recovering information from suppressed plasma and csf hiv viral load using multiple imputation

The UC San Diego AntiViral Research Center sponsors weekly presentations by infectious disease clinicians, physicians and researchers. The goal of these presentations is to provide the most current research, clinical practices and trends in HIV, HBV, HCV, TB and other infectious diseases of global significance. The slides from the AIDS Clinical Rounds presentation that you are about to view are intended for the educational purposes of our audience. They may not be used for other purposes without the presenter’s express permission.

AIDS CLINICAL ROUNDS

Recovering Information from Suppressed Plasma andCSF HIV Viral Load

Florin Vaida, PhD

Division of Biostatistics and BioinformaticsDepartment of Family and Preventive Medicine

and HIV Neurobehavioral Research Center<[email protected]>

AIDS Clinical Rounds

August 17, 2012

Florin Vaida (UCSD) Censored HIV Viral Load AIDS Clinical Rounds 1 / 23

HIV Viral Load

HIV viral load is, together with CD4 T-cell count, the main marker ofHIV disease

In treated individuals HIV viral load is “suppressed”

Suppressed VL = below the limit of detection of the assay

50 cp/ml for Roche Amplicor)

HIV VL never goes as low as 0

The unknown (censored) VL in the 0-50 range contains importantinformation for clinical research

Importance for clinical practice?

Dealing with censored VL requires more sophisticated statisticalmethods


CHARTER Study

CNS HIV Antiretroviral Therapy Effects Research (CHARTER) projectinvestigates effects of HIV infection and treatment on the brain

Multicenter observational study, including San Diego site (HNRC)

1,500+ subjects

700+ subjects in longitudinal substudy, with 4,000+ visits

HIV RNA measured in plasma and in 3,300 CSF samples

Neurocognitive functioning measured at all visits

Wide cross-sectional snapshot of HIV+ population, including treatedand untreated individuals


Plasma HIV Viral Load in CHARTER

1316 subjects are either treatment naive or on HAART

Plasma HIV VL (1296 samples)

PLASMA Undetectable Detectable Total

ART Naive 14 (5.5%) 237 (94%) 251On HAART 576 (55%) 469 (45%) 1045

CSF HIV VL (1023 samples)

CSF Undetectable Detectable Total

ART Naive 51 (25%) 157 (75%) 208On HAART 688 (84%) 127 (16%) 815


Plasma HIV Viral Load, ART Naive Subjects

ART Naive, Plasma

Plasma Log10 VL

Frequency

1 2 3 4 5 6 7

010

3050

?-3 -2 -1 0 1 2 3

12

34

56

ART Naive, Plasma

Normal Quantile

Pla

sma

Log1

0 V

L

?


CSF HIV Viral Load, ART Naive Subjects

ART Naive, CSF

CSF Log10 VL

Frequency

-1 0 1 2 3 4 5

020

4060

?-3 -2 -1 0 1 2 3

-10

12

34

5

ART Naive, CSF

Normal Quantile

CS

F Lo

g10

VL

?


Plasma HIV Viral Load, Subjects On HAART

Plasma VL, HAART

Plasma Log10 VL

Frequency

-4 -2 0 2 4 6

0200

400

600

?-3 -2 -1 0 1 2 3

-4-2

02

46

Plasma VL, HAART

Normal Quantile

Pla

sma

Log1

0 V

L

?


CSF HIV Viral Load, Subjects On HAART

CSF VL, HAART

CSF Log10 VL

Frequency

-6 -4 -2 0 2 4

0200

400

600

?-3 -2 -1 0 1 2 3

-6-4

-20

24

CSF VL, HAART

Normal Quantile

CS

F Lo

g10

VL

?


How To Analyze Viral Load?

VL (plasma and/or CSF) is a key outcome or predictor in HIV studies

How to deal with VL in analyses?

Option 1: VL detectable versus undetectable

We throw away important informationNot reasonable for ART naive subjects

Option 2: Continuous VL (use 50 for undetectable subjects)

May be OK when comparing two groups (e.g., treatment A vs.treatment B)Not OK in more complex analyses, e.g. controlling for baseline CD4Awkward for subjects on ARTBiased interpretation for means, differences b/w means


Statistical Methods for Censored Viral Load

Option 3: Use more sophisticated statistical methods!

