Journal of Pharmacokinetics and Pharmacodynamics

, Volume 39, Issue 3, pp 283–294

Misclassification and discordance of measured blood pressure from patient’s true blood pressure in current clinical practice: a clinical trial simulation case study

Authors

  • Yuyan Jin
    • PharmaTherapeutics Clinical Research, Clinical PharmacologyPfizer Inc.
  • Robert Bies
    • Division of Clinical PharmacologyIndiana University, School of Medicine
  • Marc R. Gastonguay
    • Metrum Institute
  • Norman Stockbridge
    • U.S. Food and Drug Administration
  • Jogarao Gobburu
    • Center for Translational Medicine, Schools of Pharmacy & MedicineUniversity of Maryland
    • U.S. Food and Drug Administration
Original Paper

DOI: 10.1007/s10928-012-9250-8

Cite this article as:
Jin, Y., Bies, R., Gastonguay, M.R. et al. J Pharmacokinet Pharmacodyn (2012) 39: 283. doi:10.1007/s10928-012-9250-8

Abstract

Treatment decisions for hypertension using sphygmomanometer based measurements and the current clinical practice paradigm do not account for the timing of blood pressure (BP) measurement. This study aimed to evaluate the clinical implications of discordance between measured and true BP, to quantify BP misclassification rate at a typical clinical visit in current clinical practice, and to propose a BP calibration system to decrease the impact of timing of BP measurement. A clinical trial simulation case study was performed using an in silico Monte Carlo Simulation approach. The time-courses of BPs with and without an antihypertensive treatment effect were simulated from a baseline BP model combined with an antihypertensive PK/PD model. Virtual subject characteristics were sampled from the FDA internal database. The baseline BP model was qualified using observed 24 h ambulatory BP monitoring (ABPM) data from 225 subjects by a visual predictive check as well as a global sensitivity analysis. First of all, our results showed that the measured cuff BP in current typical clinical practice deviated from the true values. (1) Cuff BP deviated from the true values by more than 5 mmHg in 57 % (95 % CI: 54–61 %) of patients and more than 10 mmHg in 26 % (95 % CI: 22–32 %) of patients respectively. (2) These discordances were reduced to 28 % (deviation ≥5 mmHg, 95 % CI: 18–40 %) and 9 % (deviation ≥10 mmHg, 95 % CI: 4–18%) of patients assuming perfect sphygmomanometer measurement and thus represent the contribution of ignoring the daily circadian rhythm of BP. Secondly, our results showed 23–32 % of patients were misclassified to an incorrect BP category for a casual clinical visit based on JNC 7 guideline. In addition, the accuracy of the measured cuff BP varied by time of clinic visit. Specifically, 11:00 AM to 3:00 PM was identified to be the better time frame, while times before 9:00 AM were the worst time frame. Therefore, clinic visit time may need to be adjusted accordingly. Finally, we proposed an easy BP calibration method for clinic use to adjust for time of day differences due to circadian variability in case that the desirable clinic visit time cannot be tailored for practical reasons.

Keywords

HypertensionSphygmomanometerCircadian rhythmModeling and simulationBlood pressure misclassificationBlood pressure calibrationPublic health

Introduction

A total of seventy antihypertensive agents from various classes are available to treatment hypertension in the US and millions of Americans are actively treated for hypertension. Despite this, the cardiovascular morbidity and mortality associated with hypertension remains a leading cause of overall morbidity and mortality [1, 2]. The National Health and Nutrition Examination Survey (NHANES) found that only 36.8 and 50.1 % percent of hypertensive patients in the US had their blood pressure (BP) well-controlled (below 140/90 mmHg) in 2003–2004 and 2007–2008, respectively [1, 2]. Numerous epidemiologic studies have demonstrated that this lack of BP control has significant public health ramifications with respect to cardiovascular related morbidity and mortality [3]. Understanding the reasons for poor BP control is an important public health issue.

The seventh report of the Joint National Committee on Prevention, Detection, Evaluation, and Treatment of High Blood Pressure (JNC 7) suggested that improper BP measurement, non-adherence to antihypertensive dosing regimen, inadequate doses, and inappropriate combination therapy may be major contributors to the observed lack of BP control [3, 4]. To address the ongoing hypertension crisis in American adults the JNC 7 has updated BP classification thresholds and corresponding drug therapies for proper BP management.

BP is most commonly measured using a sphygmomanometer (cuff BP) during routine clinic visits. This is the primary means for identifying hypertension and making treatment decision in the current clinic practice paradigm. It is widely known that cuff BP measurements are associated with significant error [515]. Cuff BP measurements are affected by white-coat effect and alert reactions. This measurement approach is also potentially affected by many factors including type of measurement device, cuff size, patient position, and the proficiency of personnel [515]. This problem has been studied in detail and various guidelines have been developed to address the issue [16, 17]. This issue is not directly addressed in the current manuscript, however, the contribution of this error towards BP measurement is accounted for by incorporating a typical error or noise level for these measurements.

