# 1 Statistical Analysis for an AIDS Clinical Trial Weiming Ke The University of Memphis St. Jude Childrens Research Hospital June 5, 2004.

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1 Statistical Analysis for an AIDS Clinical Trial Weiming Ke The University of Memphis St. Jude Childrens Research Hospital June 5, 2004

2 Outline Background Data description Study objectives Statistical approach Statistical analysis Conclusion

3 Background An HIV patient's RNA copies are a measure of his/her HIV viral load. Patients HIV RNA copies are often used in recent AIDS studies to assess treatment efficacy and etc. Usually, 500 is set to be a cut-point for HIV RNA levels (a patient is viewed having a good condition if his HIV RNA is below 500).

4 Background (cont.) An HIV patient's CD4 cell counts are a measure of her/his immunity capacity. In practical use, 400 cell counts is set to be a cut-point for CD4 counts (a patient is viewed having a good immunity if his CD4 cell counts is above 400).

5 Data Description The data were randomly collected from the hospitals at different sites in a recent AIDS clinical trial. The dataset includes the following data: –– Dependent variable: RNAWK16: HIV-RNA copies at study week 16 (study endpoint or response of interest)

6 Data Description (cont.) –– independent variables: RNAWK0: HIV-RNA copies at baseline (right before taking treatments) CD4WK0: CD4 counts at baseline (right before taking treatments) TRT: code of the treatment (1 and 2) GENDER: 1 = Female and 2 = Male SITE: code of participating sites

7 Data Description (cont.) A common practice of analyzing RNA data is to consider the log_10 transformed RNA copies instead of using the RNA copies directly. log_10 (500) = 2.7 is set to be a cut-point for HIV RNA levels (a patient is viewed having a good condition if his HIV RNA copies is below 2.7 after log_10 transformation).

8 Data Description (cont.) data HIV; input ID RNAWK0 RNAWK16 CD4WK0 TRT Gender Site; RNAWK0=log10(RNAWK0); RNAWK16=log10(RNAWK16); datalines; 1 9487.73 190 192.5 2 1 10 2 25973.30 462 193.5 2 2 10 3 21023.71 18525 233.5 1 1 1 4 10432.45 27579 634.5 2 1 8 5 33926.00 127925 381.5 2 1 8....... 110 46533.00 143138 462.5 2 1 6 111 9041.28 776 293.0 2 1 5 112 46323.86 2297 316.5 2 2 7 113 2157.56 180 430.0 1 2 10 114 1693.96 448 228.5 1 1 8 ;

9 Study objectives To compare the two treatments based on the subjects' HIV-RNA copies at study week 16. To study how HIV-RNA copies at study week 16 are associated with the levels of baseline HIV-RNA copies, CD4 counts at baseline, treatments, gender and sites.

10 Statistical Approach Analysis of Variance (ANOVA) Method Linear Regression Method T-test

11 Statistical analysis ANOVA method –– ANOVA method was used to compare the mean values of RNAWK16 between the two treatments for the whole dataset. –– The ANOVA model can be expressed as follows: Y ij = μ + α i + ε ij, Where α i = 0, ε ij ~ N(0, Ϭ ²)

12 ANOVA method SAS program for ANOVA analysis: PROC ANOVA data=HIV; class TRT; model RNAWK16=TRT; RUN;

13 Results of ANOVA analysis The SAS System The ANOVA Procedure Class Level Information Class Levels Values TRT 2 1 2 Number of observations 114 The ANOVA Procedure Dependent Variable: RNAWK16 Source DF ANOVA SS Mean Square F Value Pr >F TRT 1 6.130122 6.13012 4.48 0.0366

14 Results of ANOVA analysis (cont.) To test if the means values of the RNAWK16 for the two treatments are equal, the result showed that P-value = 0.0366 hence we can conclude that the RNA copies at week 16 are significantly different between the two treatment groups.

