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
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Published on: January 7, 2019
V Sypsa1, G Touloumi, M Kenward
1Department of Hygiene & Epidemiology, Athens University Medical School, M. Asias 75, 11527 Athens, Greece. vsipsa@cc.uoa.gr
Insights
Smoothing CD4+ T-cell count data improves HIV progression models. The ad hoc smoothing method demonstrated the best performance, offering a less biased estimation of AIDS progression in hemophiliacs.
Area of Science:
- Biostatistics
- Epidemiology
- Immunology
Background:
- Multi-state models using CD4+ T-cell counts are crucial for understanding HIV disease progression.
- CD4+ T-cell counts exhibit measurement error and short-term variability, complicating accurate modeling.
- Estimating AIDS progression requires robust methods to handle CD4+ count fluctuations.
Purpose of the Study:
- To evaluate different smoothing techniques for CD4+ T-cell counts in HIV progression modeling.
- To compare the accuracy of ad hoc, kernel, and random effects (RE) smoothing models against a no-smoothing approach and Kaplan-Meier estimates.
- To determine the optimal method for estimating the cumulative probability of progressing to Acquired Immunodeficiency Syndrome (AIDS) in HIV-1 infected individuals.
Main Methods:
- A Markov model with six CD4+ T-cell count-based states and an absorbing AIDS state was employed.
- Four methods were assessed: no smoothing, ad hoc smoothing, kernel smoothing, and random effects (RE) models.
- Estimates were compared against Kaplan-Meier survival analysis for 158 HIV-1 infected hemophiliacs with known seroconversion dates.
Main Results:
- The 'no smoothing' method showed poor agreement with Kaplan-Meier estimates.
- Ad hoc, kernel, and RE smoothing methods produced estimates within the 95% confidence intervals of the Kaplan-Meier curve.
- Simulations indicated that raw CD4+ counts lead to overestimated transition intensities; ad hoc smoothing exhibited the least bias.
Conclusions:
- Smoothing techniques are essential for accurate HIV disease progression modeling using CD4+ T-cell counts.
- The ad hoc smoothing method offers a practical and effective approach, balancing ease of implementation with improved accuracy.
- Random effects models provide a flexible alternative, particularly for individuals with sparse data, by incorporating population-level smoothing.
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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