An important aspect of improper BP measurement that is not widely studied is the timing of the BP measurement. BP varies during the day following an inherent circadian rhythm [18, 19]. Typically, a morning BP surge is observed and then the BP declines throughout the day into the evening. These patterns are widely observed as a result of the use of 24 h ambulatory BP monitoring (ABPM) devices [20]. Therefore, BP is a time dependent measurement. In addition, it has been shown [18] that time course of BP reduction upon ingestion of certain antihypertensive agents changes with actual patterns of dosage intake. Hence, the actual dosing time of certain classes of antihypertensive may be an additional confounder to clock-time dependent BP readings.

Treatment decisions are typically made based on cuff BP measurement during routine clinic visits. This does not account for the confounding factors such as measurement time with respect to the circadian rhythm of BP, as well as dose administration time, and cuff measurement errors. The widespread use of cuff BP measurement to detect elevated BP and manage ongoing hypertension without controlling for these confounding factors may contribute to inadequate clinical management.

In this paper we utilize in silico Monte Carlo Simulation methods to characterize the impact of the above mentioned factors. Monte Carlo Simulation has been widely used to predict potential trial results by combining clinical trial design and numerical models, which may include drug behavior model, human execution behavior model, and disease progress model etc. [21]. Both the true BP and the cuff measurements at either casual or specified clinic visit times were simulated in the study.

The main objective of this work was to evaluate the discordance in BP between the cuff measurements and the true underlying BP, to quantify BP misclassification rate with respect to JNC 7 guideline at casual clinic visits per the current clinical practice paradigm. The influence of the BP measurement time on the BP discordance as well as BP misclassification rate was also evaluated. This provided the basis for exploring an optimal clinic visit time for BP based treatment assignment accounting explicitly for the antihypertensive PK/PD characteristics. For both the aims, we explored the impact of cuff measurement errors.

Methods

Virtual subjects characteristics and sample size

The mean of 24 h systolic BPs of actual patients were necessary to anchor the simulation of 24 h BP profile of virtual subjects for the evaluation of the study aims. The Virtual subjects’ characteristics were obtained from the internal database of Food and Drug Administration (FDA). The mean of the 24 h systolic BP of virtual subjects were adapted from ABPM measurements of 3,840 patients with essential hypertension by pooling information at baseline of several New Drug Applications (Fig. 2). These mean blood pressures were directly incorporated into the BP simulation model to simulate each patient’s longitudinal BP profile described in the next section.

Simulation of baseline BP profile

The population baseline BP model developed by Hempel and colleagues [18] was qualified and adopted for the simulation of longitudinal baseline BP. 24 h ABPM data on multiple occasions were available to support the modeling of circadian changes in hypertensive patients in the Hempel’s paper [18]. The inter-individual variability was estimated for the rhythm-adjusted 24 h mean, amplitude of the cosine terms, and clock time. The inter-occasion variability was estimated for the rhythm-adjusted 24 h mean and clock time. Baseline BP profiles were described using a function with two cosine terms. A brief description of the model is presented below. Equation 1 is the function described in Hempel’s paper, and Eq. 2 is the function used in our simulation.
$$ {\text{Bsl}}(t) = \kappa_{{1{\text{d}}}} + \theta_{1} \exp (\eta_{1} )\left[ {1 + \sum\limits_{i = 1}^{2} {\theta_{{2{\text{i}}}} (1 + \eta_{2} )\cos \left( {\frac{{i\pi (t + \eta_{3} + \kappa_{{2{\text{d}}}} )}}{12} - \theta_{{2{\text{i}} + 1}} } \right)} } \right] $$
(1)
$$ {\text{Bsl}}(t) = \kappa_{{1{\text{d}}}} + {\text{MSBP}}\left[ {1 + \sum\limits_{i = 1}^{2} {\theta_{{2{\text{i}}}} (1 + \eta_{2} )\cos \left( {\frac{{i\pi (t + \eta_{3} + \kappa_{{2{\text{d}}}} )}}{12} - \theta_{{2{\text{i}} + 1}} } \right)} } \right] $$
(2)
where θ denotes the fixed-effect parameters and κ and η denote the random-effect parameters (inter-occasion and inter-individual variability respectively) [18]. In Eq. 1, θ1, is rhythm-adjusted 24 h mean BP, η1 is inter-individual variability on baseline [18]. Instead of θ1 and η1, MSBP (the rhythm adjusted 24 h mean in systolic BP for each patient with hypertension adapted from FDA database, n = 3840) were used in this simulation. This was done to approximate a representative distribution of rhythm adjusted 24 h mean BP in the US population. The values of the other parameters for the baseline BP model were adopted directly from Hempel’s paper [18]. Bsl(t) is BP as a function of time, t is clock time. κ1d is inter-occasion variability in rhythm-adjusted 24 h mean, d indicates different study days, θ2i is amplitude of the cosine terms, η2 is inter-individual variability in the amplitudes, θ2i + 1 is the phase shift parameter associated with cosine terms, η3 is inter-individual variability on clock time, and κ2d is inter-occasion variability on clock time [18].

