This study examined whether using a weighted average of past blood pressure (BP) measurements (antecedent BP) is a better predictor of cardiovascular disease (CVD) risk than the simple average of antecedent BP. The study used data from the Framingham Heart Study and found that while the weighted average model showed a slightly higher predictive accuracy than the simple average model based on the C-statistic, statistical tests did not show a significant improvement, indicating refinement is needed. Future work could explore different populations and weighting methods to potentially find a statistically significant improved predictive model using weighted antecedent BP.

1. Weighted Average Blood Pressure as a Predictor of
Cardiovascular Disease
Ije Okafor, Anthony Bonifonte M.S., Dr. Turgay Ayer PhD
H . Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA
• Cardiovascular disease (CVD) is America’s leading health problem, and the leading
cause of death worldwide
• High blood pressure, also known as hypertension, is the most important risk factor for
premature cardiovascular disease
• Traditional risk factors for CVD include age, sex, cholesterol, smoking, diabetes, and
elevated levels of BP
Background:
Previous Study:
Conclusions:
• Antecedent BP is a statistically significant predictor of CVD risk
• Antecedent BP is a stronger predictor of CVD risk than current BP
Study used the simple average of antecedent BP measurements
Research Objective: Study Inclusion:
Determine if weighted average antecedent
BP is a better predictor of CVD risk than
simple average antecedent BP
• Framingham Heart Study
• 3909 patients attended Baseline Exam 8
• 2127 patients met selection criteria
Core logistic regression models:
• Traditional risk factors + Current BP
• Traditional risk factors + Antecedent BP
• Traditional risk factors + Antecedent BP + Current BP
Clinical Measurements:
Current BP Model
HR (95% CI) & P
Value
Antecedent BP Model
HR (95% CI) & P Value
Current and Antecedent BP
Model
HR (95% CI) & P Value
Age 1.03 (1.02-1.04) <.001 1.03 (1.02-1.04) <.001 1.03 (1.02-1.04) <.001
Sex 1.75 (1.50-2.06) <.001 1.80 (1.52-2.10) <.001 1.79 (1.52-2.10) <.001
Smoking (yes/no) 1.31 (1.12-1.54) <.001 1.36 (1.16-1.60) <.001 1.35 (1.15-1.58) <.001
Diabetes (yes/no) 1.23 (1.04-1.47) .0186 1.24 (1.05-1.48) .0143 1.23 (1.03-1.47) .0195
Cholesterol
(10 mg/dL)
1.03 (1.01-1.05) .0019 1.03 (1.00-1.01) .0028 1.03 (1.01-1.05) .0033
Diuretics 1.80 (1.35-2.40) <.001 1.46 (1.11-2.02) .0117 1.54 (1.14-2.07) .0043
Current BP
(10 mm Hg)
1.23 (1.19-1.27) <.001 1.12 (1.06-1.18) <.001
Antecedent BP
(10 mm Hg)
1.28 (1.24-1.36) <.001 1.16 (1.09-1.24) <.001
Methodology: Exponential Smoothing
Assigns exponentially decreasing weights to older observations.
