Dynamic Marginal Structural Models Research Articles

Comparative Effectiveness of Dynamic Treatment Strategies for Medication Use and Dosage: Emulating a Target Trial Using Observational Data.

Availability of detailed data from electronic health records (EHRs) has increased the potential to examine the comparative effectiveness of dynamic treatment strategies using observational data. Inverse probability (IP) weighting of dynamic marginal structural models can control for time-varying confounders. However, IP weights for continuous treatments may be sensitive to model choice. We describe a target trial comparing strategies for treating anemia with darbepoetin in hemodialysis patients using EHR data from the UK Renal Registry 2004 to 2016. Patients received a specified dose (microgram/week) or did not receive darbepoetin. We compared 4 methods for modeling time-varying treatment: (A) logistic regression for zero dose, standard linear regression for log dose; (B) logistic regression for zero dose, heteroscedastic linear regression for log dose; (C) logistic regression for zero dose, heteroscedastic linear regression for log dose, multinomial regression for patients who recently received very low or high doses; and (D) ordinal logistic regression. For this dataset, method (C) was the only approach that provided a robust estimate of the mortality hazard ratio (HR), with less-extreme weights in a fully weighted analysis and no substantial change of the HR point estimate after weight truncation. After truncating IP weights at the 95th percentile, estimates were similar across the methods. EHR data can be used to emulate target trials estimating the comparative effectiveness of dynamic strategies adjusting treatment to evolving patient characteristics. However, model checking, monitoring of large weights, and adaptation of model strategies to account for these is essential if an aspect of treatment is continuous.

Use of a Statistical Adaptive Treatment Strategy Approach for Emulating Randomized Controlled Trials Using Observational Data: The Example of Blood-Pressure Control Strategies for the Prevention of Cardiovascular Events Among Individuals With Hypertension at High Cardiovascular Risk.

Statistical approaches to adaptive treatment strategies (ATS) can be used to mimic the sequential decision-making inherently found in clinical practice. To illustrate the use of a statistical ATS approach, we emulated a target trial of different blood pressure (BP) control plans for the prevention of cardiovascular events among individuals with hypertension at high cardiovascular risk, inspired by the Systolic Blood Pressure Intervention Trial (SPRINT). We included 103,708 patients with hypertension and a "QRISK3" estimated 10-year risk of cardiovascular disease of ≥20% who initiated an antihypertensive drug between 1998 and 2018. Dynamic marginal structural models estimated the comparative effects of treating patients with intensive (target BP: 130/80 mm Hg), standard (140/90 mm Hg), and conservative (150/90 mm Hg) BP control strategies. The adjusted hazard ratios (HRs) for the intensive versus standard strategy were 0.96 (95% confidence interval (CI): 0.92, 1.00) for major adverse cardiovascular events and 0.93 (95% CI: 0.88, 0.97) for death from cardiovascular causes. For the conservative versus standard strategy, they were 1.06 (95% CI: 1.02, 1.10) and 1.08 (95% CI: 1.03, 1.13), respectively. These results are largely compatible with SPRINT. ATS can be used to emulate randomized controlled trials of complex treatment strategies in an observational setting and represents an alternative approach for situations where randomized controlled trials are not feasible.

Maternal and neonatal outcomes associated with treating hypertension in pregnancy at different thresholds.