The baseline model was qualified using a visual predictive check that utilized time stamped two days ABPM data from 225 patients derived from University of Pittsburgh School of Medicine Medical Center before anchoring our simulation in the study. A global sensitivity analysis was performed to evaluate impact of the uncertainty distributions in the parameter estimates of the baseline model on the results of our analysis. The uncertainty distributions for the variance–covariance matrix of the parameter estimates for the baseline BP model were assumed to be multivariate normal distributions based on standard errors (SE%) associated with the estimates of the population parameters. 1,000 sets of population parameters were simulated from these distributions. These 1,000 sets of population parameters were used to for 1,000 replicate clinical trials, therefore 1,000 sets of analysis endpoints were obtained. Finally, analysis endpoints from these 1,000 clinical trials were plotted versus the uncertainty in each of the model parameters over 95 % CI range to evaluate the impact of the uncertainty of the parameter estimates on our results. Uncertainly in cuff measurement error was also incorporated in the global sensitivity analysis. BP measurement error attributable to sphygmomanometer device and personnel proficiency were assumed to be the normal distributions with standard deviations from 3 to 7 mmHg [22, 23].

One month (720 h) of continuous baseline BP measures was simulated using Monte Carlo Simulation implemented in R® (version 2.9.1) for all virtual patients.

Simulation of a continuous BP profile with one month of antihypertensive treatment

Efficacy of two types of antihypertensive agents were simulated in our study. A continuous BP profile with treatment effects for these two types of antihypertensive agents were simulated as follows:
  1. (1)

    A type I antihypertensive agents that induce a change in the shape of the BP circadian rhythm (e.g., Moxonidine, Clonidine, Nitrendipine, Nifedipine et al.). Moxonidine was used as a prototype for the first type of antihypertensive agents. The time-course of treatment effect described for moxonidine by Hempel [18] was adapted for the Monte Carlo simulation of an antihypertensive treatment effect. A moxonidine dose of 0.3 mg once daily was used as initial dose regimen for all virtual subjects. Three different dosing times (8:00 AM, 12:00 PM, and 8:00 PM) were explored to evaluate the effect of dosing time on simulation results. Perfect adherence was assumed in the simulation. One month of continuous true BP profiles with a 0.3 mg QD dose of moxonidine treatment were simulated by superimposing the moxonidine response on simulated baseline BP profiles as described above.

     
  2. (2)

    Type II antihypertensive agents in this manuscript refer to agents that elicit maximum antihypertensive effect upon repeated administration and produce a sustained lowering of BP without affecting the circadian rhythm throughout the dosing interval. These antihypertensive may include long acting antihypertensives or agents with EC50 much lower than drug concentrations at steady state). (e.g., Amlodipine, Telmisartan, or some combination therapies such as Amlodipine/Valsartan). For such agents, the 24 h-BP profile was shifted down relative to the baseline BP profile. Simulations for these type of agents assumed that the drug response follows normal distribution with a mean effect of 11.8 mmHg and a standard deviation of 10.9 mmHg (a similar treatment effect to the 0.3 mg (QD) moxonidine combined with the placebo effect).

     

The simulated duration of treatment for both antihypertensive treatments was one month (720 h). Perfect adherence was assumed in the both simulations.

Simulation strategy for cuff BP measurements

Casual clinic visit times of virtual subjects for cuff measurements after one month moxonidine treatment were assumed to follow a uniform distribution during the office working hours (8:00 AM to 6:00 PM). For every virtual subject, two casual clinic visit times to assess cuff measurement were simulated on day 30 of moxonidine treatment. True point BP values at each of the corresponding clinic visit times were captured from the simulated long term true BP profile. A placebo effect was randomly generated for the virtual subjects with a mean reduction in BP of 4 mmHg and a standard deviation of 2 mmHg [24]. Cuff BP measurement error was assumed to be normally distributed with a mean of zero and standard deviation of 5 mmHg based on a literature survey [5, 7, 10, 13, 14]. The observed cuff BP measurement at each casual clinic visit was generated by combining the true point BP and randomly generated cuff BP measurement errors (Fig. 1).
https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig1_HTML.gif
Fig. 1

Scenario of observed cuff BP measurement generation. Black dashed line and green solid line represent the typical SBP-time profiles before treatment (i.e. baseline) and after treatment (i.e. 0.3 mg 8:00 AM QD moxonidine at day 30), respectively. Red dashed vertical lines represent two randomly selected clinic visit times between 8:00 AM to 6:00 PM. Open circles are true systolic BP at randomly selected baseline clinic visit times and follow up clinic visit times. Red solid dots represent observed cuff BP measurements at corresponding clinic visit times (Color figure online)

In addition to casual clinic visits, an office hours (8:00 AM to 6:00 PM) simulation for cuff measurements under the same dosing regimen for all virtual subjects was performed to explore an optimal clock time for the cuff measurement with respect to an 8:00 AM dosing time. Cuff measurements at these visits were simulated in accordance to the method described above.

Evaluation of the discordance between measured BP and its true value

True BP decreases (ΔBP) and cuff measured ΔBP at clinic visit times from baseline in virtual patients after one month of moxonidine treatment were compared. True BPs of each virtual subject at both baseline and after treatment were defined as the mean values of BP profiles during office hours (8:00 AM to 6:00 PM) before and after treatment, respectively. True ΔBPs were defined as the difference between the true mean BP after one month treatment and initial baseline for each subject during the same office hours (8:00 AM to 6:00 PM).

