ACTG 315 Viral Dynamic Data Prepared by Hulin Wu and A. Adam Ding Note: 1. The data were generated from AIDS Clinical Trials Group, ACTG 315 protocol, which is sponsored by NIAID/NIH. If you have any question regarding the data, you may contact Dr. Hulin Wu by email, wu@sdac.harvard.edu. 2. The following data is slightly different from the data used in Wu and Ding (1999, Biometrics) since more data were added in the data base. The data were re-cleaned recently. 3. 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. 4. Negative time (days) is the measurement time before antiviral treatment. 5. Detection limit of the viral load (HIV RNA copies) assay is 100 copies per ml blood. If it is below detectable, we imputed 50 in the following data analysis. 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 (or it may result in misleading dynamic patterns). 6. Only first 12-week data are included. The rebounded viral load data are deleted based on the description in Wu and Ding (1999, Biometrics). 7. More details on this clinical study can be found in Lederman et al (1998, J. of Infect. Dis.) and Wu et al (1999, J. of Infect. Dis.). See the following references for more related analyses and models. 8. Fit the updated data using Wu and Ding (1999) method: o Delete the data at baseline (Day 0) and before treatment. o Other methods to deal with baseline data can be found in Ding and Wu (2000). o Due to convergence problems, multiple starting values (or global search algorithms) should be used to fit the 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 ------------------------------------------------------------------------------- REFERENCES: ---------- 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. Wu, H. and Ding, A. and DeGruttola. V. (1998), Estimation of HIV Dynamic Parameters, Statistics in Medicine, 17, 2463-2485. 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. 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. Ding, A.A. and Wu, H. (1999), ``Relationships between Antiviral Treatment Effects and Biphasic Viral Decay Rates in Modeling HIV Dynamics," Mathematical Biosciences, in press. Wu, H., Ruan, P., Ding, A.A., Sullivan, J.L. and Luzuriaga, K. (1999), ``Inappropriate Model-Fitting Methods May Lead To Significant Underestimates of Viral Decay Rates in HIV Dynamic Studies," Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology, in press. Ding, A.A. and Wu, H. (1999), ``A Comparison Study of Models and Fitting Procedures for Biphasic Viral Dynamics in HIV-1 Infected Patients Treated with Antiviral Therapies," to appear in Biometrics, Vol. 56, No. 1, March 2000. Wu, H. and Wu, L. (1999), ``A Multiple Imputation Method for Missing Covariates in Nonlinear Mixed-effect Models, with Application to HIV Dynamics," submitted for publication. ---------------------------------------------------------------------------- ID Day RNA 1 -35 15000 1 -7 14000 1 0 23000 1 2 23000 1 7 3400 1 8 1200 1 16 950 1 22 380 1 29 440 1 57 130 1 91 100 2 -34 1200 2 -7 2100 2 0 6200 2 2 2400 2 7 100 3 -34 54000 3 -7 52000 3 0 59000 3 7 13000 3 9 7000 3 14 1700 3 21 800 3 28 600 3 56 270 4 -40 760 4 -7 6200 4 0 8500 4 2 9000 4 7 410 4 10 410 4 14 420 4 22 440 4 28 160 4 56 100 5 -35 4000 5 -7 310000 5 0 260000 5 3 25000 5 8 7800 5 9 2900 5 14 2400 5 21 340 5 28 100 6 -7 48000 6 0 32000 6 2 65000 6 6 5500 6 9 3300 6 13 2500 6 27 540 6 51 820 6 84 860 7 -35 90000 7 -7 120000 7 0 150000 7 7 180000 7 10 88000 7 14 19000 7 21 18000 7 28 12000 7 56 1800 7 84 740 8 -21 86000 8 -7 64000 8 0 87000 8 2 77000 8 7 7500 8 10 4300 8 14 3100 8 21 1400 9 -34 80000 9 -7 37000 9 0 67000 9 7 6500 9 9 8900 9 14 1800 9 21 660 10 -33 148000 10 -7 260000 10 0 210000 10 7 27000 10 9 20000 10 14 7600 10 20 11000 10 28 3700 10 56 630 10 84 480 11 -36 7800 11 -7 13000 11 0 14000 11 7 3400 11 9 1300 11 14 340 11 20 1000 11 28 150 12 -33 290000 12 -7 600000 12 0 610000 12 2 860000 12 8 47000 12 10 33000 12 