1. J-Curve Relationships Between Risk Factors and Cardiovascular Outcomes
William J. Kostis, Ph.D., M.D.
Rutgers Robert Wood Johnson Medical School
38th Panhellenic Congress of Cardiology
Athens, Greece
October 19, 2017

2. Disclosures
No personal financial disclosures related to this presentation

3. Introduction
What is the relationship between a given risk factor and a given outcome?
Risk Factor
Outcome

4. Introduction
There are, in general, two types of risk-outcome relationships that exist in cardiovascular medicine
Monotonic relationships (linear, exponential, or otherwise), as is the case with smoking, where even one cigarette is worse than total abstinence
J-shaped (or U-shaped), as is the case for alcohol, systolic blood pressure (SBP), and body mass index (BMI)

5. Introduction
In this presentation, we will explore the J-shaped relationships between several cardiovascular risk factors and all-cause mortality
While J-shaped relationships of body mass index (BMI) and systolic blood pressure (SBP) with mortality have been described, little data are available on long-term follow-up in controlled clinical trials
We will examine the J-shaped relationships between BMI and SBP and cardiovascular risk, using data from several clinical trials (SHEP, ALLHAT, and SPRINT)
We will review potential explanations for these J-shaped relationships

6. Some J-Curves in the Literature
Patients with CHD
Denardo et al. Am J Med 2010;123:719-26

7. Some J-Curves in the Literature
Aggressive BP Lowering in ESRD
Sim et al. J Am Coll Cardiol 2014;64:588-97

8. Two Etiologies of J-Curves in Cardiovascular Medicine
PHYSIOLOGY
Physiological parameters may be associated with risk (risk factors) when elevated
Blood pressure, cholesterol, and body weight (BMI) are associated with CV events when elevated above “normal”
On the other hand, very low levels or zero values are not compatible with life
Therefore, there must be a risk factor level where the risk is minimum
This implies that a risk factor level below the optimum must be associated with increased risk
NON-HOMOGENEOUS POPULATION (A Variation of Simpson’s Paradox)
In this variation of the paradox, different subsets of patients contribute differentially to the descending (left) and ascending (right) portions of the risk factor level to risk relationship

9. Simpson’s Paradox Edward H. Simpson 1951
Simpson, Edward H. (1951). "The Interpretation of Interaction in Contingency Tables". Journal of the Royal Statistical Society, Series B 13: 238–241.

10. A J-Relationship due to
Simpson’s Paradox
A J-Relationship due to
Simpson’s Paradox
Group 2
Group 1
22-Year Probability of All-Cause Mortality
Edward H. Simpson 1951
Simpson, Edward H. (1951). "The Interpretation of Interaction in Contingency Tables". Journal of the Royal Statistical Society, Series B 13: 238–241.
BMI

11. Systolic Hypertension in the Elderly Program (SHEP)

12. Study Hypotheses
That there is a J-shaped relationship between BMI and both CV and all-cause mortality at 22 years in the Systolic Hypertension in the Elderly Program (SHEP)
That any observed J-curve may be explained in part by a variation of Simpson’s Paradox with at least two subsets of patients with different BMI-mortality relationships
That the downsloping (left) and the upsloping (right) portions of the curve may be due to identifiable subsets of patients

13. Methods
SHEP was a placebo-controlled, randomized clinical trial of antihypertensive therapy in patients with isolated systolic hypertension aged 60 and older
The relationship between CV and all-cause mortality at the 22-year follow-up with baseline BMI was examined in 4,211 SHEP participants
Logistic regression and Cox models were used to assess the relationship of baseline BMI and other factors with CV and all-cause mortality

14. J-Curves for Body Mass Index (BMI) vs. Mortality
Systolic Hypertension in the Elderly Program (SHEP) Participants (n=4736)
Select those with 15 kg/m2 ≤ BMI ≤ 45 kg/m2 (n=4631)
Subjects without missing values (n=4211), number of events=2514
Analysis Plan
Build models with BMI, BMI2, and BMI3 to predict time to death (CV death or other cause)
Model selection of covariates using GLMnet
Build models with BMI, BMI2, and BMI3 + covariates from (II)
If J-curve is highly significant in (I) but not in (III), select subsets (subset 1 with low BMI, subset 2 with high BMI)
Perform a classification with response High or Low BMI, using the covariates (I) but not including BMI; use LR, PCA, SVM, etc.