The cuff measured ΔBPs at casual clinic visit times were calculated by subtracting the observed cuff BP at clinic visit from that in the initial baseline for each virtual patient. A paired comparison between cuff measured ΔBP at casual clinic visit times and true treatment effect ΔBP was performed within the same individual. The percentage of subjects who had a difference greater than 5 and 10 mmHg were calculated.

Optimal clinic visit times for the cuff BP measurements were also identified by comparing cuff measured ΔBP at specified visit times (8:00 AM to 6:00 PM) to the true ΔBP as described above.

Evaluation of BP misclassification

The true BP for each virtual subject was defined as the mean value of the BP profiles during office hours (8:00 AM to 6:00 PM). Both the true and casual cuff BP measurements were categorized into four stages based on the JNC 7 guidelines [4]. These stages were: (i) normal (BP < 120/80); (ii) pre-hypertension (120/80–139/89); (iii) stage 1 hypertension (140/90–159/99); and (iv) stage 2 hypertension (≥160/100). A binary outcome was assigned based on whether the categorical assignment from the virtual observed response was consistent with true JNC hypertension category (i.e., whether there was a correct category assignment). The percentage of patients with a misclassified JNC 7 hypertension category was calculated for each clinic visit. The percent of patients with BP classifications that were inconsistent between two casual clinic visit times on the same day was also evaluated. Misclassification rates based on clinic visits at specified clock times were evaluated to identify whether there was an optimal clinic visit time.

The sensitivity of the analysis results to various dosing times, personal preferences for rounding to the nearest 0 or 5 as the last digit of measured BP, and taking one additional measurement at each casual clinic visit was also evaluated.

BP calibration with respect to clinic visit times at both baseline and after treatment

Whether the BP could be calibrated with respect to clinic visit times before and after treatment if patients were not able to visit clinic at optimized clinic visit time was evaluated. The population mean BP profile at baseline and with antihypertensive treatment (both type I moxonidien and type II) during office hours (8:00 AM to 6:00 PM) was calculated. The population mean of the calculated BP decreases from baseline at various clinic visit times after antihypertensive treatment were generated.

Analysis platform

NONMEM® (Version VI, University of California at San Francisco, CA) was used to simulate moxonidine concentrations in the plasma and effect compartments for virtual subjects. Simulation of the BP profiles, graphics and post-processing of NONMEM® outputs, visual predictive evaluation, and global sensitivity analysis were performed in R® (version 2.9.1) using the MIfuns implementation (Metrum Institute, Tariffville, CT). 1,000 replicates of the Monte Carlo simulation was performed to generate prediction intervals (CI) of the simulation endpoints accounting for the uncertainty in parameter estimates from baseline BP profile model.

Results

The summary demographics of the patients sampled and the distribution of their systolic BPs are shown in Table 1 and Fig. 2 respectively. The mean systolic BP was 144.3 mmHg (120.2–201.1 mmHg) representing the baseline of rhythm adjusted 24 h mean for virtual (simulation) subjects. The average age of the virtual subjects was 56 years (21–86 years) with 55 % of male and 45 % of female.
Table 1

Summary of extracted data from FDA internal database

 

n (%)

24 h mean of SBP (mmHg) mean (range)

Age (years) mean (range)

Male

2,121 (55.2 %)

144.3 (120.2–199.7)

56 (21– 84)

Female

1,719 (44.8 %)

144.2 (120.2–201.1)

57 (23–86)

All

3,840

144.3 (120.2–201.1)

56 (21– 86)

https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig2_HTML.gif
Fig. 2

Histogram of 24 h mean systolic blood pressure for virtual subjects (n = 3840). Black vertical dashed line is the mean SBP (144.3 mmHg) of the virtual population

The visual predictive check performed using actual ABPM data from 225 subjects showed that baseline BP model normalized to that from Hempel and his colleagues [18] were able to reasonably describe circadian rhythm of BP profile over clock times. (Refer to Appendix Fig. 1 as ESM for additional information).

The 24 h time courses of systolic BP over one month accounting for circadian patterns, inter-occasion and inter-individual variability were simulated for 3,840 virtual subjects before (i.e. baseline profiles) and after antihypertensive treatment (i.e. type I and type II anti-hypertensives). In these simulations, a dosage regimen of 0.3 mg moxonidine (as prototype of type I antihypertensive) once daily dose was used with administration times of 8:00 AM, 12:00 PM, and 8:00 PM. Since the type II antihypertensives are not expected to affect the time-course of BP within the inter-dosing interval, simulations for different dosing times were not conducted.