In the United States, there has been controversy over whether treatment of mild-to-moderate hypertension during pregnancy conveys more benefit than risk. The objective of the study was to compare risks and benefits of treatment of mild-to-moderate hypertension during pregnancy. This retrospective cohort study included 11,871 pregnant women with mild-to-moderate hypertension as defined by blood pressure (BP) values from three Kaiser Permanente regions between 2005 and 2014. Data were extracted from electronic health records. Dynamic marginal structural models with inverse probability weighting and informative censoring were used to compare risks of adverse outcomes when beginning antihypertensive medication treatment at four BP thresholds (≥155/105, ≥150/100, ≥145/95, ≥140/90 mm Hg) compared with the recommended threshold in the United States at that time, ≥160/110 mm Hg. Outcomes included preeclampsia, preterm birth, small-for-gestational-age (SGA), Neonatal Intensive Care Unit (NICU) care, and stillbirth. Primary analyses allowed 2 weeks for medication initiation after an elevated BP. Several sensitivity and subgroup (i.e., race/ethnicity and pre-pregnancy body mass index) analyses were also conducted. In primary analyses, medication initiation at lower BP thresholds was associated with greater risk of most outcomes. Comparing the lowest (≥140/90 mm Hg) to the highest BP threshold (≥160/110 mm Hg), we found an excess risk of preeclampsia (adjusted Risk Difference (aRD) 38.6 per 100 births, 95% Confidence Interval (CI): 30.6, 46.6), SGA (aRD: 10.2 per 100 births, 95% CI: 2.6, 17.8), NICU admission (aRD: 20.2 per 100 births, 95% CI: 12.6, 27.9), and stillbirth (1.18 per 100 births, 95% CI: 0.27, 2.09). The findings did not reach statistical significance for preterm birth (aRD: 2.5 per 100 births, 95% CI: -0.4, 5.3). These relationships were attenuated and did not always reach statistically significance when comparing higher BP treatment thresholds to the highest threshold (i.e., ≥160/110 mm Hg). Sensitivity and subgroup analyses produced similar results. Initiation of antihypertensive medication at mild-to-moderate BP thresholds (140-155/90-105 mm Hg; with the largest risk consistently associated with treatment at 140/90 mm Hg) may be associated with adverse maternal and neonatal outcomes. Limitations include inability to measure medication adherence.

Emulation of a target trial with sustained treatment strategies: an application to prostate cancer using both inverse probability weighting and the g-formula.

As with many chronic illnesses, recurrent prostate cancer generally requires sustained treatment to prolong survival. However, initiating treatment immediately after recurrence may negatively impact quality of life without any survival gains. Therefore, we consider sustained strategies for initiating treatment based on specific characteristics of prostate-specific antigen (PSA), which can indicate disease progression. We define the protocol for a target trial comparing treatment strategies based on PSA doubling time, in which androgen deprivation therapy is initiated only after doubling time decreases below a certain threshold. Such a treatment strategy means the timing of treatment initiation (if ever) is not known at baseline, and the target trial protocol must explicitly specify the frequency of PSA monitoring until the threshold is met, as well as the duration of treatment. We describe these and other components of a target trial that need to be specified in order for such a trial to be emulated in observational data. We then use the parametric g-formula and inverse-probability weighted dynamic marginal structural models to emulate our target trial in a cohort of prostate cancer patients from clinics across the United States.

Semiparametric Bayesian inference for optimal dynamic treatment regimes via dynamic marginal structural models.

Considerable statistical work done on dynamic treatment regimes (DTRs) is in the frequentist paradigm, but Bayesian methods may have much to offer in this setting as they allow for the appropriate representation and propagation of uncertainty, including at the individual level. In this work, we extend the use of recently developed Bayesian methods for Marginal Structural Models to arrive at inference of DTRs. We do this (i) by linking the observational world with a world in which all patients are randomized to a DTR, thereby allowing for causal inference and then (ii) by maximizing a posterior predictive utility, where the posterior distribution has been obtained from nonparametric prior assumptions on the observational world data-generating process. Our approach relies on Bayesian semiparametric inference, where inference about a finite-dimensional parameter is made all while working within an infinite-dimensional space of distributions. We further study Bayesian inference of DTRs in the double robust setting by using posterior predictive inference and the nonparametric Bayesian bootstrap. The proposed methods allow for uncertainty quantification at the individual level, thereby enabling personalized decision-making. We examine the performance of these methods via simulation and demonstrate their utility by exploring whether to adapt HIV therapy to a measure of patients' liver health, in order to minimize liver scarring.

Ranking tailoring variables for constructing individualized treatment rules: an application to schizophrenia.

As with many chronic conditions, matching patients with schizophrenia to the best treatment options is difficult. Selecting antipsychotic medication is especially challenging because many of the medications can have burdensome side effects. Adjusting or tailoring medications based on patients' characteristics could improve symptoms. However, it is often not known which patient characteristics are most helpful for informing treatment selection. In this paper, we address the challenge of identifying and ranking important variables for tailoring treatment decisions. We consider a value-search approach implemented through dynamic marginal structural models to estimate an optimal individualized treatment rule. We apply our methodology to the Clinical Antipsychotics Trial of Intervention and Effectiveness (CATIE) study for schizophrenia, to evaluate if some tailoring variables have greater potential than others for selecting treatments for patients with schizophrenia (Stroup et al., 2003).

