Estimating the monthly probabilities of a HIV patient's CD4 count moving to various CD4 categories or death prior to starting antiretroviral therapy is essential for larger models that consider the optimal time to initiate therapy. We developed an empirical model of the transition probability matrix and explore issues concerning censored data.

Methods:

Using approximately 11,200 HIV patients, we modeled the continuous time, pre-therapy natural history of CD4 counts by fitting a smoothing spline to each patient's observed CD4 counts prior to therapy. We cut each patient's spline into monthly intervals and recorded all of the (CD4 this month, CD4 next month) pairs represented. If the patient died within 6 weeks of the last pre-therapy CD4 date, we recorded a transition of (CD4 last date, death). Otherwise, we recorded a transition of (CD4 last date, censored). We then constructed the empirical table that tabulated the transitions among the various categories. We explored the effect of censored observations on empiric death rates by performing sensitivity analyses on how they may get distributed to the various CD4 categories and death. We compared the expected survival times of our models to a Weibull model of pre-therapy survival.

Results:

We created 5 CD4 categories: cat1: [0,50); cat2: [50,200); cat3: [200,350); cat4: [350, 500); cat5: [500, inf). We found that 15% of transitions from cat1, 11% from cat2, 9% from cat3, 7% from cat4, and 4% from cat5 were censored. If we ignored the censored data, the resulting transition probability matrix implied expected lifetimes (without therapy) of 53.6, 60.2, 63.5, 65.2, and 66.4 years for cats 1-5. If we assumed that 10% of cat1, 5% of cat2, 3% of cat3, 2% of cat4, and 1% of cat5 censored observations would have resulted in a death the next period, then the expected lifetimes of the 5 categories were: 15.7, 20.1, 22.5, 24.0, and 25.1 years. We could not replicate the results of the Weibull model for the higher CD4 categories.

Conclusion:

The estimates of expected lifetimes for HIV patients who never take therapy are sensitive to assumptions regarding the actual outcomes of censored observations. Censoring of pre-therapy survival is prevalent because as patients' CD4 counts drop, they initiate therapy.