Evaluation of the discordance between measured BP and its true value

Paired comparisons of cuff measured ΔBP to true values within the same individual indicated that measured ΔBP significantly deviated from the true ΔBP. The deviation was defined as the absolute difference of measured ΔBP from true ΔBP (Deviation = |Measured ΔBP−True ΔBP|). The deviation was over 10 mmHg in 26.3, 34.3, 24.6, 24.3 % of hypertensive patients and over 5 mmHg in 56.9, 63.1, 55.6, 55.8 % of hypertensive patients with moxonidine (type I antihypertensive) QD dosing at 8:00 AM, 12:00 PM, 8:00 PM, and type II antihypertensive respectively (Table 2). (Since type II antihypertensive do not change the patients’ BP circadian rhythm, the deviation was not impacted by dosing time.) The level of deviation above were confounded by both random sphygmomanometer BP measurement error and the fact of ignoring circadian rhythm of BP in BP measurement in current clinical practice. Additional analysis without implementing cuff measurement error indicated that nearly half of the deviation above were attributable to ignoring circadian rhythm of BP in BP measurement in current clinical practice (Table 2).
Table 2

Cuff measured ΔSBP (from baseline) at a typical (random) follow up clinic visit deviates from true ΔSBP: percent of patients with deviation ≥ 5 mmHg or 10 mmHg

Patients (%) with measured ΔBP deviating from the true (deviation = |measured ΔBP−true ΔBP|)

Type I antihypertensive (Moxonidine)

Type II antihypertensives (95 % CI)

8:00 AM QD (95 % CI)

12:00 PM QD (95 % CI)

8:00 PM QD (95 % CI)

Deviation ≥ 10 mmHg

With cuff measurement error

26.3 % (22.2–32.2%)

34.3 % (30.2–39.2 %)

24.6 % (20.4–31.2 %)

24.3 % (13.1–36.4 %)

Without Cuff Measurement Error

9.2 % (4.5–17.6 %)

20.1 % (14.1–27.2 %)

7.7 % (2.9–13.3%)

7.9 % (2.5–16.5 %)

Deviation ≥ 5 mmHg

With Cuff Measurement Error

56.9 % (53.5–61.3 %)

63.1 % (60.1–66.4 %)

55.6 % (52.3–60.2 %)

55.8 % (52.2–60.1 %)

Without Cuff Measurement Error

28.4 % (18.2–39.6 %)

48.2 % (40.8–54.8 %)

23.6 % (13.3–36.2 %)

24.8 % (20.5–30.7 %)

The results showed above assumed sphygmomanometer BP measurement error was normally distributed with a standard deviation of 5 mmHg and a mean of zero based on literature reported values [511, 25, 26]. In our study, we also tested how extent of the sphygmomanometer BP measurement error translated into clinical implementation. Our sensitivity analysis showed that BP discordance was highly correlated to the standard deviation of BP measurement error (Fig. 3).
https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig3_HTML.gif
Fig. 3

Global sensitivity analysis: fraction of patients with deviation ≥ 10 mmHg versus systolic blood pressure measurement error. (Deviation = |Measured ΔSBP−True ΔSBP|) (Color figure online)

Evaluation of the BP misclassification

Comparisons of cuff measured BP to true values within the same individual also indicated that significant percent of patients had their BP misclassified to an incorrect BP category, which may lead to incorrect treatment decision. For type I antihypertensives, approximately, 24 % of patients’ BP was misclassified based on their true BPs using an 8:00 AM 0.3 mg once daily dosing regimen of moxonidine. The percentage of patients with BP misclassifications was 32.0 % and 23.5 % using 12:00 and 8:00 PM dosing times respectively as shown in Table 3. For type II anti-hypertensive agents a misclassification rate of 22.8 %, similar to the morning or evening dose of moxonidine was observed (Table 3). Additional analysis without implementing cuff measurement error indicated that over half of BP misclassification rate mentioned above were attributable to ignoring circadian rhythm of BP in BP measurement in current clinical practice. BP was misclassified in 14.6, 26.1, 12.3, and 12.5 % of patients with moxonidine (type I antihypertensive) QD dosing at 8:00 AM, 12:00 PM, 8:00 PM, and type II antihypertensive, respectively, purely due to ignoring circadian rhythm of BP in current clinical practice (Table 3).
Table 3

Percent of patients with systolic blood pressure misclassification by cuff measured systolic blood pressure at a typical follow up clinic visit

Patients (%) with BP misclassification

Type I antihypertensive (Moxonidine)

Type II antihypertensives (95 % CI)

8:00 AM QD (95 % CI)

12:00 PM QD (95 % CI)

8:00 PM QD (95 % CI)

With cuff measurement error

24.4 % (22.5 – 27.3 %)

32 % (29.3 – 34.8 %)

23.5 % (20.9 – 27.1 %)

22.8 % (19.8 – 26.0 %)

Without cuff measurement error

14.6 % (11.5 – 19.1 %)

26.1 % (22.8 – 29.7 %)

12.3 % (8.2 – 18.3 %)

12.5 % (7.8 – 18.0 %)

