Pauker & Kassirer Test-Treatment Threshold Methodology
The purpose of this calculator is gain a better understanding of the components involved in the Pauker & Kassirer "threshold approach" to clinical decision-making. Users can explore how interpretation of the available evidence for high risk conditions and the evaluation of pre-test probability can affect diagnostic and management decisions.
The Pauker & Kassirer (1980) threshold approach is a framework for decision-making in situations where the clinician needs to decide whether to perform further testing, treat without testing, or withhold further investigation. The calculation incorporates data about the risks and benefits of disease treatment, the risks of testing, and the reliability of the test (false-positive and false-negative rates), each represented as probabilities.
Using the equations presented below, two thresholds are calculated: the "testing" threshold and the "test-treatment" threshold:
Testing Threshold (Tt): "The probability of disease at which there is no difference between the value of withholding treatment and that of performing the test"
Test-Treatment Threshold (Ttx): "The probability of disease at which there is no difference between the value of performing the test and that of administering treatment"
The probability of disease is derived from the pre-test probability. It can be estimated from the observed prevelence of disease in the study population (e.g. ~10% of patients presenting with headache have SAH) or clinical assumptions (e.g., < 15% gestalt risk for pulmonary embolism).
In clinical practice, we often perform tests in sequence depending on the assessment of the reliability of the first test to exclude the disease in question (e.g., CT → LP for SAH, or clinical assessment → D-dimer or PERC → CTPA for PE). In these cases, the post-test probability from the first test or decision tool becomes the pre-test probability for the second test decision. Bayes' theorem can be used to calculate the post-test probability of disease after a negative result for the first test in the sequence. This result will be used to compare whether the probability of disease falls above or below each threshold.
In this demonstration application, two of the parameters for calculating Bayes' theorem (test sensitivity and specificity) are derived from the specific study or subgroup analysis selected. In practice, these values may be derived from a variety of sources, including published studies, clinical guidelines, or expert consensus. Because pre-test probability is somewhat subjective and may be influenced by factors such as clinical assessment, tools such as the Wells score, or interpretation of the specific study population, a slider is provided to allow the user to adjust the pre-test probability to reflect their assessment of the patient's risk of disease. The post-test probability is then calculated using Bayes' theorem, which will be compared to the threshold values to consider the next clinical management steps. The "Probability explorer" info pop-up provides explanations of default pre-test probability considerations and a sample calculation of Bayes' theorem.
Clinical interpretation
- Below Tt: Withhold further testing (probability too low to justify testing or treatment)
- Between Tt and Ttx: Perform the test (test result will guide treatment decision)
- Above Ttx: Treat without testing (probability high enough to justify empirical treatment)
Testing and treatment equations
Testing Threshold:
$$T_t = \frac{(1-\text{Specificity}) \times R_{rx} + R_t}{(1-\text{Specificity}) \times R_{rx} + \text{Sensitivity} \times B_{rx}}$$
Test-Treatment Threshold:
$$T_{tx} = \frac{\text{Specificity} \times R_{rx} - R_t}{\text{Specificity} \times R_{rx} + (1-\text{Sensitivity}) \times B_{rx}}$$
Note on Benefit of treatment (Brx) calculation
This calculator uses absolute risk reduction values:
- Brx (benefit of treatment) = risk if disease present and untreated - risk if disease present and treated = rD - rT (absolute mortality/morbidity reduction)
- Rrx (risk of treatment) = rT,noD (absolute risk of treating when no disease)
- Rt (risk of test) = rtest (absolute risk of the diagnostic test)
This approach was also used in the Carpenter 2016 SAH paper (rD = 30% mortality if SAH untreated; rT 5% mortality if SAH treated; Brx = 25% mortality reduction if SAH treated) and implicitly in the Kline 2004 PE/PERC paper (15% absolute reduction in death from anticoagulation).
The original Pauker-Kassirer paper used utility-weighted outcomes rather than simple probability differences. For example, in considering the benefits of steroids for treating AKI from vascultis, they calculated steroid complications (Rrx) = 5%, probability of improvement = 20%, and a utility ratio of longterm benefit of improved renal function being 2x the value of avoiding steroid complications. Therefore they calculated Brx = 20% x2 x 95% = 38%. In a second example, they calculated the Brx as the relative survival gain.
One can see that it is relatively arbitrary to calculate the overall benefit of treatment as the difference between the risk of disease present and untreated and the risk of disease present and treated. Pauker and Kassirer acknowledged that the assessment of risks and benefits is not simple, noting that patient values, economic costs, and varying interpretations of "survival" may all be a component of a single utility value. I have chosen to use absolute risk reduction to approximate treatment benefit because it is an intuitive and simple approach that can be justified using available data on the risks of treatment and disease. Note that the equations do take the risk of treatment into account when calculating the threshold.
The user can also modify the Brx value by adjusting the risk of disease untreated and risk of disease treated inputs. For example, the clinical symptoms might correlate with a clinical grading scale (e.g. Hunt and Hess for SAH or PESI for PE) that helps determine the mortality risks if the disease is present. Of course, values that are used in these scales may also contribute to the clinician's estimate of the pre-test probability; the point overall is to demonstrate how different aspects of assessment and interpretation of available evidence can effect the parameters of the testing and treatment threshold values.