Two main classes of statistical methods:1 Methods for censored data2 Imputation methods


Methods for Censored Viral Load

Methods for censored data: usually treat VL as a censored response

Methods are developed in the context of survival analysis

E.g., if assuming that Log10 VL has a normal distribution, regressionmethods are equivalent to those for log-normal time-to-event

Accelerated failure times (AFT) models


CSF VL as a function of CD4 cell counts, ART Naives

ART naives: 25% undetectable in CSF

Study association of CSF VL with CD4

Naive approach (use 50 cp/ml for undetectables):

Regression equation: Log10 CSF VL = 3.506 - 0.00128 CD4

Moreover, non-linear association is suggested by plot

0 500 1000 1500

2.0

3.0

4.0

5.0

CD4 T-cell Count

Log1

0 C

SF

VL


CSF VL as a function of CD4 cell counts, ART Naives

Log-normal AFT model, i.e. correct for censoring:Regression equation: Log10 CSF VL = 3.701 - 0.00198 CD4

0 500 1000 1500

2.0

3.0

4.0

5.0

CD4 T-cell Count

Log1

0 C

SF

VL

100 additional CD4 cells are associated with a CSF VL lower by 0.20logs, not 0.12 logs

Intuitively, the adjusted line is treating the censored CSF VL as if theywere lower than 50 cp/ml


Multiple Imputation

Impute (generate) censored CSF VL from the interval (0, 50)Multiple imputation accounts for uncertainty in censored valuesBest to impute using association with other variables, such as CD4Usually assume normal distribution for log10 VL (fully observed)Distribution assumption more critical as proportion of censoringincreases, e.g. for subjects on ARTAlternative distributions are available, one can do a sensitivity analysis

0 500 1000 1500

12

34

5

CD4 T-cell Count

Log1

0 C

SF

VL

xxxxx x xx x x xx xx x xx xxx xx x xxx xxxx xxx xxxx xxxx xx xxx x x x xx


Viral Load in Longitudinal Studies

VL collected over time is common in HIV studies

Longitudinal studies present additional challenges:

Modeling the time trajectoryDealing adequately with within-subject correlationDealing with dropout

Mixed-effects models and Generalized estimating equations (GEE) arepowerful tools for longitudinal data

Special methods are necessary to adjust for censored VL


Censored Viral Load in Longitudinal Studies

One of my research interests: censored data in longitudinal studies(mixed effects models)Multiple imputation for MEM: Fitzgerald, Vaida, & DeGruttola (Statin Medicine 2002)MEM with censored data:

Vaida, Fitzgerald & DeGruttola (Comp Stat Data Analysis 2007)Vaida & Liu (J Comp Graph Stat 2009)lmec package in R (Vaida & Liu)

0 3 6 9 12 15 18 21 24

23

45

6

Month of Treatment Interruption

log1

0 H

IV−

1 R

NA

N=71 58 57 43 34 24 13


Treatment Interruption of HIV (Saitoh et al., 2008)

Unstructured Rx interruption in 72 adolescents, 4 sites in the US;observational study

0 3 6 9 12 15 18 21 24

010

2030

4050


CD

4 %



Observed mean CD4% seems to recover after 6 months

0 3 6 9 12 15 18 21 24

010

2030

4050


CD

4 %

N=70 59 57 44 34 24 12



CD4 % modeled via a mixed effects (random intercept) model:

CD4%ij = µj + bi + eij

Subject trajectories = parallel curvesModel accounts for dropout (red), shows continuing CD4% decline:

0 3 6 9 12 15 18 21 24

010

2030

4050


CD

4 %

N=70 59 57 44 34 24 12


Treatment Interruption of HIV (Saitoh et al., 2008):Plasma VL

Mixed-effects (random intercept) profile model for log10 HIV VL,account for censoring (black line)

0 3 6 9 12 15 18 21 24

23

45

6


log1

0 H

IV−

1 R

NA

N=71 58 57 43 34 24 13


Bi-exponential model for Viral Decay in ACTG315 (Vaida,Fitzgerald, & DeGruttola, 2007)

Single-arm ART study (ZDV/3TC/RTV) in ART-naive patients

Bi-exponential model for viral decay:

VL(t) = A1 exp(−β1t) +A2 exp(−β2t)

Use a mixed-effects model with random subject effects for β1, β2

Account for censoring BLD


Bi-exponential model for Viral Decay in ACTG315


Joint modeling of plasma and CSF VL in CHARTER

MI using joint modeling of CSF and plasma VLUse correlation with CD4, duration of infection; ART naive subjectsUltimately, use imputed values to study association of VL withneurocognitive impairmentR21 application submitted


recovering information from suppressed plasma and csf hiv viral load using multiple imputation

Health & Medicine