The percentage of patients with a BP misclassification varies with different BP measurement clock times and is observed for both types of anti-hypertensive agents (Fig. 4a, b). Rate of BP misclassification for type I antihypertensive (i.e. moxonidine) was impacted by both dosing time (i.e. 8:00 AM, 12:00 PM, 8:00 PM) and clinic visit time (BP measurement clock time). Since type II antihypertensive didn’t change the patients’ BP circadian rhythm, the rate of BP misclassification was not impacted by dosing time. However, our results showed that rate of BP misclassification for type II antihypertensive was impacted by patients’ clinic visit time (BP measurement clock time) as expected. Cuff measurements at specific clock times performed better than randomly selected times for both types of anti-hypertensive agents. Early morning (8:00–11:00 AM) or late afternoon (3:00–6:00 PM) was identified as the time intervals most likely to result in BP misclassification for both type I and type II anti-hypertensives. Specifically, 45 % of patients were misclassified to an incorrect BP treatment group with a 8:00 AM clinic visit using an 8:00 AM QD dosing regimen of moxonidine or 6:00 PM clinic visit using a 12:00 PM QD dosing regimen of moxonidine. The moxonidine 12:00 PM QD dosing regimen had highest percentage misclassification. The best clinic visit time for this dosing regimen was 1:00 PM where the percent of patients with BP misclassification was around 22 % (Fig. 4a, b).
https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig4_HTML.gif
Fig. 4

a Systolic blood pressure misclassification rate depends on the time of day when the systolic blood pressures are measured. b Systolic blood pressure misclassification rate depends on the time of day when the systolic blood pressures are measured and type of antihypertensives (Color figure online)

The best clinic visit time frame for both type I and type II antihypertensive agents was between 11:00 AM–3:00 PM. Additionally, an 8:00 AM or 8:00 PM QD dosing regimen for moxonidine (type I antihypertensive agent) resulted in a further decreased rate of BP misclassification. Despite of fixed dosing time and an optimal clinic visit time, the BP misclassification rate was ~20 %.

The results showed above assumed sphygmomanometer BP measurement error was normally distributed with a standard deviation of 5 mmHg and a mean of zero based on literature reported values [511, 25, 26]. In our study, we also tested how extent of the sphygmomanometer BP measurement error translated into clinical implementation. Our sensitivity analysis showed that BP misclassification rate was linearly correlated to the standard deviation of BP measurement error (Fig. 5).
https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig5_HTML.gif
Fig. 5

Global sensitivity analysis: fraction of patients with systolic blood pressure misclassifications versus systolic blood pressure measurement error (Color figure online)

BP calibration based on clinic visit time

Therefore, clinic visit time may need to be adjusted accordingly. However, the desirable clinic visit time may not be tailored for practical reasons for some patients. We proposed an easy BP calibration system for clinic use to adjust for time of day differences due to circadian variability. The potential for BP calibration based on patients’ clinic visit times at both baseline and with 0.3 mg 8:00 AM once daily dose of moxonidine treatment are shown in Fig 6a, b. The population mean of the systolic BP at each specified clock time visit for both baseline and after 0.3 mg moxonidine treatment are summarized in Fig. 6a, b illustrates BP calibration at four representative baseline measurement times with a fixed dosing time of 8:00 AM. Given an 8:00 AM baseline BP measurement, 12:00 PM after treatment visit may best measure true ∆BP (11.8 mmHg) from baseline. If 9:00 AM is the after treatment visit time, a measured cuff BP at 9:00 AM could be calibrated to a 4:00 PM measurement by adding 4 mmHg.
https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig6_HTML.gif
Fig. 6

a Typical systolic blood pressure time profiles before treatment (i.e. baseline) and after treatment with type I anti-hypertensive (i.e. 0.3 mg 8:00 AM QD moxonidine at day 30). b Systolic blood pressure calibration scale for moxonidine (type I antihypertensive) (Color figure online)

Similar BP calibration is also suggested for type II antihypertensive agents. The BP measurements at various baseline and after treatment visit times can be calibrated as shown in Fig. 7a, b.
https://static-content.springer.com/image/art%3A10.1007%2Fs10928-012-9250-8/MediaObjects/10928_2012_9250_Fig7_HTML.gif
Fig. 7

a Typical systolic blood pressure time profiles before treatment (i.e. baseline) and after treatment with type II anti-hypertensive (i.e. antihypertensives which don’t change the circadian rhythm of BP). b Systolic blood pressure calibration scale for type II antihypertensvies which don’t change the circadian rhythm of BP (Color figure online)

Global sensitivity analysis: impact of the uncertainty distributions in the parameter estimates of the baseline model on the results of our analysis

  1. (1)

    Global sensitivity analysis for BP discordance endpoint showed that our analysis endpoints were robust across the uncertainty in all parameters reported in Hempel’s paper with the exception of the amplitude parameter for first cosine term and the random effect parameter for the inter-individual variability on clock time (h) as shown (Appendix Fig. 2 as ESM). The 95 % CI of BP discordance endpoint (the ±10 mmHg categories) were shown in Appendix Fig. 2 as ESM. The percentage of patients whose measured BP deviated from true values (i.e.: for the ±10 mmHg categories: 13.7–8 % without measurement error and 30–24 % with measurement error) were negatively correlated to the amplitude parameter for the first cosine term (95 % CI: −0.087 to −0.048). The inter-individual variability term on clock time (variance 95 % CI: 3.59–28.47 h) was positively correlated to percentage of patients whose measured BP deviated from true values significantly (i.e.: for the ±10 mmHg categories: 7–15 % without measurement error and 24.5–30 % with measurement error). Improved estimates for these two population parameters are critical to evaluating the simulation results (Appendix Fig. 2 as ESM and Table 1 as ESM).

