Models for residual time to AIDS

Comparison of joint modeling and landmarking for dynamic prediction under an illness-death model

Dynamic prediction incorporates time-dependent marker information accrued during follow-up to improve personalized survival prediction probabilities. At any follow-up, or "landmark", time, the residual time distribution for an individual, conditional on their updated marker values, can be used to produce a dynamic prediction. To satisfy a consistency condition that links dynamic predictions at different time points, the residual time distribution must follow from a prediction function that models the joint distribution of the marker process and time to failure, such as a joint model. To circumvent the assumptions and computational burden associated with a joint model, approximate methods for dynamic prediction have been proposed. One such method is landmarking, which fits a Cox model at a sequence of landmark times, and thus is not a comprehensive probability model of the marker process and the event time. Considering an illness-death model, we derive the residual time distribution and demonstrate that the structure of the Cox model baseline hazard and covariate effects under the landmarking approach do not have simple form. We suggest some extensions of the landmark Cox model that should provide a better approximation. We compare the performance of the landmark models with joint models using simulation studies and cognitive aging data from the PAQUID study. We examine the predicted probabilities produced under both methods using data from a prostate cancer study, where metastatic clinical failure is a time-dependent covariate for predicting death following radiation therapy.

Prediction of residual time to AIDS and death based on markers and cofactors

A model was constructed that estimates the probability of an HIV-infected individual developing AIDS or dying within a certain time span if left untreated, based on the most recent CD4 lymphocyte count, HIV-1 RNA load, and HIV-1 phenotype, together with age, time since seroconversion, and two genetic cofactors. The model helps clinicians in deciding when to start highly active antiretroviral treatment (HAART). Data from the Amsterdam Cohort Study among homosexual men restricted to individuals with an estimated date of seroconversion (N = 280) were used. Individual predictions based on several combinations of marker and cofactor values were obtained, and their accuracy was measured using two indices of predictive value. CD4 lymphocyte count and HIV RNA load have the highest predictive value and act independently. The predictive value of the HIV phenotype is only slightly lower and greatly enhances predictions at high CD4 counts. The CCR5-Delta32 and CCR2-64I alleles have no additional predictive value. Some predictive value is lost by not knowing time since seroconversion, and some effect of calendar period is present. In summary, for prognosis, the markers CD4 count, HIV-1 RNA load, and HIV-1 phenotype (at a high CD4 count) are equally important, and the genetic cofactors considered are of no use.

Calculation and use of an HIV-1 disease progression score

OBJECTIVE

The pathogenesis of human disease is often multifactorial. For fatal diseases, it is common to combine survival information in relation to different aspects of pathogenesis. Here we explored a scoring system for HIV disease markers that combines measures of immunodeficiency (CD4 cell count), plasma viral burden, and immune activation (CD38 expression on CD8 T cells)

DESIGN

Observational data from 252 HIV-infected individuals from the Multicenter AIDS Cohort Study (MACS) was used for model development.

METHODS

A statistical model was used to develop a system that related marker values to the outcomes of clinical AIDS or death.

RESULTS

Mathematical formulae were derived to calculate AIDS and death progression scores. These scores give the number of days at which there is a 50% probability that a person may develop AIDS or die. Graphs were constructed that can be used to determine the probability that a person will be AIDS-free or alive for times between 6 months and 4 years. The model was valid when tested on data from 240 additional people from the MACS cohort.

CONCLUSIONS

These formulae and graphs are a convenient way for individuals and their physicians to apply existing MACS cohort data to HIV disease markers in order to estimate probabilities of progression to AIDS or death. Further investigation is needed to determine whether modifications of the formulae are required to predict outcome accurately in those patients on highly active antiretroviral therapy or in other demographic groups.

Statistical models for longitudinal biomarkers of disease onset

We consider the analysis of serial biomarkers to screen and monitor individuals in a given population for onset of a specific disease of interest. The biomarker readings are subject to error. We survey some of the existing literature and concentrate on two recently proposed models. The first is a fully Bayesian hierarchical structure for a mixed effects segmented regression model. Posterior estimates of the changepoint (onset time) distribution are obtained by Gibbs sampling. The second is a hidden changepoint model in which the onset time distribution is estimated by maximum likelihood using the EM algorithm. Both methods lead to a dynamic index that represents a strength of evidence that onset has occurred by the current time in an individual subject. The methods are applied to some large data sets concerning prostate specific antigen (PSA) as a serial marker for prostate cancer. Rules based on the indices are compared to standard diagnostic criteria through the use of ROC curves adapted for longitudinal data.