Estimating optimal dynamic treatment strategies under resource constraints using dynamic marginal structural models.

Methods for estimating optimal treatment strategies typically assume unlimited access to resources. However, when a health system has resource constraints, such as limited funds, access to medication, or monitoring capabilities, medical decisions must account for competition between individuals in resource usage. The problem of incorporating resource constraints into optimal treatment strategies has been solved for point exposures (1), that is, treatment strategies entailing a decision at just one time point. However, attempts to directly generalize the point exposure solution to dynamic time-varying treatment strategies run into complications. We sidestep these complications by targeting the optimal strategy within a clinically defined subclass. Our approach is to employ dynamic marginal structural models to estimate (counterfactual) resource usage under the class of candidate treatment strategies and solve a constrained optimization problem to choose the optimal strategy for which expected resource usage is within acceptable limits. We apply this method to determine the optimal dynamic monitoring strategy for people living with HIV when resource limits on monitoring exist using observational data from the HIV-CAUSAL Collaboration.

Outcomes of HIV-positive patients with cryptococcal meningitis in the Americas

BackgroundCryptococcal meningitis (CM) is associated with substantial mortality in HIV-infected patients. Optimal timing of antiretroviral therapy (ART) in persons with CM represents a clinical challenge, and the burden of CM in Latin America has not been well described. Studies suggest that early ART initiation is associated with higher mortality, but data from the Americas are scarce. MethodsHIV-infected adults in care between 1985–2014 at participating sites in the Latin America (the Caribbean, Central and South America network (CCASAnet)) and the Vanderbilt Comprehensive Care Clinic (VCCC) and who had CM were included. Survival probabilities were estimated. Risk of death when initiating ART within the first 2 weeks after CM diagnosis versus initiating between 2–8 weeks was assessed using dynamic marginal structural models adjusting for site, age, sex, year of CM, CD4 count, and route of HIV transmission. Findings340 patients were included (Argentina 58, Brazil 138, Chile 28, Honduras 27, Mexico 34, VCCC 55) and 142 (42%) died during the observation period. Among 151 patients with CM prior to ART 56 (37%) patients died compared to 86 (45%) of 189 with CM after ART initiation (p=0.14). Patients diagnosed with CM after ART had a higher risk of death (p=0.03, log-rank test). The probability of survival was not statistically different between patients who started ART within 2 weeks of CM (7/24, 29%) vs. those initiating between 2-8 weeks (14/53, 26%) (p=0.96), potentially due to lack of power. InterpretationIn this large Latin-American cohort, patients with CM had very high mortality rates, especially those diagnosed after ART initiation. This study reflects the overwhelming burden of CM in HIV-infected patients in Latin America.

Initiation of erythropoiesis-stimulating agents and outcomes: a nationwide observational cohort study in anaemic chronic kidney disease patients.

In 2012, new clinical guidelines were introduced for use of erythropoiesis-stimulating agents (ESA) in chronic kidney disease (CKD) patients, recommending lower haemoglobin (Hb) target levels and thresholds for ESA initiation. These changes resulted in lower blood levels in these patients. However, there is limited evidence on just when ESA should be initiated and the safety of a low Hb initiation policy. In this observational inception cohort study, Swedish, nephology-referred, ESA-naïve CKD patients (n = 6348) were enrolled when their Hb dropped below 12.0 g/L, and they were followed for mortality and cardiovascular events. Four different ESA treatments were evaluated applying dynamic marginal structural models: (i) begin ESA immediately, (ii) begin ESA when Hb <11.0 g/dL, (iii) begin ESA when Hb <10.0 g/dL and (iv) never begin ESA in comparison with 'current practice' [the observed (factual) survival of the entire study cohort]. The adjusted 3-year survival following ESA begun over a range of Hb (from <9.0 to 12.0 g/dL) was evaluated, after adjustment for covariates at baseline and during follow-up. Overall, 36% were treated with ESA. Mortality during follow-up was 33.4% of the ESA-treated and 27.9% of the non-treated subjects. The adjusted 3-year survival associated with ESA initiation improved for subjects with initial Hb <9.0 to 11 g/dL and then decreased again for those with Hb above 11.5 g/dL. Initiating ESA at Hb <11.0 g/dL and <10.0 g/dL was associated with improved survival compared with 'current practice' [hazard ratio (HR) 0.83; 95% confidence interval (CI) 0.79-0.89 and 0.90; 95% CI 0.86-0.94, respectively] and did not increase the risk of a cardiovascular event (HR 0.93; 95% CI 0.87-1.00). In non-dialysis patients with CKD, ESA initiation at Hb < 10.0-11.0 g/dL is associated with improved survival in patients otherwise treated according to guidelines.