15. Linear vs. Quadratic vs. Tricubic Fit
Model Terms:
Fit the Logistic (or Cox) Models with
(M1) Death = BMI
(M2) Death = BMI + BMI2
(M3) Death = BMI + BMI2 + BMI3
Test for the relationship (M3 > M2 > M1)
If true, this suggests a J-curve
Add covariates to the model and if the effect disappears then is possible that a Simpson’s paradox exists. This can be verified by partitioning the data into subgroups.

16. Available Baseline Variables That May Be Associated With Mortality
Randomization group
Age
Gender
Race
Glucose
Smoking
BMI
SBP
DBP PP
History of MI
LV Failure
Carotid Bruit
WBC
Heart Rate
Abnormal EKG
EtOH Use

17. Results (SHEP)
In unadjusted analyses, a J-relationship was observed between BMI and
All-cause mortality (linear term p=0.0318, quadratic term p=0.3217, and tricubic term p=0.0046)
CV mortality (linear term p=0.0962, quadratic term p=0.6866, and tricubic term p=0.0908)

18. In SHEP, the tricubic model fit was highly significant without covariates, but both tricubic and quadratic effects were attenuated after adding covariates
to the respective models
Tricubic
22-Year Probability of All-Cause Mortality
Quadratic
BMI

19. Hazard Ratios of BMI for All-Cause Mortality
Using Adjusted and Unadjusted Models
Log Hazard Ratio of All-Cause Mortality
BMI

20. Hazard Ratios of BMI for All-Cause Mortality
Using Adjusted and Unadjusted Models (Plus Covariates Alone)
Log Hazard Ratio of All-Cause Mortality
BMI

21. Results (SHEP)
The lowest risk was at a BMI of 25.9 kg/m2 for all-cause mortality and a BMI of 25.5 kg/m2 for CV mortality
The J-shaped relationship between BMI and mortality was attenuated after adjustment for age, gender, comorbidities (e.g. diabetes, heart failure), and other risk factors for CV disease (e.g. smoking and dyslipidemia)
Age and gender were significant univariate predictors of mortality
age (p<0.0001), female gender (p=0.0063) for all-cause mortality
age (p<0.0001), female gender (p=0.0004) for CV mortality

22. Attenuation of the J-shaped relationship between BMI and mortality was seen after adjustment for age, gender, and comorbidities (SHEP)
A model based on demographics, risk factors, and comorbidities alone (without BMI) results in a similar curve as the unadjusted BMI model
This implies that these factors mediate or explain much of the BMI-mortality J-shaped relationship
This point is also evidenced by the fact that the BMI-mortality J-shaped relationship is attenuated after adjustment

23. Low and High BMI Subgroups (SHEP)
For simple thresholds,
BMI < 20 and BMI > 40 may be used
These correspond to approximately the upper and lower 20% of the distribution
BMI
<20
>40
Log Hazard Ratio of All-Cause Mortality
BMI

24. Factors Associated with Low / High BMI
Logistic regression models were used to determine which covariates were associated with the extrema of BMI
High BMI was associated with older age
Low BMI was associated with smoking, fasting glucose, and elevated WBC
Principal component analysis was also used to identify covariates associated with the the extrema of BMI
High BMI was associated with older age, SBP, and PP
Low BMI was associated with diabetes and fasting glucose
GLM- and SVM-based models were able to classify patients into the low BMI and high BMI groups with reasonable accuracy (80.6% and 84.4%, respectively)