     
  2. (2)

    Global sensitivity analysis for BP misclassification endpoints showed that the BP misclassification rates in our analysis were robust across the uncertainty in all parameters reported in Hempel’s paper except for the amplitude of the first cosine term and the random effects parameter for the inter-individual variability on clock time (h). The 95 % CI for BP misclassification endpoints were shown in Appendix Fig. 3 as ESM. The percentage of patients with BP misclassification (26–23 %) were negatively correlated with the amplitude of the first cosine term (95 % CI: −0.087 to −0.048). The inter-individual variability on clock time (variance 95 % CI: 3.59–28.47 h) was positively correlated with the percent of patients with BP misclassification (23–26.5 %). Therefore, robust estimates of these two population parameters in baseline blood pressure model to describe the daily circadian rhythm are important in understanding the BP misclassification rate.

     

Discussion

The simulation conducted in this paper demonstrated, as a result of issues relating to current clinical practice and cuff BP measurement error, cuff measured ΔBPs systematically over or under-estimate the actual ΔBP in a typical clinical practice setting, leading to a significant percent of patients misclassified to an incorrect BP category, hence incorrect treatment decisions. This simulation accounted for confounding factors such as internal circadian rhythm of BP, antihypertensive treatment effect on the BP profile, clinic visit times, and BP measurement error. This BP misclassification rate is sensitive to the time of cuff BP measurement as well as PK/PD characteristics (type of anti-hypertensive). An optimal time frame for baseline and time after dosage administration exists that improves the accuracy of the cuff measured BP classification. Optimizing the clinic visit time based on dosage administration time and baseline improved the accuracy of the cuff measured ΔBP.

The deviation of cuff measured ΔBPs from the true ΔBPs have been demonstrated in the following ways. Firstly, with casual clinic visit times, the difference between true ΔBP and measured ΔBP was over 5 and 10 mmHg in 56.9 and 26.3 % of patients. The percentage of patients with BP misclassification rates ranged from 23 to 32 % at a casual clinic visit times depending on type of antihypertensive. Secondly, clinic visit time (i.e. between 8:00 AM and 6:00 PM) was found to impact BP misclassification rate, ranging from 20 to 45 % depending on the time of day of the measurement. The BP misclassification rate can be decreased to 19 % by selecting a optimal clinic visit time frame (12:00 PM–3:00 PM) for both types of antihypertensive.

Clinic visits during this pre-defined optimal time frame may not be feasible for many patients in clinical practice. The analysis suggests a useful BP calibration scale for physicians to decrease the effect of clinic visit times by considering the circadian rhythm of patient specific BP profile before and after treatment. However, BP calibration scales for the cuff SBP measurement in this study may not be applicable to all antihypertensives and may vary with PK/PD characteristics of the medication and dosing regimen prescribed as the BP reduction upon ingestion of an antihypertensive agent depends on the PK/PD properties of that agent. Therefore, clinical visit time selection and BP calibration must account for the dosing times and the PK/PD properties of the antihypertensive(s) used. In addition, BP calibration scale presented in this study was based on average BP rhythm in a population (mean) level. It is a very easy method for BP calibration across patients. However, BP circadian rhythm might be slightly different for individuals due to differences in physiological factors or daily activities. Hence, patient specific 24 h ABPM data before and after treatment should be taken, whenever is feasible, to derive patients’ specific BP calibration scale, which could be easily used on a day-to-day basis for any physician without knowledge in pharmacometrics.

Optimal clinic visit time or BP calibration method proposed above mitigated the BP misclassification rate resulting from ignoring the inherent circadian rhythm in the BP measurement. The BP misclassification decreased from 45 % (early morning visits) to 19 % (optimal times: e.g. 12:00–3:00 PM). It didn’t, however, completely correct the measurement bias due to existence of random cuff measurement error from other recourse such as device, cuff size, and personnel proficiency. The results showed above assumed sphygmomanometer BP measurement error was normally distributed with a standard deviation of 5 mmHg and a mean of zero based on literature reported values [511, 25, 26]. Our additional sensitivity analysis showed that BP misclassification rate from the measurement error was linearly associated to the standard deviation of BP measurement error (3–10 mmHg). To the best of our knowledge, this is the first quantification on clinical benefit associated to the decreases in sphygmomanometer BP measurement error. Hence it emphasizes the importance of calibrating BP measurement devices on a regular basis, training level of the medical personnel, as well as the compliance to sphygmomanometer BP measurement guidelines.

Two types of antihypertensive agents were tested in this study: (1) type I: agents that change the circadian rhythm and (2) type II: agents that shifts the entire BP profile downward. It is worth noting that the dosing time does not change the BP misclassification rate for type II anti-hypertensive drugs as administration does not change the circadian rhythm of BP. These drugs could have delayed effect or their concentrations at steady state are much higher than their own EC50 (typically seen in ACEs inhibitors and ARBs.)

In this study, we tested our results in two populations: hypertensive patients from NDAs in the internal database of FDA and NHANES Adult Database (BPs ≥ 140 mmHg). Baseline BP distributions from the two population likely represent the US adult population to the best of our knowledge. Our simulation showed that our analysis results from FDA data base could be extended to the NHANES population.

