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The 12-month risk of disease progression was estimated by a previously described "person-intervals" method (Stats Med 1992, 11:1731-1745) 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 re-set 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. 12-month risk calculated from 1-exp(-λ). An approximate 6-month risk can be calculated from 1-exp(-0.5λ).

The parameters a, b, and k were allowed to depend on age:
loge(a)=a1+a2.age, loge(b)=b1+b2.age, loge(k)=k1+k2.age. Models were estimated using the ml command in Stata (StatCorp, College Station, TX). Goodness of fit, as assessed by log-likelihood, was improved by first applying a marker-specific age transformation. The maximum likelihood estimates are shown in the following table.

Marker

Endpoint

a1

a2

b1

b2

k1

k2

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

7-log10(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 (age-4) if age > 4 years.

Example: Estimated 12-month probability of AIDS for a 5¾ year old child with a current CD4 cell count of 430 cells/mm³.

  1. Transformed age = 4 + (5.75-4)/10 = 4.175
  2. Transformed CD4 count = (430+1)/10 = 43.1
  3. loge(a) = -1.9137 - 0.3557 x 4.175 = -3.3987
  4. a = exp(-3.3987) = 0.03342
  5. loge(b) = 0.5124 - 0.1908 x 4.175 = -0.2842
  6. b= exp(-0.2842) = 0.7526
  7. loge(k) = -4.4111 + 0.5660 x 4.175 = -2.0480
  8. k = exp(-2.0480) = 0.1290
  9. λ = 0.03342 + 0.7526 x exp (-0.1290 x 43.1) = 0.03632
  10. 12-month probability of AIDS = 1-exp(-0.03632) = 0.0357 or 3.57%