Biases in identifying risk factor thresholds: A new look at the "lower-is-better" controversy for cholesterol, blood pressure and other risk factors

Ian Marschner

Pfizer Australia & NHMRC Clinical Trials Centre

Linear Relationship

• Relationship between a risk factor and the occurrence of a disease event is essentially linear on an appropriate scale (usually the log-incidence scale)

• Existence of a linear relationship suggests a “lower-is-better” approach to risk factor modification

Example – Coronary and Vascular events related to cholesterol and blood pressure

Law & Wald. BMJ 2002.

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Threshold Relationship

• Threshold: point at which a predominantly linear relationship between a risk factor and a disease event becomes effectively constant

• Existence of a threshold relationship can suggest less aggressive risk factor modification strategies since modification is of no benefit beyond a certain point

Example – CARE Trial

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J-Curve Relationship

• J-curve: predominantly linear positive relationship between a risk factor and a disease event reverses and becomes negative

• Existence of a J-curve relationship can suggest less aggressive risk factor modification strategies since modification is of no benefit and may even be harmful beyond a certain point

Example – Framingham Study

Note: J-curves havealso been observedfor stroke events

Randomised Studies

• Randomised studies of intensive versus moderate lowering of cholesterol support lower-is-better e.g. PROVE-IT study:

Example – CARE Trial

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Randomised Studies

• Randomised studies of intensive versus moderate lowering of cholesterol support lower-is-better e.g. PROVE-IT study:

Conflicting Evidence

• Existence of conflicting evidence has complicated the assessment of whether lower-is-better for cholesterol and blood pressure

• One explanation for this is that bias has led to spurious non-linear threshold or J-curve relationships in some studies, particularly those on primary or secondary prevention cohorts

Explanation for conflicting evidence

• Confounding of primary risk factor and residual risk level in primary or secondary prevention studies– E.g. cholesterol level confounded with non-cholesterol

risk level• Effect modification often exists between primary

risk factor and residual risk level– E.g. risk coronary event increases more quickly with

cholesterol when the individual has lower non-cholesterol risk level

• Combined effect of confounding and effect modification is a spurious non-linear relationship even when the underlying relationship is a linear lower-is-better one

Plan for rest of talk

1. Provide evidence that there is confounding in primary and secondary prevention studies

2. Provide evidence that effect modification can exist, particularly in cardiovascular contexts

3. Explain how the two can combine to produce spurious non-linear relationships that could explain the apparent threshold and J-curve relationships seen in some prior studies

Confounding• In patients selected because they have had a

previous event (secondary prevention) or because they have not had a previous event (primary prevention) the risk factor and the residual risk level is confounded

• Example 1: In order to have had a prior heart attack, patients with low cholesterol have more non-cholesterol risk factors

• Example 2: In order not to have had a prior heart attack, patient with high cholesterol have less non-cholesterol risk factors

Example – Simulation Results

Assumptions for simulated population:Incidence of coronary event is related to 8 risk factors (incl. cholesterol) according to a modelNo relationship between cholesterol and no. of non-cholesterol risk factors in the full populationCoronary events simulated according to the risk factor modelPrimary and secondary prevention sub-populations identified

Example – LIPID Trial

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Effect Modification

• Effect Modification: Event rate increases less quickly as the risk factor increases in patients with higher residual risk

• Examples: Coronary and vascular event rate increases less quickly with cholesterol level and blood pressure in patients with higher non-cholesterol and non-BP risk level

ExamplesLIPID: Rate ratio of coronary event for each unit of cholesterolLaw: Rate ratio of coronary event for each unit of cholesterol

PSC: Rate ratio of vascular event for each unit of blood pressure

Combination of Confounding and Effect Modification

• Confounding alone leads to linear attenuation of the risk factor relationship– Strength of association between risk factor and

disease event may be under-estimated

• Combination of confounding and effect modification leads to non-linear attenuation– Association may appear to be threshold or J-curve

Linear Attenuation(confounding only)

• Risk level: P = primary risk factor

R = residual risk level• Incidence rate:

logt;P,R) = logt) + aP + bR

• Confounding: R = c + dP (d<0)• Apparent relationship:

logt;S) = logt) + (a+bd)P

• Attenuation: a > a+bd

Cholesterol level (mmol/L)

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AHypothetical Effect

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Non – linear attenuation(confounding and effect modification)

• Risk level: P = primary risk factor

R = residual risk level• Incidence rate:

logt;S,NS) = logt) + (a+a0R)P + bR

• Confounding: R = c + dP (d<0)• Apparent relationship:

logt;S) = logt) + (a+a0c+bd)P + a0dP2

• Attenuation: apparent quadratic relationship

Cholesterol level (mmol/L)

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Theoretical Calculations(under the assumption that lower-is-better)

Apparent Relationships

• Bias can lead to apparent thresholds and J-curves even when the underlying model is linear

Adjustment for measurement error (regression dilution)

• Measurement error accounts for some but not all of the attenuation

Conclusions

• Analyses showing an apparent threshold relationship may not be inconsistent with a linear “lower is better” relationship

• Aggressive treatment strategies may be warranted despite an apparent threshold or J-curve in the risk factor

• Analyses adjusting for residual risk level are crucial and may ameliorate the bias

Randomised Studies

• Intervention strategies are best based on randomised trials comparing (less aggressive) threshold-based intervention with (more aggressive) non-threshold-based intervention

• Example: Despite earlier suggestions of a cholesterol threshold, large scale trials have now confirmed aggressive treatment of high risk patients even at lower cholesterol levels

Final Word• Even when we are confident that there is no bias in

the risk factor model, assessment of risk factor intervention strategies can be dangerous based solely on risk factor models derived from prospective cohort studies

• Degree of improvement in the risk factor may not be a complete “surrogate” for the effect of the intervention

• Randomised studies capture the complete effects of the intervention and are therefore preferable for assessing risk factor interventions strategies

Randomised Studies

• Intervention strategies are best based on randomised trials comparing (less aggressive) threshold-based intervention with (more aggressive) non-threshold-based intervention

• Example: Despite earlier suggestions of a cholesterol threshold, large scale trials have now confirmed aggressive treatment of high risk patients even at lower cholesterol levels

Example – Simulation Results

Assumptions for simulated population:Incidence of coronary event is related to 8 risk factors (incl. cholesterol) according to a modelNo relationship between cholesterol and no. of non-cholesterol risk factors in the full populationCoronary events simulated according to the risk factor modelPrimary and secondary prevention sub-populations identified