The population baseline BP model developed by Hempel and colleagues [18] was qualified and adopted for the simulation of long term baseline BP in our simulation. Several other models were also available in the literature to describe the daily based variability of BP. Some models focused on the BP deference between daytime and nighttime BP such as the square wave fit model [27], some model focused on the transit phase between day time and night-time BP changes such as double logistic model [20, 28, 29]. The limitation of these models is the lack of description of the important features regarding BP fluctuations. In addition, between individual variability as well as inter-occasion variability within individuals are rarely estimated. Cosinor models and fourier analysis with different number of harmonics etc. [18, 19, 30] focused on describing the 24 h BP curve. With more than one cosine term, cosinor and fourier models share a similar description to circadian BP changes. The baseline BP profiles were described in this work use a function with two cosine terms. This model quantifies the time-course of the baseline BP in hypertensive patients accounting for variability between and within patients. The advantage of the model is the estimation of the inter-individual variability for the rhythm-adjusted 24 h mean, amplitude of the cosine terms, and clock time as well as the inter-occasion variability for the rhythm-adjusted 24 h mean and clock time. Visual predictive checks performed in the study using actual ABPM data from 225 subjects showed that the baseline BP model were able to reasonably describe the circadian rhythm of the BP profile over clock times (see Electronic Supplementary Material for additional information).

In this study, the mean BP during office hours (8:00 AM to 6:00 PM) was selected as the true BP for the virtual patients’ BP. The time window selected reasonably accounts for the time of the BP measurement that drives the treatment decision making. BP measurements made at a specific times during the office-hours are assumed to represent the individual’s average. In addition, the cardiovascular risk models published were developed based on BP measurement during the day time window. This allows the extension of the simulations to explore potential public health outcomes.

Finn-Home study [31] recently showed that when BP was measured both in the morning and evening for a period of at least 7 days, the BP seems to correlate well to cardiovascular events. We performed similar trial simulation using population BP model to imitate the protocol of Finn-Home study. Both office cuff BP (mean of two measures at a typical clinic visit) and Home BP (mean of 28 measures both in the morning between 6 and 9 AM and evening between 6 and 9 PM for 7 days) were simulated and compared to simulated “true” BP of the patients. Home BP correlated well to patients’ “true” BP than Office BP, which was in line with the results from Finn-Home study. Hence, the result further validated the population BP model adopted in our clinical trial simulation. Better correlation of home BP to cardiovascular risk than office measurement in the Finn-Home study as well as better correlation of home BP to “true” BP than office BP in our simulation may attribute to the following factors: (1). 6:00–9:00 AM and 6:00–9:00 PM were the time frame where BP tended to changes significantly due to morning surge and evening decline. One BP measurement may be different from the other significantly during the time frame, which has been verified in our simulation. However, if we took enough measurements within the time frame, mean value should be close to patients’ true BP since we were taking average of low and high values. This also explains why BP misclassification rate was higher during the time frame in our simulation results. (2) home measurement was a mean value out of 28 measurements. Random measurement error associated to the mean value was very low. Office measurement was mean of two measurements, hence random measurement error associated would be definitely higher. Instead of suggesting to take repeated home BP, the primary goal of Finn-Home study was to identify demographic, lifestyle, clinical and psychological characteristics suggestive of masked hypertension because it is not feasible to measure home BP on all office normotensive individuals. Our clinical simulation was also tried to provide some methods such as optimal clinic visit times, BP calibration et al. to improve accuracy of office BP measures.

In conclusion, as a result of issues relating to current clinical practice and cuff BP measurement error, cuff measured ΔBPs systematically over or under-estimate the actual ΔBP in a typical clinical practice setting, leading to a significant percent of patients misclassified to an incorrect BP category, hence incorrect treatment decisions. This BP misclassification rate is sensitive to the time of cuff BP measurement as well as type of anti-hypertensives. In general, early morning (8:00–10:00 AM) or late afternoon (16:00–18:00 PM) was identified to be the worst time frame for clinic visit and provided highest BP misclassification rate for all scenarios. Selecting a optimal clinic visit time or BP calibration based on patients’ baseline and after treatment visit times to better account for the circadian rhythm of the BP profile may decrease the BP misclassification in a typical clinical visit.

Acknowledgment

The authors would like to thank Dr. Karen A. Matthews (Distinguished Professor of Psychiatry, Professor of Epidemiology and Psychology, Director, Pittsburgh Mind–Body Center Director, Cardiovascular Behavioral Medicine Research Program, Department of Psychiatry, University of Pittsburgh School of Medicine) for providing ABPM data to evaluate baseline BP model. The project was also supported by Indiana Clinical and Translational Sciences Institute (Dr. Robert Bies). Funded by FDA-Pharmacometrics Critical Path Fellowship.

Disclaimer

The views expressed in this article are those of the authors and do not necessarily reflect the official views of the FDA.

Supplementary material

10928_2012_9250_MOESM1_ESM.doc (347 kb)
Supplementary material 1 (DOC 347 kb)

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© Springer Science+Business Media, LLC (outside the USA) 2012