The 12month risk of disease progression was estimated by a previously
described "personintervals" method (Stats Med 1992, 11:17311745)
with some modifications. Each measurement contributed a unit of observation to a
survival analysis, with time projected up to a maximum of 12 months i.e.,
the time scale was reset to zero at each new measurement, and age at each
measurement and CD4 percent or viral load defined the "baseline" covariates. The
hazard rate of disease progression, λ, was expressed as λ=a+b.exp(k.x) where
x=marker value. 12month risk calculated from 1exp(λ).
An approximate 6month risk can be calculated from 1exp(0.5λ).
The parameters a, b,
and k were allowed to depend on age: log_{e}(a)=a_{1}+a_{2}.age,
log_{e}(b)=b_{1}+b_{2}.age, log_{e}(k)=k_{1}+k_{2}.age.
Models were estimated using the ml command in Stata (StatCorp, College
Station, TX). Goodness of fit, as assessed by loglikelihood, was improved by
first applying a markerspecific age transformation. The maximum likelihood
estimates are shown in the following table.
Marker

Endpoint

a_{1}

a_{2}

b_{1}

b_{2}

k_{1}

k_{2}

CD4 percent

AIDS

2.2422

0.7753

0.3000

0.2557

2.3422

0.4130

Death

3.4948

1.1472

0.0005

0.4523

2.0135

0.3354

(CD4 count+1)/10

AIDS

1.9137

0.3557

0.5124

0.1908

4.4111

0.5660

Death

3.0564

0.6700

0.0514

0.2455

4.0416

0.5121

7log_{10}(viral load)

AIDS

2.4231

0.8246

0.3937

0

0.3487

0

Death

4.0474

1.1982

1.0972

0

0.3637

0

TLC/1000

AIDS

2.1740

0.5188

0.3285

0.1215

0.5048

0.6914

Death

3.6393

0.6402

0.1210

0.0520

0.2254

0.6069

Age transformation for CD4 percent, TLC, and viral load: loge(age+0.3) with age
recorded in years.
Age transformation for CD4 count: age=4+0.1 x (age4) if age > 4 years.
Example: Estimated 12month probability of AIDS for a 5¾
year old child with a current CD4 cell count of 430 cells/mm³.
 Transformed age = 4 + (5.754)/10 = 4.175
 Transformed CD4 count = (430+1)/10 = 43.1
 log_{e}(a) = 1.9137  0.3557 x 4.175 = 3.3987
 a = exp(3.3987) = 0.03342
 log_{e}(b) = 0.5124  0.1908 x 4.175 = 0.2842
 b= exp(0.2842) = 0.7526
 log_{e}(k) = 4.4111 + 0.5660 x 4.175 = 2.0480
 k = exp(2.0480) = 0.1290
 λ = 0.03342 + 0.7526 x exp (0.1290 x 43.1) = 0.03632
 12month probability of AIDS = 1exp(0.03632) = 0.0357 or 3.57%
