**2. Bayesian approaches in clinical decision making**

#### **2.1 Clinicians and statistics**

Health-care professionals at all levels of training and expertise often struggle with conceptualizing many statistical and probability ideas [17, 18]. Even for the most experienced mathematicians, the complex calculations involved in large decision making scenarios using Bayesian approaches are hard to comprehend, far less compute [13].

To follow Bayesian approaches in clinical decision making, it does require the understanding of some key statistical concepts. We hope to present this in an easy to follow format that is based in evidence [19].

The widely referenced Harvard Medical School cognitive experiment (see Appendix A) (and the research which followed) has provided much useful insight into how we approach probability testing. Two of these insights are:

**13**

*Application of Bayesian Principles to the Evaluation of Coronary Artery Disease...*

i.Medical professionals often fall victim to what is referred to as the "base-rate neglect" fallacy. Here-in they place unwarranted reliability to the outcome of a test—positive or negative, ignoring the relevance of prevalence in the population.

Stated differently: A positive test result for a rare disease is more likely to be a false positive, regardless of how well the test can detect the presence of disease (sensitivity). The converse is also true, that a negative test result in a population in

ii.When results are presented as frequencies rather than probabilities, they are easier to follow. Take this example from Fenton and colleagues [13]:

1.Out of 1 million people 1000 are likely to die from treatment A, but only

2.The probability of dying from treatment A is 0.001, but the probability

Before applying Bayes' theorem to the evaluation of chest pain, we will review some of the key statistical and probability concepts necessary to gain an under-

There are a few characteristics of diagnostic tests which are paramount to the understanding and use of Bayesian arguments. These include sensitivity, specificity, positive predictive value, negative predictive value and likelihood ratios. There are

Sensitivity and specificity are often explained in complex statistical terminol-

• **Sensitivity (Sens.):** The ability to pick up disease when disease is present

• **Specificity (Spec.):** The ability to rule out disease when there is no disease

Let us use the example of a hypothetical test designed to detect patients with

The sensitivity and specificity of any test or maneuver are usually compared to a "gold-standard" test. In the case of suspected coronary artery disease, that test is

In clinical practice, it is often more helpful to gauge the performance of a test based on the prevalence of the disease of interest. This introduces the concepts of

CAD called 'CAD Finder'. We have two Groups of patients, Groups A and B (**Figure 1**). The 100 patients in Group A have proven CAD and the 100 in Group B are proven to be without CAD. To measure the sensitivity of the 'CAD Finder' we use it on patients in Group A and see how many have a positive result (93%). This is the sensitivity of the 'CAD Finder' for picking up CAD. To measure specificity, we perform the 'CAD Finder' on Group B and see how many have a negative result (80%). This would be the specificity for the 'CAD Finder' for ruling out CAD. It should also be noticed that, 7 out of 100 patients with CAD will falsely test negative

which there is a very high prevalence, is more likely to be a false negative.

10 are likely to die from treatment B.

of dying from treatment B is 0.00001.

many factors which influence the reliability or these values.

and 20 out of 100 without CAD will get a false positive result.

*DOI: http://dx.doi.org/10.5772/intechopen.89440*

Instead of:

standing of Bayesian approaches.

invasive coronary angiography.

positive and negative predictive value [15].

**2.2 The characteristics of diagnostic tests**

ogy, however, they can be defined very simply:

*Application of Bayesian Principles to the Evaluation of Coronary Artery Disease... DOI: http://dx.doi.org/10.5772/intechopen.89440*

i.Medical professionals often fall victim to what is referred to as the "base-rate neglect" fallacy. Here-in they place unwarranted reliability to the outcome of a test—positive or negative, ignoring the relevance of prevalence in the population.

Stated differently: A positive test result for a rare disease is more likely to be a false positive, regardless of how well the test can detect the presence of disease (sensitivity). The converse is also true, that a negative test result in a population in which there is a very high prevalence, is more likely to be a false negative.

	- 1.Out of 1 million people 1000 are likely to die from treatment A, but only 10 are likely to die from treatment B.

Instead of:

*Differential Diagnosis of Chest Pain*

(iv) increase in health care costs.

need for further testing.

ments in the new era of precision medicine.

follow format that is based in evidence [19].

**2.1 Clinicians and statistics**

compute [13].