25. Principal component clusters for two extreme BMI groups (<20 vs
Second principal component
First principal component

26. Variables contributing to the first principal component in the two groups
Diabetes
0.00
0.65
-0.65
Glucose
0.13
0.68
-0.55
WBC
0.02
0.15
-0.13
LV Failure
0.08
0.18
-0.1
Active Rx
0.01
0.03
-0.02
Smoking
0.07
0.06
Sex
0.26
0.11
Alcohol
0.23
0.17
Age
0.37
0.12
0.25
SBP
0.58
0.51
Pulse Pressure
0.62
0.54

27. Factors Associated with Overweight
Insulin resistance and hyperinsulinemia
Diabetes (Type II)
Metabolic Syndrome
High LDL, Low HDL, high triglycerides, high ApoB100
Hypertension
Left ventricular hypertrophy
Heart failure
Arrhythmias
Sudden death
Sympathetic overactivity
Prolonged QT
Endothelial dysfunction
Obstructive sleep apnea
Underweight – BMI <18.5 kg/m2
Normal weight – BMI 18.5 to 24.9 kg/m2
Overweight – BMI 25.0 to 29.9 kg/m2
Obesity – BMI ≥30 kg/m2
Obesity class I – BMI of 30.0 to 34.9 kg/m2
Obesity class II – BMI of 35.0 to 39.9 kg/m2
Obesity class III – BMI ≥40 kg/m2
(severe, extreme, or massive obesity)
Underweight: BMI < 18.5 kg/m2
Overweight: BMI > 25 kg/m2

28. Factors Associated with Underweight
Smoking
Stress
Comorbidities
Heart failure
Cancer
COPD
Renal Disease
Frailty
Effect observed only in the first one or two years of follow-up (attrition/survivorship effect)
Aging
Underweight: BMI < 18.5 kg/m2
Overweight: BMI > 25 kg/m2

29. SHEP Summary
There is a J-shaped relationship between BMI and both CV and all-cause mortality at 22 years in the Systolic Hypertension in the Elderly Program (SHEP)
The J-curve BMI-mortality relationship is markedly attenuated after adjustment for demographics, risk factors, and comorbidities
High BMI was associated with older age, SBP, and PP
Low BMI was associated with smoking, fasting glucose, and elevated WBC
The J-curve may be explained in part by a variation of Simpson’s Paradox: two subsets of patients with different BMI-mortality relationships

30. SHEP Conclusions
This study indicates that both very low and very high BMI are markers of high risk
The J-relationship between BMI and mortality is mediated by age, sex, comorbidities, and other risk factors for cardiovascular disease

31. Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT)

32. Study Hypotheses
That there is a J-shaped relationship between BMI and all-cause mortality in the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT)
That any observed J-curve may be explained in part by a variation of Simpson’s Paradox with two at least two subsets of patients with different BMI-mortality relationships
That the downsloping (left) and the upsloping (right) portions of the curve may be due to identifiable subsets of patients

33. Methods
ALLHAT was a randomized, double-blind, practice-based clinical trial that included 32,819 hypertensive participants with at least one other CHD risk factor, aged at least 55 years, and who were followed for 8 years for all-cause mortality.
We examined the relationship between baseline BMI and all-cause mortality in unadjusted and adjusted analyses. Patients randomized to doxazosin and those with missing values were excluded.
This relationship between baseline BMI and all-cause mortality was also studied using linear, quadratic, and cubic spline models.
Univariate analyses were performed to study the individual relationships between baseline characteristics, BMI, and all-cause mortality.
Multivariate analyses were performed to study the relationship between BMI and all-cause mortality.

