Pharmaceutical companies point to the growth of blood pressure drugs as a sign of progress in combating hypertension, the “silent killer”. There are currently more than sixty hypertension drugs broadly divided into eleven classes: 1. ACE inhibitors (angiotensin-converting enzyme inhibitors); 2. Aldosterone Receptor Antagonists; 3. Alpha Blockers; 4. Alpha-Beta Blockers; 5. 6. Beta Blockers; 7. Calcium Channel Blockers; 8. Central Antagonists; 9. Direct Renin Inhibitors; 10. Diuretics, and 11. Vasodilators.
Large numbers of drug-dose combinations present a
challenge for physicians searching for effective treatment options
Most hypertensive patients are prescribed two and up to five different drugs in a variety of doses, as clinicians strive to find effective drug-dosage combinations. To be practical, they must quickly find patient-specific drug-dose combinations that lower individual patients' blood pressure below 140/80 mmHg. The longer the process takes, the higher the odds of their patients becoming non-compliant by quitting diagnostic and treatment processes. Based on the literature and discussions with clinicians, we concluded that clinicians find effective drug-dosage combinations within twelve months of diagnosis for 30-60% of their patients. The rest will require lengthier, more extensive efforts involving a variety of tests, multiple ABPM profiles, and evaluations of additional drugs and dosage combinations.
This paper explores the challenges faced by clinicians attempting to find effective patient-specific drug combinations by quantifying the number of available drugs and dose options. We developed models based on the number of available blood pressure drugs, the number of drug classes, and common doses. The analysis illuminated decision-making barriers to quickly identifying patient-specific, high-efficacy drug-dose combinations. We then assessed the implications for patient engagement and compliance.
Models and calculations
We applied combinatorics to calculate the number of possible treatment combinations given an initial set of drugs and doses. The approximate number of available blood pressure drugs is known (63) and estimated average doses per drug were varied from two to five based on current practices. The number of combinations was calculated using the binomial coefficient equation:
s = n! / ((n-k)! * k!)
Where s is the number of potential solutions, n is the number of available drugs or drug-dose combinations, and k is the number of drugs in a treatment plan, or the number of drugs multiplied by the average number of doses. For example, if four drugs are prescribed and the average number of doses per drug is three, then k is four times three, or twelve.
We used this method to develop models based on disease definitions and prescription practices. The first models were based on the number of available blood pressure drugs and treatment protocols documented in the literature and validated with clinicians. Dosage was not considered in this version because the magnitude of results rendered it useless.
A second model was based on the number of drug classes (11), and common dosages (2 and 3) used in developing treatment strategies. Two additional models were based on documented definitions for resistive hypertension and refractive hypertension for which treatments include at least four drugs and three to five doses.
The models also calculated the amount of time required for all drug and drug-dose combinations in each set to be prescribed and evaluated. It assumes patients are prescribed a combination of drugs at specific doses and are then asked to return after three weeks to evaluate treatment efficacy. Changes to drugs and dosage are made in cases of poor efficacy. These calculations helped frame the process in the context of time constraints and patient collaboration and compliance.
Hypertension Models
The first model used the number of blood pressure drugs (63) as the set of options to calculate the number of possible combinations for each of two to five drugs. It then calculated the number of weeks and years required for a doctor to prescribe and evaluate all available combinations. The results for four and five drug combinations were too large to offer useful insights.
Models based on Drug Classes and Dosage
The following models are based on drug classes (11) and an average of two and three doses per drug resulting in (n) 22 and 33 drug-dose options, respectively. This modeling strategy reflects practices reported in the literature and described by clinicians. It assumes that only one drug per class is used in treatment development.
Calculations based on an average of two doses per drug in each drug-dose combination.
Calculations based on an average of three doses per drug in each drug-dose combination.
Application to resistive and refractory hypertension
The number of available drug-dose combinations has implications for clinical decision-makers and raises questions about resistive and refractory hypertension, which are diagnosed based on the number of drugs and doses used to bring patient blood pressure within established norms. In this context, resistive hypertension is described as:
· The patient is taking three different blood pressure medications at their maximally tolerated doses.
· One of the blood pressure medications is a diuretic.
· The patient’s blood pressure exceeds recommended levels (usually 130/80 mmHg),
· OR: The patient requires four or more medications to control their blood pressure[1].
A related condition, refractory hypertension, is “defined as uncontrolled blood pressure despite the use of ≥5 antihypertensive agents of different classes, including a long-acting thiazide-like diuretic and an MR (mineralocorticoid receptor) antagonist, at maximal or maximally tolerated doses.[2]” Taking the number of drug classes (11) and multiplying them by 3 and 4 doses yields 33 and 44 options, respectively, which were used to calculate the number of possible drugs-doses combination(s):
Implications
While the number of possible drug-dose combinations can be calculated, the number of solutions (patient-specific combinations with high efficacy) in each set of combinations is not knowable. For clinicians, the challenge of finding high-efficacy solutions is akin to finding the right needle(s) in a bucket of needles. Time and patient compliance are constraints since patient-specific treatments must be identified quickly enough to secure patient collaboration. Patients are the ultimate boundary condition since noncompliance increases as time, inconvenience, and costs mount with each failed attempt.