**2. Bayesian approaches in clinical decision making**

We aim to cover the following in our chapter review:

test likelihood and test characteristics.

testing, conflict with Bayesian principles.

to further increase certainty. Evaluation of chest pain has been no different. The number of available testing strategies has increased over the last few decades, and the technologies underlying these tests are constantly being refined. Despite the growing number of options, many clinicians remain unsure how to utilize these modalities [5, 11]. The increasing utilization of these tests often leads to: (i) further investigation, (ii) physician and patient uncertainty/anxiety [12], (iii) harm and

i.Briefly simplify the principles of Bayes' theorem. Give a brief overview of the concepts of how the post-test probability of disease varies based on pre-

ii.Review key stratification methods for the likelihood of significant CAD.

iv.Use practical examples to show how the use of low sensitivity/specificity testing in varying patient groups can lead to post-test uncertainty and the

iii.Outline the test characteristics of the main functional and anatomic imaging modalities used in chest pain evaluation based on available evidence.

v.Explain how many of the currently available appropriate use criteria guiding

Bayes' theorem has been previously applied in many clinical scenarios, including the evaluation of chest pain [13–16]. This chapter will neither be burdened with complex statistical formulas nor difficult to follow calculations. Rather, it will provide a practical approach to decision making and dealing with diagnostic uncertainty in patients with stable chest pain. Though many of the concepts expressed here are not original to the authors, we hope that this review will provide a comprehensive approach to testing—considering patient outcomes and resource utilization. The almost three century old principles of the Bayesian approach to decision making are just as relevant today with the growing technological advance-

Health-care professionals at all levels of training and expertise often struggle with conceptualizing many statistical and probability ideas [17, 18]. Even for the most experienced mathematicians, the complex calculations involved in large decision making scenarios using Bayesian approaches are hard to comprehend, far less

To follow Bayesian approaches in clinical decision making, it does require the understanding of some key statistical concepts. We hope to present this in an easy to

The widely referenced Harvard Medical School cognitive experiment (see Appendix A) (and the research which followed) has provided much useful insight

into how we approach probability testing. Two of these insights are:

**12**

2.The probability of dying from treatment A is 0.001, but the probability of dying from treatment B is 0.00001.

Before applying Bayes' theorem to the evaluation of chest pain, we will review some of the key statistical and probability concepts necessary to gain an understanding of Bayesian approaches.

#### **2.2 The characteristics of diagnostic tests**

There are a few characteristics of diagnostic tests which are paramount to the understanding and use of Bayesian arguments. These include sensitivity, specificity, positive predictive value, negative predictive value and likelihood ratios. There are many factors which influence the reliability or these values.

Sensitivity and specificity are often explained in complex statistical terminology, however, they can be defined very simply:


Let us use the example of a hypothetical test designed to detect patients with CAD called 'CAD Finder'. We have two Groups of patients, Groups A and B (**Figure 1**). The 100 patients in Group A have proven CAD and the 100 in Group B are proven to be without CAD. To measure the sensitivity of the 'CAD Finder' we use it on patients in Group A and see how many have a positive result (93%). This is the sensitivity of the 'CAD Finder' for picking up CAD. To measure specificity, we perform the 'CAD Finder' on Group B and see how many have a negative result (80%). This would be the specificity for the 'CAD Finder' for ruling out CAD. It should also be noticed that, 7 out of 100 patients with CAD will falsely test negative and 20 out of 100 without CAD will get a false positive result.

The sensitivity and specificity of any test or maneuver are usually compared to a "gold-standard" test. In the case of suspected coronary artery disease, that test is invasive coronary angiography.

In clinical practice, it is often more helpful to gauge the performance of a test based on the prevalence of the disease of interest. This introduces the concepts of positive and negative predictive value [15].

#### **Figure 1.**

*Percentage of persons classified with and without CAD by the CAD finder.*


PPV and NPV vary inversely with the prevalence of a disease in a population. The relevance of this becomes apparent when tests which have been "studied" in a subgroup are applied in another population with different characteristics and disease prevalence. This brings us to our final concept worth defining:

• **Likelihood ratios:** "the likelihood that a given test result would be expected in a patient with the target disorder compared to the likelihood that that same result would be expected in a patient without the target disorder." [20]

Using the formula:

LR+ = sensitivity/(1-specificity).