Prognostic significance of plasma markers of immune activation, HIV viral load and CD4 T-cell measurements

OBJECTIVE

To evaluate the prognostic significance for AIDS occurrence of plasma levels of immune activation markers in comparison with and in conjunction with HIV viral load and CD4 T-cell measurements.

DESIGN

A retrospective analysis was conducted of three plasma activation markers, the soluble tumor necrosis factor (TNF) receptor II (TNF-RII), neopterin and soluble interleukin-2 receptor levels, and of CD4 T-cell levels and plasma HIV viral load.

SUBJECTS

The participants were 659 men taking part in the University of California Los Angeles Multicenter AIDS Cohort Study who were HIV-seropositive but AIDS-free in 1985.

MAIN OUTCOME MEASURE

Clinically defined AIDS within 3 years. Failure time statistical regression models for the time to development of AIDS were used to assess prognostic capacity of the parameters alone and in combination.

RESULTS

All the markers had prognostic capability. The levels of the three plasma activation markers correlated well with each other (median r = 0.61). They related less well with HIV RNA plasma levels (median r = 0.50) and least well with CD4 cell levels (median r = 0.36). Furthermore, plasma marker levels were shown to be able to stratify patients for prognosis within all the major categories of CD4 T-cell and HIV RNA levels.

CONCLUSIONS

Plasma levels of soluble TNF-RII and other soluble markers of immune activation have prognostic capabilities which are different from HIV and CD4 T-cell levels. Combination of a single plasma activation marker measurement (such as soluble TNF-RII) with CD4 T-cell levels improved the prognostic capability of each. A new graphic technique for presenting prognostic capability indicated that plasma soluble TNF-RII and CD4 cell levels are better prognostic factors than HIV plasma level with CD4 cells < 200 x 10(6)/l. Inexpensive tests for one of the plasma activation markers, such as soluble TNF-RII or neopterin, can be useful for evaluations of HIV disease course, especially when expensive equipment, technical expertise and funding required for flow cytometry and for HIV load measurements are not readily available.

Replacing time since human immunodeficiency virus infection by marker values in predicting residual time to acquired immunodeficiency syndrome diagnosis. Multicenter AIDS Cohort Study

It is widely assumed that the time since human immunodeficiency virus (HIV) infection is an important indicator of HIV disease stage, yet for most infected individuals the date of infection is unknown. We consider whether marker values, such as CD4 lymphocyte number or percent and levels of serum beta2 microglobulin or serum neopterin, render time since infection unimportant for predicting the residual time to acquired immunodeficiency syndrome (AIDS) diagnosis. The Multicenter AIDS Cohort Study (MACS) contains a subsample of homosexual men whose date of HIV seroconversion is known within +/-6 months and who provide data for this analysis. From this subsample, we extract two overlapping data subsets. The first subset consists of 370 persons whose 3,723 study visits include complete data on the cellular markers CD4 lymphocyte number and percent for a period of 9 years. The second consists of 272 persons whose 1,593 visits include complete information on cellular markers and on the serological markers beta2-microglobulin and neopterin for a period of 5 1/2 years. We model the residual time to AIDS diagnosis with a regression model, in which cellular and serologic markers are the explanatory covariates (independent variables) and the residual time to AIDS is the responses variable (dependent variable). A robust estimate of the variance-covariance matrix corrects for the dependence of repeated measurements in the same individual. In the case of CD4 number and percent, the results indicate that time since infection is of none or at most little importance if the marker value is known, suggesting that time since infection can be adequately replaced by the combination of marker values. However, the serological markers alone do not eliminate the importance of the time since infection.

Marker processes in survival analysis

In the development of many diseases there are often associated variables which continuously measure the progress of an individual towards the final expression of the disease (failure). Such variables are stochastic processes, here called marker processes, and, at a given point in time, they may provide information about the current hazard and subsequently on the remaining time to failure. Here we consider a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. We develop some basic calculations based on this model. Interest is focused on statistical applications for markers related to estimation of the survival distribution of time to failure, including (i) the use of markers as surrogate responses for failure with censored data, and (ii) the use of markers as predictors of the time elapsed since onset of a survival process in prevalent individuals. Particular attention is directed to potential gains in efficiency incurred by using marker process information.