# ACTG 315 Short-Term Viral Dynamic Data for NLME Model Fitting

### Data

1. The data were produced from AIDS Clinical Trials Group, ACTG 315 study, which is sponsored by NIAID/NIH. If you have any questions regarding the data, you may contact Dr. Hulin Wu by email, hwu@bst.rochester.edu.

2. The detailed biomedical findings from this study and more detailed description of the study design can be found from the primary and secondary publications of this study, Lederman et al (1998) and Connick et al. (2000) (see below for these references).

3. Some early viral dynamic modeling analyses based on this study are reported in the following papers:

- Wu and Ding and DeGruttola (1998, Statistics in Medicine)
- Wu, Kuritzkes and McClernon, et al (1999, J of Infect Dis)
- Wu and Ding (1999, Biometrics)
- Ding and Wu (1999, Mathematical Biosciences)
- Ding and Wu (2000, Biometrics)

Some further viral dynamic analyses for this study (including long-term viral dynamics and covariates analyses) can be found in other pages of our website.

4. This data set was slightly modified from the data used in Wu and Ding (1999, Biometrics). More data were added in the database. The data were re-cleaned after the analysis of Wu and Ding (1999). Only first 12-week data are included. The rebounded viral load data are deleted based on the description in Wu and Ding (1999).

5. Among total 53 patients accrued in this study, five patients dropped out before Week 12 due to intolerance and other problems. They are excluded from our analysis. Negative time (days) is the pre-entry measurements before antiviral treatment initiated.

6. Detection limit of the viral load (HIV RNA copies) assay is 100 copies per ml blood. If it is below detection, we imputed 100 in the data set although we imputed as 50 in our analysis (Wu and Ding 1999). If more than one measurement below detectable level for an individual, we just impute the first measurement and exclude the rest of them in our analysis (otherwise it may result in misleading dynamic patterns).

7. Fit the updated data using Wu and Ding (1999) method:

- Delete the data at baseline (Day 0) and before treatment.
- Other methods to deal with baseline data can be found in Ding and Wu (2000).
- Due to convergence problems, multiple starting values (or global search algorithms) should be used to fit the NLME models. The starting point in the following Splus code was chosen after comparing the results using many different starting values.

SPLUS CODE:

######################### Beginning of Splus Code ########################

# Input Data: assume that the data at the end is stored in an ASCII file

# named "data".

workd<-read.table(file="data",header=T,row.names=NULL)

# The measurements before treatment initiation are not used in the analysis.

workd<-workd[workd$Day>0,]

# Impute below detectable viral measurement by 50.

workd$RNA[workd$RNA==100]<-50

# Define functions representing Model (12) and Model (13)

# of Wu and Ding (1999).

exp.model12<-function(p0, p1, d1, X)

{

P0 <- exp(p0)

P1 <- exp(p1)

P0 + P1 * exp( - d1 * X)

}

exp.model13<-function(p1, d1, p2, d2, X)

{

P1 <- exp(p1)

P2 <- exp(p2)

P1 * exp( - d1 * X) + P2 * exp( - d2 * X)

}

# Fit Model (12) and Model (13) by NLME

actg315.model12<-nlme(Y ~ log10(exp.model12(p0, p1, d1, X)),

fixed = list(p0~., p1~., d1~.),

random = list(p0~., p1~., d1~.),

cluster = ~ Z,

data = data.frame(Y=log10(workd$RNA), X=workd$Day, Z=workd$ID),

start = list(fixed= c(5,11,0.5)),verbose=T)

actg315.model13<-nlme(Y ~ log10(exp.model13(p1, d1, p2, d2, X)),

fixed = list(p1~., d1~., p2~., d2~.),

random = list(p1~., d1~., p2~., d2~.),

cluster = ~ Z,

data = data.frame(Y=log10(workd$RNA), X=workd$Day, Z=workd$ID),

start = list(fixed= c(12,0.4,7,0.03)),verbose=T)

anova(actg315.model12,actg315.model13)

###################### End of Splus Code ######################################

RESULTS:

--------

Model Df AIC BIC Loglik Test Lik.Ratio P value

actg315.model12 1 10 433.03 470.69 -206.52

actg315.model13 2 15 257.98 314.46 -113.99 1 vs. 2 185.05 0

Fixed Effects Estimates from Model (12):

LogP0 LogP1 delta_p

5.666933 11.10344 0.2246409

Fixed Effects Estimates from Model (13):

LogP1 delta_p LogP2 lamba_l

12.32537 0.4759455 7.945189 0.04134005

**********************************************************************************

8. Please cite the following references if appropriate when you use the data in your paper:

REFERENCES:

----------

1) Connick E, Lederman MM, Kotzin BL, et al. (2000), "Immune reconstitution in the first year of potent antiretroviral therapy and its relationship to virologic response," Journal of Infectious Diseases, 181:358-63.

2) Ding, A.A. and Wu, H. (1999), "Relationships between Antiviral Treatment Effects and Biphasic Viral Decay Rates in Modeling HIV Dynamics," Mathematical Biosciences, 160. 63-82.

3) Ding, A.A. and Wu, H. (2000), "A Comparison Study of Models and Fitting Procedures for Biphasic Viral Dynamics in HIV-1 Infected Patients Treated with Antiviral Therapies," Biometrics, 56, 293-300.

4) Lederman MM, Connick E, Landay A, et al. (1998), "Immunologic responses associated with 12 weeks of combination antiretroviral therapy consisting of zidovudine, lamivudine and ritonavir: results of AIDS Clinical Trials Group Protocol 315," Journal of Infectious Diseases, 178: 70-79.

5) Wu, H. and Ding, A. (1999), "Population HIV-1 Dynamics in Vivo: Applicable Models and Inferential Tools for Virological Data from AIDS Clinical Trials," Biometrics, 55, 410-418.

6) Wu, H. and Ding, A. and DeGruttola. V. (1998), "Estimation of HIV Dynamic Parameters," Statistics in Medicine, 17, 2463-2485.

7) Wu, H., Kuritzkes, D.R., and McClernon, D.R. et al. (1999), "Characterization of Viral Dynamics in Human Immunodeficiency Virus Type 1-Infected Patients Treated with Combination Antiretroviral Therapy: Relationships to Host Factors, Cellular Restoration and Virological Endpoints," Journal of Infectious Diseases, 179(4):799-807.

---------------------------------------------------------------------------