Comparing results from multiple imputation and dynamic marginal structural models for estimating when to start antiretroviral therapy.

Optimal timing of initiating antiretroviral therapy has been a controversial topic in HIV research. Two highly publicized studies applied different analytical approaches, a dynamic marginal structural model and a multiple imputation method, to different observational databases and came up with different conclusions. Discrepancies between the two studies' results could be due to differences between patient populations, fundamental differences between statistical methods, or differences between implementation details. For example, the two studies adjusted for different covariates, compared different thresholds, and had different criteria for qualifying measurements. If both analytical approaches were applied to the same cohort holding technical details constant, would their results be similar? In this study, we applied both statistical approaches using observational data from 12,708 HIV-infected persons throughout the USA. We held technical details constant between the two methods and then repeated analyses varying technical details to understand what impact they had on findings. We also present results applying both approaches to simulated data. Results were similar, although not identical, when technical details were held constant between the two statistical methods. Confidence intervals for the dynamic marginal structural model tended to be wider than those from the imputation approach, although this may have been due in part to additional external data used in the imputation analysis. We also consider differences in the estimands, required data, and assumptions of the two statistical methods. Our study provides insights into assessing optimal dynamic treatment regimes in the context of starting antiretroviral therapy and in more general settings. Copyright © 2016 John Wiley & Sons, Ltd.

Comparing results from multiple imputation and dynamic marginal structural models for estimating when to start antiretroviral therapy

Comparing results from multiple imputation and dynamic marginal structural models for estimating when to start antiretroviral therapy

The Impact of Different CD4 Cell-Count Monitoring and Switching Strategies on Mortality in HIV-Infected African Adults on Antiretroviral Therapy: An Application of Dynamic Marginal Structural Models.

In Africa, antiretroviral therapy (ART) is delivered with limited laboratory monitoring, often none. In 2003–2004, investigators in the Development of Antiretroviral Therapy in Africa (DART) Trial randomized persons initiating ART in Uganda and Zimbabwe to either laboratory and clinical monitoring (LCM) or clinically driven monitoring (CDM). CD4 cell counts were measured every 12 weeks in both groups but were only returned to treating clinicians for management in the LCM group. Follow-up continued through 2008. In observational analyses, dynamic marginal structural models on pooled randomized groups were used to estimate survival under different monitoring-frequency and clinical/immunological switching strategies. Assumptions included no direct effect of randomized group on mortality or confounders and no unmeasured confounders which influenced treatment switch and mortality or treatment switch and time-dependent covariates. After 48 weeks of first-line ART, 2,946 individuals contributed 11,351 person-years of follow-up, 625 switches, and 179 deaths. The estimated survival probability after a further 240 weeks for post-48-week switch at the first CD4 cell count less than 100 cells/mm3 or non-Candida World Health Organization stage 4 event (with CD4 count <250) was 0.96 (95% confidence interval (CI): 0.94, 0.97) with 12-weekly CD4 testing, 0.96 (95% CI: 0.95, 0.97) with 24-weekly CD4 testing, 0.95 (95% CI: 0.93, 0.96) with a single CD4 test at 48 weeks (baseline), and 0.92 (95% CI: 0.91, 0.94) with no CD4 testing. Comparing randomized groups by 48-week CD4 count, the mortality risk associated with CDM versus LCM was greater in persons with CD4 counts of <100 (hazard ratio = 2.4, 95% CI: 1.3, 4.3) than in those with CD4 counts of ≥100 (hazard ratio = 1.1, 95% CI: 0.8, 1.7; interaction P = 0.04). These findings support a benefit from identifying patients immunologically failing first-line ART at 48 weeks.

