Correctly modeling CD4 cell count in Cox regression analysis of HIV-positive patients

1. Correctly modeling CD4 cell count in Cox regression analysis of HIV-positive patients Allison Dunning, M.S. Research Biostatistician Weill Cornell Medical College

2. Outline • Background • Motivation • Methods • Data Management • Results • Conclusion

3. Background • Results from the primary open-label clinical trial have previously been published in the New England Journal of Medicine.

4. Background • Results of the clinical trial have shown that starting antiretroviral therapy earlier (‘Early’) rather than waiting for onset of symptoms (‘Standard’) in HIV patients significantly decreases mortality. • Between 2005 and 2008 a total of 816 participants – 408 per group – were enrolled and followed. • After stopping the clinical trail all participants were immediately put on antiretroviral therapy. • Researchers have continued to follow and collect data on the 816 participants.

5. Motivation • As a follow-up, researchers are interested in determining if ‘Early’ therapy significantly decreases time to first Tuberculosis (TFTB) diagnosis. • CD4 cell count has long been considered a measure of overall health in HIV patients. • Therefore investigators felt it was important to adjust for CD4 cell count in the analysis of TFTB diagnosis.

6. Motivation • The problem arose of how best to adjust for CD4 cell count. • Typically CD4 recorded at the beginning of the study is used for analysis; known as baseline CD4 cell count. • Per protocol CD4 cell counts were collected every 6 months for all participants. • Investigators felt it was important to account for changing CD4 cell counts, especially after therapy initiation, in the analysis.

7. Motivation • Our analysis was not interested in predicting survival just whether or not drug start time was a predictor of TB diagnosis. • In order to allow survival analysis to account for changing CD4 cell counts we decided to conduct a Cox Proportional Hazards Regression analysis using a mixture of fixed and time-dependent covariates.

8. What is a Time Dependent Covariate • Time-dependent covariates are those that may change in value over the study period • Most variables in survival analysis are collected at one time point, typically at the start of the study, these include demographic and risk factor variables • Sometimes we may collect a lab variable or risk factor that can vary over the study period.

9. Example of Time Dependent Variables • Lab Values: • Blood Pressure • Most studies will only use blood pressure collected at start of study, sometimes called baseline blood pressure. • However, in theory, blood pressure could be collected at multiple time during the study period. • Risk Factors: • Smoking Status • Again this can be collected only at start of study, or baseline or could be tracked over time • Some patients may quit smoking, start smoking, or quit and relapse smoking during the study period.

10. Fixed Covariates • Fixed Covariates is a term used to represent variables that stay constant, or do not change, during the study period. • These are typically things like patient gender, race/ethnicity, risk factors such as diabetes or hypertension, etc. • We as researchers must develop a method to analyze time to event data while including both these fixed covariate and time-dependent covariates

11. Methods • STATA 12.0 was used to perform two Cox regression models to analyze the effect of ART start time on TFTB. • The first model included baseline CD4 cell count only as a predictor • While the second model treated CD4 cell count as a time-varying predictor. • Both models were adjusted for history of TB diagnosis prior to clinical trial and baseline BMI

12. Methods • Regular Cox Proportional Hazards Model: • Log[hi(t)] = α(t) + β1xi1 + … + βkxik • Where α(t) = log [λ0(t)] • Proportional Hazards Model with time-varying covariate: • Log[hi(t)] = α(t) + β1xi1 + β2xi2(t) • Where α(t) = log [λ0(t)]

13. Data Management • Problems we encountered: • Missing CD4 cell count • Some patients missed a scheduled lab visit during the study, therefore CD4 cell count was missing for one of the six month intervals. • Multiple CD4 cell counts within a six month interval • For various reasons, several patients visited the lab multiple times within a six month interval, therefore multiple CD4 cell counts were collected in the six month time frame.

14. Data Management • What we did – Missing Data: • If only one interval was missing, the previous CD4 cell count was used in a carry the last forward approach • If at least two consecutive intervals were missing, the patient was excluded from the study; 13 patients in total were excluded for this reason. • What we did – Multiple Observations: • The minimum CD4 cell count collected in the six month interval was the value used in analysis for that time frame.

16. Results – Regular Cox Regression

17. Results • Regular cox regression analysis showed that ‘Early’ therapy results in a significant decrease in TFTB, after adjustment for previous TB diagnosis, baseline BMI, and baseline CD4 cell count.

18. Data Management • Data was collected with one row per participant:

19. Data Management • In STATA, using reshape command, we reformatted dataset for analysis:

21. Results – Cox Regression with time-dependent covariates

22. Results • When treating CD4 cell count as time-varying predictor in Cox regression, we find that ART start time is not a significant predictor of TFTB.

23. Conclusion • Failing to adjust for the change in CD4 cell counts over time led to reporting that ‘Early’ therapy significantly reduces risk of TB diagnosis. Modeled correctly, the effect becomes non-significant. This result has substantial consequence on treatment decision making.

24. Conclusion • Our results help us to consider that TFTB diagnosis in HIV positive patients is not associated with start time of ART when overall patient health is considered. • Further analysis is needed before we are comfortable making this conclusion.

25. Looking Forward • We are currently in the process of further examining the relationship between CD4 cell count and ART start. • Currently collecting data to examine time from ART start to first TB diagnosis. For the Early group this data does not change, however, for the Standard group this may have a significant effect on the analysis.

26. Acknowledgements • Daniel W. Fitzgerald, M.D • Sean Collins, M.D • Sandra H. Rua, Ph.D

27. Thank You ald2018@med.cornell.edu