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

Department of Hygiene & Epidemiology, Athens University Medical School, M. Asias 75, 11527 Athens, Greece.
Statistics in Medicine (Impact Factor: 1.83). 12/2001; 20(24):3667-76. DOI: 10.1002/sim.1080
Source: PubMed


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.

2 Reads
  • [Show abstract] [Hide abstract]
    ABSTRACT: Human immunodeficiency virus type 1 (HIV-1)-uninfected Ethiopians have lower CD4 T cell counts than do other populations in Africa and industrialized countries. We studied whether this unique immunological profile results in shorter survival times in HIV-1-infected Ethiopians. Data from an open cohort study of 149 HIV-1-infected factory workers in Ethiopia for 1997-2002 were used. To estimate survival times, a continuous-time Markov model was designed on the basis of CD4 T cell counts and World Health Organization clinical staging. By use of a random-effects model, decline in CD4 T cell counts was compared between HIV-1-infected Ethiopian and Dutch individuals. Median survival times were in the range of 9.1-13.7 years, depending on the approach used. This range is similar to that for populations in industrialized countries before the advent of antiretroviral therapy. Ethiopians had a lower annual decline in CD4 T cell counts than did Dutch individuals, which remained when groups with similar CD4 T cell count categories were compared. Moreover, the slower decline in CD4 T cell counts was not due merely to lower HIV-1 RNA loads or an absence of syncytium-inducing/X4 HIV-1 subtype C strains in Ethiopians. Low baseline CD4 T cell counts do not imply shorter survival times in Ethiopians than in other populations, presumably because of a slower decline in CD4 T cell counts.
    The Journal of Infectious Diseases 10/2005; 192(5):739-48. DOI:10.1086/432545 · 6.00 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The purpose of this study was to evaluate the evolution of HIV infected patients and to bring out some significant factors associated with this pathology. The main criteria revealing the State of illness is viral load measurement (VL). However the CD4 lymphocytes also represent an important marker as these reflect the State of the immune reservoir. Many studies have been carried out in this field and different models have been proposed with a view to a better understanding of this disease. Multi State Markov models defined in terms of CD4 counts, or in terms of viral load, have proved to be very useful tools for modelling HIV disease progression. The model we have developed in this study is based on both the CD4 lymphocytes counts and VL. Markov models are characterized by transition intensities. In this paper we explored several structures in succession. First, we used a homogeneous continuous time Markov process with four states defined by crossed values of CD4 and VL in a given patient at a given time. Then, the effect of certain covariates on the infection process was introduced into the model via the transition intensity functions, as with a Cox regression model. Since the hypothesis of homogeneity may be unrealistic in certain cases, we also considered piecewise homogeneous Markov models. Finally, the effects of covariates and time were combined in a piecewise homogeneous model with a covariate. We applied these methods to data from 1313 HIV-infected patients included in the NADIS cohort.
    Biometrical Journal 12/2005; 47(6):834-46. DOI:10.1002/bimj.200410164 · 0.95 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.
    Methodology And Computing In Applied Probability 08/2007; 9(3):389-397. DOI:10.1007/s11009-007-9033-7 · 0.91 Impact Factor
Show more