34. The Relationship of Body Mass Index to All-Cause Mortality
at 8 Years of Follow-Up in ALLHAT

40. BMI

42. Results (ALLHAT)
A J-shaped relationship between BMI and all-cause mortality was observed at 8 years in the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT)
There was increased risk among those with higher BMI and the highest risk among those with very low BMI
In analyses adjusted for age, gender, comorbidities, and risk factors (e.g. DM, smoking) for CV disease, the J-shaped mortality versus BMI curves were markedly attenuated, suggesting that these factors may mediate this relationship

43. Systolic Blood Pressure Intervention Trial (SPRINT)

44. Study Hypotheses
That there is a J-shaped relationship between SBP and all-cause mortality in the Systolic Blood Pressure Intervention Trial (SPRINT)
That any observed J-curve may be explained in part by a variation of Simpson’s Paradox with two at least two subsets of patients with different SBP-mortality relationships
That the downsloping (left) and the upsloping (right) portions of the curve may be due to identifiable subsets of patients

45. Methods
SPRINT is a randomized clinical trial of antihypertensive therapy comparing an intensive-treatment (target SBP <120 mm Hg) to a standard-treatment (target SBP <140 mm Hg) strategy in patients aged 50 years or older with hypertension and increased cardiovascular risk, but without diabetes or history of stroke
Increased cardiovascular risk was defined by one or more of the following:
clinical or subclinical cardiovascular disease other than stroke
chronic kidney disease with eGFR of 20 to less than 60 mL/min per 1.73 m2 BSA
a 10-year risk of cardiovascular disease of 15% or greater on the basis of the Framingham risk score*
age of 75 years or older
The primary composite outcome was myocardial infarction, other acute coronary syndromes, stroke, heart failure, or death from cardiovascular causes

46. Methods
SPRINT was terminated early due to a finding of benefit in the intensive-control group
On August 20, 2015, the NHLBI director accepted a recommendation from the DSMB to inform the investigators and participants of the cardiovascular-outcome results after analyses of the primary outcome exceeded the monitoring boundary at two consecutive time points thus initiating the process to end SPRINT early
The median follow-up on August 20, 2015, was 3.26 years of the planned average of 5 years

47. Methods
We studied the relationship of SBP at 3 months of treatment to all-cause mortality and cardiovascular mortality in 8,905 patients randomized to the intensive-treatment or standard-treatment groups in SPRINT
Univariate and multivariate (unadjusted and adjusted) models were used to assess the relationship of SBP at 3 months and other factors with all-cause mortality

48. Log HR for All-Cause Mortality in the Standard-Treatment Group
as a Function of SBP at 3 Months in SPRINT
Log Hazard Ratio for All-Cause Mortality
SBP at 3 Months (mm Hg)

49. Results (SPRINT)
In the standard-treatment group, a J-shaped relationship between SBP and all-cause death was observed in unadjusted analyses as well as in analyses adjusted for demographics or for all covariates (p<0.001 for all)
These relationships were similar for cardiovascular (CV) and non-CV death (p<0.001 for all)
Patients with low SBP were more likely to be Hispanic, have history of CV disease, and to take a statin
Patients with high SBP were more likely to be Black, have higher Framingham risk, and have higher LDL cholesterol

50. Results (SPRINT)
A J-shaped relationship between SBP at 3 months and all-cause mortality was observed in the standard-treatment group of SPRINT after a median follow-up of 3.26 years (the study was terminated early for benefit of intensive-treatment)
For SBP ≥ 130 mm Hg, there was a positive linear relationship (p=0.025), while for SBP < 110 mm Hg, the relationship was negative (p=0.007)
There was increased risk among those with both high (≥130 mm Hg) and low (< 110 mm Hg) SBP at 3 months
These effects were not statistically significant in the intensive-treatment group

51. Conclusions
J-shaped relationships are not uncommon in cardiovascular medicine
We have found J-shaped relationships between both BMI and SBP and all-cause mortality in three large clinical trials
The J-shaped relationships in each case appear to be mediated by additional risk factors, as evidenced by the attenuation of the J-shaped relationships when additional risk factors are included in adjusted models

52. Implications
Further study into potential benefits and harms to population subsets being treated for various cardiovascular risk factors is warranted
Differing therapies may be appropriate for the different population subsets identified in such analyses

53. Thank you