Optimal CD4 Count for Initiating HIV Treatment

In HIV infection, dynamic marginal structural models have estimated the optimal CD4 for treatment initiation to minimize AIDS/death. The impact of CD4 observation frequency and grace periods (permitted delay to initiation) on the optimal regimen has not been investigated nor has the performance of dynamic marginal structural models in moderately sized data sets-two issues that are relevant to many applications. To determine optimal regimens, we simulated 31,000,000 HIV-infected persons randomized at CD4 500-550 cells/mm to regimens "initiate treatment within a grace period following observed CD4 first <x cells/mm," x = 200, 210, …, 500. Natural history and treatment response were simulated using previous model estimates from CASCADE data. Optimal treatment regimens for the observation frequencies and grace periods were defined by highest 10-year AIDS-free survival. To evaluate the performance of dynamic marginal structural models, we simulated 1000 observational studies (n = 3,000) with CD4-dependent treatment initiation. Decreasing the frequency of CD4 measurements from monthly to every 3, 6, and 12 months increased the optimal regimen from a CD4 level of 350 (10-year AIDS-free survival, 0.8657) to 410 (0.8650), 460 (0.8634), and 490 (0.8564), respectively. Under a regimen defined by x = 350 with annual CD4s, 10-year AIDS-free survival dropped to 0.8304. Extending the grace period from 1 to 3 or 6 months, with 3-monthly CD4s, maintained the optimal regimen at 410 for 3 months and increased it to 460 for 6 months. In observational studies with 3-monthly CD4s, the mean (SE) estimated optimal regimen was 402 (76), 424 (66), and 430 (63) with 1-, 3-, and 6-month grace periods; 24%, 15%, and 14% of estimated optimal regimens resulted in >0.5% lower AIDS-free survival compared with the true optimal regimen. The optimal regimen is strongly influenced by CD4 frequency and less by grace period length. Dynamic marginal structural models lack precision at moderate sample sizes.

Targeted Maximum Likelihood Estimation for Dynamic and Static Longitudinal Marginal Structural Working Models.

This paper describes a targeted maximum likelihood estimator (TMLE) for the parameters of longitudinal static and dynamic marginal structural models. We consider a longitudinal data structure consisting of baseline covariates, time-dependent intervention nodes, intermediate time-dependent covariates, and a possibly time-dependent outcome. The intervention nodes at each time point can include a binary treatment as well as a right-censoring indicator. Given a class of dynamic or static interventions, a marginal structural model is used to model the mean of the intervention-specific counterfactual outcome as a function of the intervention, time point, and possibly a subset of baseline covariates. Because the true shape of this function is rarely known, the marginal structural model is used as a working model. The causal quantity of interest is defined as the projection of the true function onto this working model. Iterated conditional expectation double robust estimators for marginal structural model parameters were previously proposed by Robins (2000, 2002) and Bang and Robins (2005). Here we build on this work and present a pooled TMLE for the parameters of marginal structural working models. We compare this pooled estimator to a stratified TMLE (Schnitzer et al. 2014) that is based on estimating the intervention-specific mean separately for each intervention of interest. The performance of the pooled TMLE is compared to the performance of the stratified TMLE and the performance of inverse probability weighted (IPW) estimators using simulations. Concepts are illustrated using an example in which the aim is to estimate the causal effect of delayed switch following immunological failure of first line antiretroviral therapy among HIV-infected patients. Data from the International Epidemiological Databases to Evaluate AIDS, Southern Africa are analyzed to investigate this question using both TML and IPW estimators. Our results demonstrate practical advantages of the pooled TMLE over an IPW estimator for working marginal structural models for survival, as well as cases in which the pooled TMLE is superior to its stratified counterpart.

Dynamic marginal structural modeling to evaluate the comparative effectiveness of more or less aggressive treatment intensification strategies in adults with type 2 diabetes