Standard Formula: Ft+1 = (λ)Dt + (1-λ) Ft
• Ft+1 = Final weighted observation
• Dt = Current observation
• Ft = Previous observation
• λ = A weighing factor referred to as the smoothing constant
0.70048
0.7005
0.70052
0.70054
0.70056
0.70058
0.7006
0.70062
0.28 0.285 0.29 0.295 0.3 0.305 0.31 0.315 0.32
C-Index
Smoothing Constant (λ )
Optimal Smoothing Constant
Results:
Weighted Average Model vs. Simple Average Model
Current BP + Weighted Antecedent BP
HR (95% CI) & P Value
Current and Antecedent BP Model
HR (95% CI) & P Value
Age 1.03 (1.02-1.04) <.001 1.03 (1.02-1.04) <.001
Sex 1.78 (1.51-2.09) <.001 1.79 (1.52-2.10) <.001
Smoking (y/n) 1.35 (1.15-1.58) <.001 1.35 (1.15-1.58) <.001
Diabetes (y/n) 1.23 (1.03-1.46) .0217 1.23 (1.03-1.47) .0195
Cholesterol
(mg/dL)
1.03 (1.01-1.05) .0039 1.03 (1.01-1.05) .0033
Diuretics 1.53 (1.14-2.05) .0051 1.54 (1.14-2.07) .0043
Current BP 1.11 (1.05-1.17) <.001 1.12 (1.06-1.18) <.001
Antecedent BP
(Simple Avg)
1.16 (1.09-1.24) <.001
Antecedent BP
(Weighted Avg)
1.17 (1.09-1.25) <.001
Conclusion:
• Using a weighted antecedent BP average over a simple average showed some
improvements; however, this data was not statistically significant
• Refinement to this study may bring statistically significant results
Study Limitations:
• Predominately white study population
• Older population; more cases of CVD
• Sensitive smoothing constant
Future Work:
• Conduct a similar study on a more diverse population
• Explore all possible smoothing constant values; apply to additional models
• Explore weighing options outside of exponential smoothing
Acknowledgements: References:
1. Bonifonte, Anthony, MS, Turgay Ayer, PhD, Emir Veledar, PhD, Allison
Clark, BA, and Peter W.F. Wilson, MD. "Antecedent Blood Pressure as a
Predictor of Cardiovascular Disease." Journal of American Society of
Hypertension (2015): 690-96. Web.
1. Vasan, Ramachandran S., Joseph M. Massaro, Peter W.F. Wilson, Sudha
Seshadri, Philip A. Wolf, Daniel Levy, and Ralph B. D'Agostino.
"Antecedent Blood Pressure and Risk of Cardiovascular Disease: The
Framingham Heart Study." Journal of the American Heart
Association(2001): 48-53. Web
2. Chen, Ruijun, Kumar Dharmarajan, Vivek T. Kulkarni, Natdanai
Punnanithinont, Aakriti Gupta, Behnood Bikdeli, Purav S. Mody, and
Isuru Ranasinghe. "Most Important Outcomes Research Papers on
Hypertension." Journal of the American Heart Association (2013): 26-35.
Web.
• Anthony Bonifonte, Graduate Advisor
• Dr. Turgay Ayer, Faculty Advisor
• SURE Program, Summer 2016
Results: C-Statistic
Traditional risk factors + Current BP:
• C-Statistic 0.727 [ 0.704 - 0.75 ]
Traditional risk factors + Current BP + Antecedent
BP (simple average):
• C-Statistic: 0.734 [ 0.711 - 0.756 ]
Traditional risk factors + Current BP + Antecedent
BP (weighted average):
• C-Statistic: 0.735 [ 0.712 - 0.757 ]
The C-Statistic is a standard measure of the predictive accuracy of a logistic regression
model; equivalent to the area under the receiver operating characteristic curve
The weighted average BP model had a slightly higher C-statistic than the simple
average BP model, indicating an improvement between models
Results: IDI & NRI Tests
• NRI (Categorical): considers movement between predefined ranges of risk
• NRI (Continuous): tests the incremental differences in predicted probabilities
• IDI: measures the new models’ improvement in average sensitivity without reduction in
average specificity
Current BP
vs.
Current BP + Simple Avg Ant BP
95% CI; P-value
Current BP + Simple Avg Ant BP
vs.
Current BP + Weighted Avg Ant BP
95% CI; P-value
NRI
(Categorical)
0.0143 [ 0.0058 - 0.0227 ]; 0.0001 -7e-04 [ -0.0044 - 0.003 ]; 0.705
NRI
(Continuous)
0.2366 [ 0.1447 - 0.3284 ]; 0 0.0902 [ -0.0023 - 0.1827 ]; 0.056
IDI 0.0072 [ 0.0029 - 0.0115 ]; 0.0011 7e-04 [ -5e-04 - 0.0019 ]; 0.260
*Test showed statistically significant improvements when
antecedent BP was added to the model; confirmed
previous studies’ findings
*Test showed a positive continuous NRI,
suggesting some improvement between models;
however, this value was not statistically significant
Weighted Antecedent BP= λ(E7) + λ(1-λ)(E6) + λ(1-λ)2 (E5) + λ(1-λ)3 (E4) + λ(1-λ)4 (E3) + λ(1-λ)5 (E2) + (1-λ)6 (E1)
λ = 0.31
1-Specifity
Sensitivity
Area = 0.830