events within systems may form causes and effects that are constantly conjoined via particular mechanisms. Bunge supports the views of the evidence-based medicine movement that randomized controlled trials (RCTs) provide the best evidence to establish the truth of causal hypothesis; in fact, he argues that only RCTs have this ability. Here, we argue that Bunge neglects the important feature of patients being open systems which are in steady interaction with their environment. We show that accepting this feature leads to counter-intuitive consequences for his account of medical hypothesis testing. In particular, we point out that (i) the confirmation of hypotheses is inherently stochastic and affords a probabilistic account of both confirmation and evidence which we provide here; (ii) RCTs are neither necessary nor sufficient to establish the truth of a causal claim; (iii) testing of causal hypotheses requires taking into account background knowledge and the context within which an intervention is applied. We conclude that there is no “best” research methodology in medicine, but that different methodologies should coexist in a complementary fashion

Simpson's Paradox and Causality

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based approaches are compared by means of an experiment to show that SP is not basically causal

Emergence and evidence: a close look at Bunge’s philosophy of medicine

In his book “Medical Philosophy: Conceptual issues in Medicine“, Mario Bunge provides a unique account of medical philosophy that is deeply rooted in a realist ontology he calls “systemism”. According to systemism, the world consists of systems and their parts, and systems possess emergent properties that their parts lack. Events within systems may form causes and effects that are constantly conjoined via particular mechanisms. Bunge supports the views of the evidence-based medicine movement that randomized controlled trials (RCTs) provide the best evidence to establish the truth of causal hypothesis; in fact, he argues that only RCTs have this ability. Here we argue that Bunge neglects the important feature of patients being open systems which are in steady interaction with their environment. We show that accepting this feature leads to counter-intuitive consequences for his account of medical hypothesis testing. In particular, we point out that (i) the confirmation of hypotheses is inherently stochastic and affords a probabilistic account of both confirmation and evidence which we provide here; (ii) RCTs are neither necessary nor sufficient to establish the truth of a causal claim; (iii) testing of causal hypotheses requires taking into account background knowledge and the context within which an intervention is applied. We conclude that there is no “best” research methodology in medicine, but that different methodologies should co-exist in a complementary fashion