Chronic disease care typically involves treatment decisions that are frequently adjusted to the patient's evolving clinical course (e.g., hemoglobin A1c monitoring and treatment intensification in diabetes patients). Thus, in comparative effectiveness and safety research (CER), it often is less clinically relevant to contrast the health effects of static treatment decisions than to compare the effectiveness of competing medical guidelines, that is, adaptive treatment strategies that map the patient's unfolding clinical course to subsequent treatment decisions. With longitudinal observational studies, treatment decisions at any point in time may be influenced by clinical factors that also are risk factors for the outcome of interest. Such time-dependent confounders cannot be properly handled with standard statistical approaches, because such confounders may be influenced by previous treatment decisions and may thus lie on causal pathways between the very outcomes and early treatment decisions whose effects are under study. Under explicit assumptions, we motivate the application of inverse probability weighting estimation to fit dynamic marginal structural models (MSMs) in observational studies to address pragmatic CER questions and properly adjust for time-dependent confounding and informative loss to follow-up. We review the principles behind this modeling approach and describe its application in an observational study of type 2 diabetes patients to investigate the comparative effectiveness of four adaptive treatment intensification strategies for glucose control on subsequent development or progression of urinary albumin excretion. Results indicate a protective effect of more aggressive treatment intensification strategies in patients already on two or more oral agents or basal insulin. These conclusions are concordant with recent randomized trials. Inverse probability weighting estimation to fit dynamic MSM is a viable and appealing alternative to inadequate standard modeling approaches in many CER problems where time-dependent confounding and informative loss to follow-up are expected.

Methods for developing and analyzing clinically rich data for patient‐centered outcomes research: an overview

Methods for developing and analyzing clinically rich data for patient‐centered outcomes research: an overview

Comparative effectiveness of dynamic treatment regimes: an application of the parametric g-formula.

Ideally, randomized trials would be used to compare the long-term effectiveness of dynamic treatment regimes on clinically relevant outcomes. However, because randomized trials are not always feasible or timely, we often must rely on observational data to compare dynamic treatment regimes. An example of a dynamic treatment regime is "start combined antiretroviral therapy (cART) within 6 months of CD4 cell count first dropping below x cells/mm3 or diagnosis of an AIDS-defining illness, whichever happens first" where x can take values between 200 and 500. Recently, Cain et al (2011) used inverse probability (IP) weighting of dynamic marginal structural models to find the x that minimizes 5-year mortality risk under similar dynamic regimes using observational data. Unlike standard methods, IP weighting can appropriately adjust for measured time-varying confounders (e.g., CD4 cell count, viral load) that are affected by prior treatment. Here we describe an alternative method to IP weighting for comparing the effectiveness of dynamic cART regimes: the parametric g-formula. The parametric g-formula naturally handles dynamic regimes and, like IP weighting, can appropriately adjust for measured time-varying confounders. However, estimators based on the parametric g-formula are more efficient than IP weighted estimators. This is often at the expense of more parametric assumptions. Here we describe how to use the parametric g-formula to estimate risk by the end of a user-specified follow-up period under dynamic treatment regimes. We describe an application of this method to answer the "when to start" question using data from the HIV-CAUSAL Collaboration.

When to Initiate Combined Antiretroviral Therapy to Reduce Mortality and AIDS-Defining Illness in HIV-Infected Persons in Developed Countries

Most clinical guidelines recommend that AIDS-free, HIV-infected persons with CD4 cell counts below 0.350 × 10(9) cells/L initiate combined antiretroviral therapy (cART), but the optimal CD4 cell count at which cART should be initiated remains a matter of debate. To identify the optimal CD4 cell count at which cART should be initiated. Prospective observational data from the HIV-CAUSAL Collaboration and dynamic marginal structural models were used to compare cART initiation strategies for CD4 thresholds between 0.200 and 0.500 × 10(9) cells/L. HIV clinics in Europe and the Veterans Health Administration system in the United States. 20, 971 HIV-infected, therapy-naive persons with baseline CD4 cell counts at or above 0.500 × 10(9) cells/L and no previous AIDS-defining illnesses, of whom 8392 had a CD4 cell count that decreased into the range of 0.200 to 0.499 × 10(9) cells/L and were included in the analysis. Hazard ratios and survival proportions for all-cause mortality and a combined end point of AIDS-defining illness or death. Compared with initiating cART at the CD4 cell count threshold of 0.500 × 10(9) cells/L, the mortality hazard ratio was 1.01 (95% CI, 0.84 to 1.22) for the 0.350 threshold and 1.20 (CI, 0.97 to 1.48) for the 0.200 threshold. The corresponding hazard ratios were 1.38 (CI, 1.23 to 1.56) and 1.90 (CI, 1.67 to 2.15), respectively, for the combined end point of AIDS-defining illness or death. CD4 cell count at cART initiation was not randomized. Residual confounding may exist. Initiation of cART at a threshold CD4 count of 0.500 × 10(9) cells/L increases AIDS-free survival. However, mortality did not vary substantially with the use of CD4 thresholds between 0.300 and 0.500 × 10(9) cells/L.