15 Linear regression method A regression model was used to examine the relationship between the explanatory variables and the values of RNAWK16. The regression coefficients may be interpreted as describing the direction and strength of the relationship of each explanatory variable on the effect of the values of RNAWK16.

16 Linear regression method (cont.) The Linear regression model can be expressed as : Y = α + β i X i + ε, Where ε ~ N(0, Ϭ ²) For this data set, the regression model can be expressed as : RNAWK16 = α + β 1 ·TRT + β 2 ·RNAWK0 + β 3 ·CD4WK0 + β 4 ·Gender + β 5 ·Site + ε

17 Linear regression method (cont.) SAS program for regression analysis: PROC REG data=HIV; model RNAWK16=TRT RNAWK0 CD4WK0 Gender Site; RUN;

18 Results of linear regression The SAS System The REG Procedure Dependent Variable: RNAWK16 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr>|t| Intercept 1 1.70459 0.93410 1.82 0.0708 TRT 1 -0.50609 0.19776 -2.56 0.0119 RNAWK0 1 0.70851 0.16739 4.23 <.0001 CD4WK0 1 -0.00042 0.00062 -0.68 0.4991 Gender 1 0.15003 0.19661 0.76 0.4471 SITE 1 -0.07207 0.03448 -2.09 0.3902

19 Results of linear regression (cont.) The results showed that the p-value is 0.0119 for treatment and less than 0.001 for RNAWK0. hence we conclude that the treatment and RNAWK0 (HIV-RNA copies at baseline) have significant effects on the values of RNAWK16. CD4WK0, Gender and Site do not have significant effects on RNAWK16.

20 Results of linear regression (cont.) Based on the estimated parameters, The fitted regression model can be expressed as: RNAWK16 = 1.7 – 0.5·TRT + 0.7·RNAWK0 – 0.00042·CD4WK0 + 0.15·Gender – 0.07·Site Negative coefficient of TRT means that treatment 2 tends to have small values of RNA copies at week 16. Positive coefficient of RNAWK0 means that the patients who have large values of RNA copies at baseline tend to have large values of RNA copies at week 16.

21 T-test T-test can be used to compare two samples. Here we use T-test to compare RNAWK16 between the patients in the two treatment groups to see if there is a significant difference between the two treatments. To examine which treatment will result in lower level of HIV-RNA copies at week 16.

22 T-test (cont.) SAS program for t-test: proc sort data=HIV; by TRT; proc means data=HIV; var RNAWK16; by TRT; output out=new; proc ttest data=new; class TRT; var RNAWK16; run;

23 Results of t-test The SAS System The T-TEST Procedure Statistics Lower CL Upper CL Variable TRT N Mean Mean Mean Std Err RNAWK16 1 56 3.6834 4.0023 4.3212 0.1591 RNAWK16 2 58 3.2361 3.5385 3.8408 0.151 RNAWK16 Diff(1-2) 0.0295 0.4639 0.8982 0.2192 T-Tests Variable Method Variances DF t Value Pr > |t| RNAWK16 Pooled Equal 112 2.12 0.0366

24 Results of t-test (cont.) T-test showed that the mean values of RNA copies at week 16 resulted by treatment 2 is significantly lower than that resulted by treatment 1. VariableTreatmentMean 95% Confidence Interval P-value RANWK16 14.00(3.68, 4.32) 0.0366 23.54(3.24, 3.84) Diff (1-2)0.46(0.03, 0.90)

25 Conclusion Based on the statistical analysis, We conclude that The treatment and the baseline RNA copies have significant effects on the RNA copies at week 16. CD4 count at baseline, gender and site do not have significant effects on the RNA copies at week16.

26 Conclusion (cont.) The patients under treatment 2 have significantly lower values of RNA copies at week 16 than those patients under treatment 1. The patients who have lower values of RNA copies at the beginning of study tend to have lower values of RNA copies at week 16.

27 Thank You !

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