15 14000 12 21 9500 12 28 8900 12 59 2200 12 85 720 13 -35 120000 13 -7 250000 13 0 340000 13 2 170000 13 6 21000 13 9 6900 13 14 1700 13 21 1400 13 28 730 13 56 100 14 -35 39000 14 -7 320000 14 2 320000 14 8 67000 14 10 37000 14 21 11000 14 28 10000 14 56 5100 14 79 1100 15 -40 180000 15 -7 100000 15 0 180000 15 2 190000 15 7 18000 15 10 4600 15 21 3000 15 28 2300 16 -27 16000 16 -7 72000 16 0 57000 16 2 39000 16 6 26000 16 9 7300 16 13 620 16 21 1700 16 29 300 16 56 470 16 84 150 17 -33 53000 17 -7 86000 17 0 86000 17 2 330000 17 6 10000 17 9 3500 17 13 340 17 21 520 17 29 460 17 56 280 17 84 100 18 -29 25000 18 -7 19000 18 0 20000 18 2 25000 18 6 5800 18 9 4600 18 14 970 18 21 540 18 29 520 18 56 420 18 84 170 19 -46 100 19 -7 13000 19 0 11000 19 2 35000 19 6 2500 19 10 800 19 13 810 19 20 1200 19 28 360 19 59 230 19 84 100 20 -7 860000 20 0 280000 20 2 960000 20 6 120000 20 9 16000 20 13 5300 20 20 2400 20 28 960 20 58 250 21 -7 170000 21 0 130000 21 3 75000 21 6 28000 21 9 8400 21 13 2300 21 21 1200 21 29 1300 21 56 710 22 -33 110000 22 -7 130000 22 0 300000 22 2 100000 22 6 62000 22 9 4800 22 13 3200 22 21 1400 22 28 990 22 63 300 22 84 160 23 -36 65000 23 -7 90000 23 0 85000 23 2 75000 23 7 5300 23 10 7200 23 13 5700 24 -7 140000 24 0 69000 24 2 41000 24 7 6900 24 9 11000 24 14 3300 24 20 1900 24 28 1300 24 56 100 25 -8 110000 25 0 160000 25 2 130000 25 5 57000 25 8 10000 25 12 24000 25 19 1700 25 28 1300 25 65 340 26 -36 29000 26 -7 56000 26 0 36000 26 2 64000 26 7 9700 26 10 4500 26 13 4400 26 31 990 26 59 480 26 77 240 27 -33 93000 27 -7 170000 27 0 130000 27 2 260000 27 6 71000 27 9 25000 27 13 8300 27 20 13000 27 28 2900 27 56 350 27 77 100 28 -56 99000 28 -9 150000 28 -1 160000 28 4 140000 28 7 110000 28 11 12000 28 18 7800 29 -35 1900 29 -7 7900 29 0 9900 29 6 3300 29 10 430 30 -42 29000 30 -7 38000 30 0 29820 30 2 59000 30 6 9700 30 10 2700 30 13 1700 30 20 810 30 28 310 30 56 200 30 84 100 31 -41 28000 31 -6 57000 31 0 68000 31 2 65000 31 5 29000 31 8 10000 31 12 3800 31 19 2600 31 28 1400 31 56 280 31 84 100 32 -47 120000 32 -7 200000 32 0 110000 32 2 140000 32 7 9500 32 9 6900 32 14 3100 32 21 1700 32 28 1200 32 42 630 32 77 100 33 -7 380 33 0 280 33 2 170 33 6 160 33 16 100 34 -35 14000 34 -7 25000 34 0 20000 34 2 19000 34 7 2200 34 9 1100 34 15 2000 34 21 710 34 28 1400 34 57 100 35 -24 890000 35 -7 720000 35 0 810000 35 2 1600000 35 7 170000 35 10 67000 35 16 29000 35 22 8800 35 29 5300 35 59 690 36 -14 54000 36 -8 62000 36 0 69000 36 2 43000 36 6 12000 36 9 4200 36 13 4400 36 20 1500 36 27 790 36 57 820 36 77 100 37 -33 75000 37 -7 13000 37 0 240000 37 2 270000 37 7 11000 37 9 5400 37 14 1100 37 21 1300 37 28 540 37 58 160 38 -35 97000 38 -7 7000000 38 0 1200000 38 2 1100000 38 7 170000 38 9 80000 38 14 20000 38 21 26000 38 27 33000 38 57 4400 38 90 900 39 -39 130000 39 -7 58000 39 0 190000 39 2 79000 39 7 13000 39 10 4400 39 14 930 39 22 280 39 29 100 40 -36 120000 40 -7 220000 40 0 320000 40 2 450000 40 7 56000 40 12 37000 40 16 6400 40 22 8700 40 29 2000 40 57 4000 40 84 450 41 -35 460 41 -7 38000 41 0 12000 41 2 47000 41 7 1900 41 9 530 41 14 270 41 21 170 41 28 280 41 56 100 42 -41 120000 42 -7 430000 42 0 570000 42 2 110000 42 6 16000 42 8 5300 42 13 2800 42 21 1300 42 27 520 42 51 110 42 77 100 43 -35 13000 43 -7 160000 43 0 150000 43 2 99000 43 8 3300 43 10 4400 43 16 1500 43 21 700 43 37 520 44 -35 44000 44 -7 76000 44 0 270000 44 2 260000 44 7 35000 44 10 9900 44 14 2200 44 21 2800 44 28 1200 45 -39 33000 45 -7 42000 45 0 96000 45 2 110000 45 7 7900 45 10 1400 45 14 1500 45 21 1000 45 29 2900 45 57 190 45 85 100 46 -40 110000 46 -7 120000 46 0 71000 46 2 100000 46 7 34000 46 10 14000 46 15 3600 46 22 310 46 28 1100 46 58 750 46 86 450 47 -36 5400 47 0 190000 47 2 180000 47 7 120000 47 12 30000 47 14 17000 47 21 7900 47 27 3100 47 55 1400 47 90 120 48 -28 110000 48 -7 150000 48 0 55000 48 2 68000 48 7 6900 48 10 1500 48 14 620 48 21 900 48 28 420