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

Outline Background Motivation Methods Data Management Results Conclusion

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

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.

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.

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.

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.

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.

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.

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

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

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)

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.

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.

Results – Regular Cox Regression

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.

Data Management Data was collected with one row per participant:

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

Results – Cox Regression with time-dependent covariates

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.

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.

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.

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.

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

Thank You ald2018@med.cornell.edu