Description

The clinical rule for predicting renal artery stenosis in the previous section was derived from a probability equation using variables from a multivariate logistic regression model. This study was done at the Hospital Dijkzigt, Rotterdam, the Netherlands.


Patients selected: 18 to 75 years of age with preserved renal function (serum creatinine <= 200 µmol/L) and either:

(1) drug resistant hypertension, or

(2) increase in serum creatinine concentration during therapy with an angiotensin-converting enzyme (ACE) inhibitor

 

Parameters used for the multivariate logistic regression model:

(1) age in years

(2) gender

(3) smoking history

(4) signs and symptoms of atherosclerotic vascular disease

(5) duration of hypertension

(6) body mass index (BMI)

(7) presence of abdominal bruit

(8) serum creatinine

(9) serum cholesterol and/or history of cholesterol lowering drug therapy

 

Parameter

Finding

Points

smoking history

never smoked

0

 

ever smoked

1

gender

male

1

 

female

0

signs and symptoms of atherosclerotic vascular disease

absent

0

 

present

1

onset of hypertension

within <= 2 years

1

 

more than 2 years

0

body mass index

< 25 kg/m^2

0

 

>= 25 kg/m^2

1

abdominal bruit

absent

0

 

present

1

serum cholesterol

<= 6.5 mmol/L and not on cholesterol lowering therapy

0

 

<= 6.5 mmol/L and on cholesterol lowering therapy

1

 

> 6.5 mmol/L

1

 

where:

• Signs or symptoms of atherosclerotic vascular disease include: femoral or carotid bruit, angina pectoris, claudication, myocardial infarction, cerebrovascular accident, or vascular surgery.

 

linear predictor after shrinking (LPs) =

= (-7.033) + (0.052 * (age in years)) + (0.029 * (75 - (age in years)) * (ever smoker)) - (0.877 * (sex)) + (0.515 * (atherosclerotic vascular disease)) + (0.565 * (recent onset)) - (0.904 * (obesity)) + (1.490 * (abdominal bruit)) + (0.441 * (hypercholesterolemia)) + (0.028 * (serum creatinine concentration))

 

where:

• The initial coefficients derived from the multivariate logistic regression model were shrunk using a factor of 0.88 after bootstrapping procedures.

 

probability of renal artery stenosis =

= 1 / (1 + EXP((-1) * (LPs)))

 

The average standard error of the rounded linear predictor values is used to calculate the 95% confidence intervals, as follows:

 

95% confidence intervals =

= 1 / (1 + EXP((-1) * ((LPs) + (1.96 * (standard error)))))

= 1 / (1 + EXP((-1) * ((LPs) - (1.96 * (standard error)))))

 

Development of clinical prediction rule:

(1) The equation subtracts values for male sex and obesity. It appears that to create the clinical prediction rule the opposite findings (female sex, non-obesity) had values added.

(2) To develop the points for the clinical prediction rule, the rescaled regression coefficients were multiplied by 2, then rounded.


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