Table 1.

Intuitive presentation of the threshold model

Note how the manuscript’s formal threshold equations 1-3 effectively capture everyday clinical intuition.
Equation 1 states that the administration of treatment depends on consideration of the benefits and harms of treatment adjusted for the patient's V&P regarding how they feel about the burden of disease (eg, VTE) vs the adverse events of treatment (eg, major bleeding).
Technically, we refer to the effects of treatment on patient outcomes as “utility.”

  • Treatment threshold (when tests are not taken into consideration)

Clinically, we are interested in finding out at which probability of disease or outcome we should act [“how high is “high” for us to give treatment; how low is “low” for us not to administer it]. Intuitively when benefits do not exceed harms, we are uncertain how to proceed. That is, we are at the treatment “threshold.” According to a decision-analytical theory, the threshold is equal to the expected utility∗ of administering treatment vs not administering treatment. From here, we can obtain a simple formula for the treatment threshold3:

Pt=Absoluteriskofmajorbleeding(bleed)Relativeriskreduction(RRR)


in which Pt is the probability of disease or outcome (eg, recurrence of VTE). Treatment should be given if the benefit of treatment exceeds its harms at the given probability of disease (eg, VTE recurrence) and patients' V&P. Thus, if the probability of VTE (pVTE) >Pt, we should administer treatment (eg, anticoagulants). If Pt < pVTE, we should not give treatment. Importantly, our decisions whether to test (and act according to the test result) are also contrasted against Pt, which serves as an action threshold against which testing decisions are compared.

  • Testing thresholds

    • Test–no treatment threshold (Ptt)

Equation 2 tells us what every physician intuitively knows: when the probability of disease is fittingly very small, we can forgo testing and treatment. It is also self-evident that Ptt must be smaller than Pt (ie, Ptt < Pt).‡ Generally, we can forgo testing when the pretest probability of disease is so low that even with a positive test result, the posttest probability would have always been below the action threshold Pt

  • Test-treatment threshold (Prx)

Equation 3 also agrees with clinicians' intuition: we don't always need diagnostic confirmation to act. We can forgo testing when the pretest probability of disease is so high that even with a negative test result, the posttest probability would have always been above the action threshold, Pt. Here too, it is self-evident that Prx must be larger than Pt (ie, Prx > Pt).§,

These results reflect an old clinical wisdom: “do not order a test that will not change your management.”

To decide about thrombophilia testing, we contrast the overall risk (probability) of VTE recurrences (pVTE) against these thresholds. According to the threshold model, the thrombophilia testing should only be done for Ptt<pVTE < Prx. No testing/no treatment should be recommended for < Ptt. Treatment with anticoagulants should be recommended for pVTE > Prx (Figure 4; also see the visual abstract). 
Note how the manuscript’s formal threshold equations 1-3 effectively capture everyday clinical intuition.
Equation 1 states that the administration of treatment depends on consideration of the benefits and harms of treatment adjusted for the patient's V&P regarding how they feel about the burden of disease (eg, VTE) vs the adverse events of treatment (eg, major bleeding).
Technically, we refer to the effects of treatment on patient outcomes as “utility.”

  • Treatment threshold (when tests are not taken into consideration)

Clinically, we are interested in finding out at which probability of disease or outcome we should act [“how high is “high” for us to give treatment; how low is “low” for us not to administer it]. Intuitively when benefits do not exceed harms, we are uncertain how to proceed. That is, we are at the treatment “threshold.” According to a decision-analytical theory, the threshold is equal to the expected utility∗ of administering treatment vs not administering treatment. From here, we can obtain a simple formula for the treatment threshold3:

Pt=Absoluteriskofmajorbleeding(bleed)Relativeriskreduction(RRR)


in which Pt is the probability of disease or outcome (eg, recurrence of VTE). Treatment should be given if the benefit of treatment exceeds its harms at the given probability of disease (eg, VTE recurrence) and patients' V&P. Thus, if the probability of VTE (pVTE) >Pt, we should administer treatment (eg, anticoagulants). If Pt < pVTE, we should not give treatment. Importantly, our decisions whether to test (and act according to the test result) are also contrasted against Pt, which serves as an action threshold against which testing decisions are compared.

  • Testing thresholds

    • Test–no treatment threshold (Ptt)

Equation 2 tells us what every physician intuitively knows: when the probability of disease is fittingly very small, we can forgo testing and treatment. It is also self-evident that Ptt must be smaller than Pt (ie, Ptt < Pt).‡ Generally, we can forgo testing when the pretest probability of disease is so low that even with a positive test result, the posttest probability would have always been below the action threshold Pt

  • Test-treatment threshold (Prx)

Equation 3 also agrees with clinicians' intuition: we don't always need diagnostic confirmation to act. We can forgo testing when the pretest probability of disease is so high that even with a negative test result, the posttest probability would have always been above the action threshold, Pt. Here too, it is self-evident that Prx must be larger than Pt (ie, Prx > Pt).§,

These results reflect an old clinical wisdom: “do not order a test that will not change your management.”

To decide about thrombophilia testing, we contrast the overall risk (probability) of VTE recurrences (pVTE) against these thresholds. According to the threshold model, the thrombophilia testing should only be done for Ptt<pVTE < Prx. No testing/no treatment should be recommended for < Ptt. Treatment with anticoagulants should be recommended for pVTE > Prx (Figure 4; also see the visual abstract). 
∗

Expected utility is the average of all possible outcomes weighted by their corresponding probabilities.

†

To simplify exposition, we avoid the consideration of V&P; please refer to the main manuscript and Appendix for full technical details. Note that there are many metrics for treatment benefits and harms that may result in different threshold formulas. Here, we show a formula pertinent to the treatment of patients at risk of VTE recurrence.

‡

According to the expected EUT, the most widely used decision-analytical theory and that used in this manuscript.

§

See footnote †.

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