Comparison of smoothing techniques for CD4 data in a Markov model with states defined by CD4: an example on the estimation of the HIV incubation time distribution.
ABSTRACT Multi-state models defined in terms of CD4 counts are useful for modelling HIV disease progression. A Markov model with six progressive CD4-based states and an absorbing state (AIDS) was used to estimate the cumulative probability of progressing to AIDS in 158 HIV-1 infected haemophiliacs with known seroconversion (SC) dates. A problem arising in such analysis is how to define CD4-based states, since this marker is subject to measurement error and short timescale variability. Four approaches were used: no smoothing, ad hoc smoothing (to move to a later/previous state two consecutive measurements to later/previous states are needed), kernel smoothing and random effects (RE) models. The estimates were compared with the Kaplan-Meier estimate based solely on data concerning time to AIDS. There was an apparent lack of agreement between the Kaplan-Meier and the "no smoothing" estimate. With the exception of the "no smoothing" method, "ad hoc", kernel and RE estimates fell within the range of the 95 per cent CIs of the Kaplan-Meier curve. Simulations demonstrated that the use of raw CD4 counts provides overestimated transition intensities. Compared to the kernel method, ad hoc is easier to implement and overcomes the problem of the choice of bandwidth. The RE approach leads to simple models, since it usually results in very few transitions to previous states, and can handle individuals with sparse data by smoothing their predictions towards the population mean. Ad hoc was the method that performed better, in terms of bias, than the other smoothing approaches.
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ABSTRACT: We used continuous-time Markov models based on CD4 cell counts and anti-CD3 reactivity (i.e., measure for T-cell quality) to study the progression of HIV infection in a cohort study of homosexual men in Amsterdam. We also compared the effectiveness of anti-CD3 reactivity as a marker for disease progression with that of CD4 cell counts. We used data from 467 men (6905 visits) with visits at 3-month intervals between October 1984 and March 1993. To account for measurement error and short time-scale variability, the immunological stage at each visit was determined using a kernel smoother on log-transformed data from each individual. The Markov model had six marker-defined stages and a seventh stage for clinical AIDS. The initial stage-occupation probabilities for seroconverters were used to estimate the incubation time from infection to AIDS. Confidence intervals were calculated using the bootstrap method to account for the effect of smoothing on the variability of our estimates. The CD4 staging scheme estimated the median time from seroconversion to AIDS at 8.3 years [95% confidence interval (CI), 8.1-8.6], and a similar estimate was obtained with the anti-CD3 staging model. The CD4 model predicts that 10.2% (95% CI, 9.9-13.1) will remain AIDS-free 15 years after seroconversion. The mean number of stages visited before AIDS is lower with the CD4 model (7.4; 95% CI, 7.2-7.7) than with the anti-CD3 model (11.3; 95% CI, 10.8-12.0), implying that anti-CD3 predicts progression less well than CD4 cell count. CD4 lymphocyte counts and anti-CD3 reactivity are each associated with an increased hazard for progression to AIDS. Therefore, men in different CD4-stages (anti-CD3 stages) follow different incubation period distributions to AIDS. However, anti-CD3 predicts progression less well than CD4 cell count. Staged time-continuous Markov models are useful to study immunological markers for HIV disease progression.AIDS 07/1996; 10(6):649-56. · 6.41 Impact Factor
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ABSTRACT: We modeled the decline of CD4+ T-lymphocytes (T4 cells) in HIV-infected individuals with a continuous-time Markov process. The model partitions the HIV infection period into six progressive T4-cell count intervals (states), followed by a seventh state: a definitive HIV-infection end point, i.e., AIDS diagnosis or Walter Reed stage 6 (opportunistic infections). The Markov model was used to estimate the state-specific progression rates from data as functions of important progression cofactors. We applied the model to data on 1,796 HIV-positive individuals in the U.S. Army. The estimated mean waiting time from seroconversion to when the T4-cell count persistently drops below 500/mm3, but is greater than 349/mm3, is 4.1 years, and the waiting time to a T4-cell count of less than 200/mm3 is estimated at 8.0 years. The estimated rate of T4-cell decline was higher for HIV-infected individuals with initially high numbers of T4 cells, but the estimated rate of decline remains relatively uniform when the T4-cell count dropped persistently below 500/mm3. The opportunistic infection incubation period, i.e., the time from seroconversion to opportunistic infection diagnosis, is estimated at 9.6 years. Age is found to be an important cofactor. The estimated mean opportunistic infection incubation periods are 11.1, 10.0, and 8.9 years for the youngest (less than or equal to 25 years old), the middle (26-30 years old), and the oldest (greater than 30 years old) age groups, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)Journal of acquired immune deficiency syndromes 02/1991; 4(11):1141-7.
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ABSTRACT: Our objectives are to describe the progression of HIV disease and to assess the influence of hemophilia-related variables, age at infection, and antibodies to cytomegalovirus infection (anti-CMV) in a Greek cohort of 158 HIV-1-positive hemophilic men, who received prospective follow-up for up to 16 years after infection. A total of 79 patients had died, representing a cumulative progression rate of 72.4% (95% confidence interval [CI], 56.6-83.3). A significant proportion of the mortality (30%) resulted from conditions not formally related to AIDS, with liver failure and cerebral hemorrhage predominant. At 16 years after seroconversion, 66 patients had developed clinical AIDS, a cumulative progression rate of 58.2% (95% CI, 47.1%-86.3%) whereas 15 years after infection 81.5% (95% CI, 74.2%-87.9%) of the patients had AIDS or a CD4 cell count <200 cells/mm3. Hemophilia-related variables or presence of anti-CMV were not significantly associated with disease progression. Age at infection was a strong prognostic factor for all three endpoints. Appropriate modeling showed a nonlinear age effect, with a steeper increase of relative hazard for patients >40 years of age at seroconversion. The age effect remained significant even after controlling for current CD4 cell count. Further investigation is required to elucidate the mechanisms of the age effect and the contribution of HCV coinfection on the disease progression.Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 09/1998; 19(1):89-97.