Discussion
The literature and conversations with clinicians suggest that many doctors are confident in their ability to find effective drug-dosage combinations within practical timeframes, i.e., three months to a year. Performance numbers reported in peer-reviewed journals suggest that there is much overconfidence in these beliefs.
Our experiences and continuing research across fields including medicine suggest that experts frequently overestimate their capacity to accurately predict outcomes including the efficacy of their solutions (treatments). Researchers and practitioners including Daniel Kahneman (psychology, economics, decision-making), Friedrich Hayek (economics, decision-making), Thomas Sowell (economics and decision-making), Philip Tetlock (psychology), and Nate Silver (statistics and probability) have documented the limits of expert predictions and experts’ predictive overconfidence
Published research and studies by agencies including the Centers for Disease Control and Prevention (CDC) have documented the intractably low efficacy of hypertension treatment strategies and clinical predictive accuracy. Gaps in applicable knowledge are also reflected in conflicting analyses. For example, despite the often quoted “Only about 1 in 4 adults (24%) with hypertension have their condition under control[3],” published research documents greater variability in outcomes based on treatment strategies and patient-specific factors:
“Despite the development of new antihypertensive medications and a better understanding of the physiology of high BP, control rates remain low. Data available from the National Health and Nutrition Examination Survey 2003–2004 show that two out of three patients with hypertension had uncontrolled BP, and control rates decreased according to age. In the same study, control rates were 71.7, 63.5 and 50.0% among treated hypertensive patients aged 18–39, 40–59 and ⩾60 years, respectively[4].”
The published prevalence of resistant hypertension reflects broader gaps in knowledge and lower diagnostic and treatment predictive accuracy. For example, estimates "of the prevalence of resistant hypertension have varied widely, with reported figures ranging from 2% to 40%.[5]” That’s barely better than a coin toss.
Conclusions
The results of our investigation suggest that the vast number of treatment options structurally guarantee poor treatment strategy formulation and treatment outcomes among patients who do not respond positively to initial treatment strategies. Clinicians face insurmountable odds in identifying effective treatment combinations out of unmanageably large sets of options. They lack tools to help them sort through large sets of options to identify those most likely to succeed in helping patients achieve effective blood pressure control.
Published research and investigations suggest that clinicians overestimate the predictive accuracy of treatment selection. There are many instances in the literature of patients being blamed for quitting before an effective solution is found. It's unrealistic, however, to expect patient collaboration and compliance when the process becomes unpredictably long. Overconfidence is not unique or exclusive to medicine. Researchers across fields have documented expert predictive overconfidence that undermines the quality of decision-making. Leading researchers, including Nobel Laureate Daniel Kahneman, have long reported this tendency:
“People’s exaggerated confidence in their predictive judgment underestimates their objective ignorance as well as their biases. There is a limit to the accuracy of our predictions, and this limit is often quite low. Nevertheless, we are generally comfortable with our judgments. What gives us this satisfying confidence is an internal signal, a self-generated reward for fitting the facts and the judgment into a coherent story. Our subjective confidence in our judgments is not necessarily related to their objective accuracy.[6]”
In the context of hypertension, our calculations suggest that high confidence in clinicians' abilities to find effective drug-dose combinations among unmanageably larger sets is problematic. These conclusions are supported by published diagnostic, treatment, and efficacy variability. It’s likely, therefore, that hypertension treatment efficacy and patient outcomes will remain intractably low until clinicians adopt improved technologies and decision-support tools with which to quickly sort through large sets of treatment options and identify those with a high probability of success.
References
[1] Pathan MK, Cohen DL. Resistant Hypertension: Where are We Now and Where Do We Go from Here? Integr Blood Press Control. 2020 Aug 5;13:83-93. doi: 10.2147/IBPC.S223334. PMID: 32801854; PMCID: PMC7415451. [2] Maria Czarina Acelajado, Zachary H. Hughes, Suzanne Oparil, David A. Calhoun, Treatment of Resistant and Refractory Hypertension, March 28, 2019, AHA Journals, https://www.ahajournals.org/doi/10.1161/CIRCRESAHA.118.312156# [3] Facts about hypertension, Centers for Disease Control and Prevention, accessed May 29, 2023, https://www.cdc.gov/bloodpressure/facts.htm# [4] Pimenta, E., Stowasser, M. Uncontrolled hypertension: beyond pharmacological treatment. Hypertens Res 32, 729–731 (2009). https://doi.org/10.1038/hr.2009.108 [5] Pathan MK, Cohen DL. Resistant Hypertension: Where are We Now and Where Do We Go from Here? Integr Blood Press Control. 2020 Aug 5;13:83-93. doi: 10.2147/IBPC.S223334. PMID: 32801854; PMCID: PMC7415451. [6] Kahneman, Daniel; Sibony, Olivier; Sunstein, Cass R.. Noise (p. 367). Little, Brown and Company. Kindle Edition.