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: 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. · 0.65 Impact Factor
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ABSTRACT: The aim was to investigate the impact of the main prognostic factors on HIV evolution. A multi-state Markov model was applied in a cohort of 2126 patients to estimate impact of these factors on patients' clinical and immunological evolutions. Clinical progression and immunological deterioration shared most of their prognostic factors: male gender, intravenous drug use, weight loss, low haemoglobin level (<110 g/l), CD8 cell count (<500/mm(3)) and HIV viral load (>5 log(10) copies/ml). Highly active retroviral therapy reduced the risks of clinical progression and immune deterioration whatever patients' CD4 cell count. Risk reductions were 41-60% for protease inhibitor-based and 27-68% for non-nucleoside reverse transcriptase inhibitor-based regimens. Three-year transition probabilities showed that only patients with a CD4 cell count >or=350 CD4/mm(3) could in most cases maintain their immunity. This model provides 'real life' transition probabilities from one immunological stage to another, allowing decision analyses that could help determine the beneficial therapeutic strategies for HIV-infected patients.Epidemiology and Infection 01/2009; 137(9):1272-82. · 2.87 Impact Factor
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ABSTRACT: The prediction of erosion and co-deposition processes for ITER is necessary information for the design and material choice of the first wall. A model has been developed that describes this coupling of local erosion to the global impurity transport and re-deposition processes in a self-consistent way. The erosion and deposition on each surface element of first wall is described by an ordinary differential equation (ODE). The resulting system of ODEs is coupled via the impurity influx, which is derived from the re-distribution of the erosion fluxes through the global impurity transport as calculated by DIVIMP. As a test case, the model is applied to a standard ITER reference discharge calculating the re-distribution of Be, C and W inside the ITER vessel with time.Journal of Nuclear Materials 01/2011; · 2.02 Impact Factor