Using the Prognostic Model of Hayllar et al to Predict Survival in Cystic Fibrosis

 

Parameters:

(1) height in meters

(2) presence or absence of hepatomegaly

(3) observed FVC as percent of predicted FVC

(4) observed FEV1 as percent of predicted FEV1

(5) WBC count

 

predictive index =

= (-3.41 * (height in meters)) + (0.99 * (hepatomegaly value)) - (0.038 * (observed FVC as percent of predicted)) - (0.059 * (observed FEV1 as percent of predicted)) + (0.090 * (WBC value))

 

where:

• hepatomegaly value = 0 if absent or 1 if present

• WBC value = (WBC count per µL / 1000)

• predicted FVC and FEV1 can be predicted in adults using the equations of Crapo et al (1981)

 

Interpretation:

• The probability of survival is read from Figure 2, page 315.

• There are two sigmoid curves: 1 year survival and 6 month survival versus predictive index.

 

Approximation to Curves in Figure 2

Index	Probability of 1 Year Survival
<= -10	1.0
-10 to -7 (curved)	(-0.016667 * ((index) ^2)) - (0.35 * (index)) - 0.83333
-7 to -5 (linear)	(-0.35 * (index)) - 1.66
-5 to -4 (curved)	< 0.10
> -4	0

 

 

Index	Probability of 6 Month Survival
<= -9	1.0
-9 to –6 (curved)	(-0.025208 * ((index) ^2)) - (0.493546 * (index)) - 1.396958
-6 to –4.25 (linear)	(-0.310811 * (index)) - 1.196622
-4.25 to –3.25 (curved)	< 0.10
> -3.25	9

 

Alternative to Curve Approximation

 

probability of survival = 1 - (probability of mortality)

 

probability of mortality =

= EXP (X) / (1 + EXP(X))

 

Hypothesis: If a constant were added to the predictive index, then this value could be used to calculate the probability of mortality.

 

Since a predictive index of -6.4 has a 1 year survival probability of 0.58 (mortality probability of 0.42) and a 6 month survival probability of 0.75 (mortality probability of 0.25), then the following constants can be calculated.

 

constant for 6 month course: 5.3004

constant for 1 year course: 6.0772

 

probability of mortality at 1 year =

= EXP((predictive index) + 6.0772) / (1 + EXP((predictive index) + 6.0772))

 

probability of mortality at 6 months =

= EXP((predictive index) + 5.3004) / (1 + EXP((predictive index) + 5.3004))

 

It will be interesting to see how well this performs in predicting the curve in Figure 2.