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)

– Where α(t) = log [λ0(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.

baseline_cd4 .9971885 .0025613 -1.10 0.273 .992181 1.002221 history_tb 2.162748 .5280383 3.16 0.002 1.340244 3.490022baseline_bmi .9142055 .032393 -2.53 0.011 .8528707 .9799511 Early .423655 .0948775 -3.83 0.000 .2731402 .6571113 _t Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -589.04713 Prob > chi2 = 0.0000 LR chi2(4) = 35.48Time at risk = 150407.5714No. of failures = 94No. of subjects = 760 Number of obs = 760

Cox regression -- Breslow method for ties

Iteration 0: log likelihood = -589.04713Refining estimates:Iteration 3: log likelihood = -589.04713Iteration 2: log likelihood = -589.04905Iteration 1: log likelihood = -589.78547Iteration 0: log likelihood = -606.78841

analysis time _t: weeks_to_tb failure _d: incident_tb == 1

. stcox Early baseline_bmi history_tb baseline_cd4

last observed exit t = 330.5714 earliest observed entry t = 0 150407.6 total analysis time at risk, at risk from t = 0 94 failures in single record/single failure data 760 obs. remaining, representing 0 exclusions 760 total obs.

exit on or before: failureobs. time interval: (0, weeks_to_tb] failure event: incident_tb == 1

. stset weeks_to_tb, failure(incident_tb==1)

. rename grp1 Early

. quietly tabulate rxcode, generate(grp)

. use "C:\Documents and Settings\ald2018\Desktop\STATA Conference 2013\JSM Abstract\STATA Abstract Reg Data.dta"

Results – Regular Cox Regression

baseline_cd4 .9972554 .0025424 -1.08 0.281 .9922849 1.002251 history_tb 2.163769 .5184032 3.22 0.001 1.352935 3.460546baseline_bmi .9067024 .0322029 -2.76 0.006 .8457326 .9720676 Early .4388986 .096901 -3.73 0.000 .2847305 .6765415 _t Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -600.92881 Prob > chi2 = 0.0000 LR chi2(4) = 36.32Time at risk = 153457.4286No. of failures = 96No. of subjects = 773 Number of obs = 773

Cox regression -- Breslow method for ties

Iteration 0: log likelihood = -600.92881Refining estimates:Iteration 3: log likelihood = -600.92881Iteration 2: log likelihood = -600.93058Iteration 1: log likelihood = -601.71285Iteration 0: log likelihood = -619.08645

analysis time _t: weeks_to_tb failure _d: incident_tb == 1

. stcox Early baseline_bmi history_tb baseline_cd4

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:

cd4_count .9911868 .0010495 -8.36 0.000 .9891321 .9932458baseline_bmi .9376221 .0327094 -1.85 0.065 .8756554 1.003974 history_tb 1.991573 .4914993 2.79 0.005 1.227803 3.230456 Early .8041764 .1881104 -0.93 0.351 .5084414 1.271926 _t Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -535.89226 Prob > chi2 = 0.0000 LR chi2(4) = 115.16Time at risk = 148364No. of failures = 92No. of subjects = 760 Number of obs = 5411

Cox regression -- Breslow method for ties

Iteration 0: log likelihood = -535.89226Refining estimates:Iteration 4: log likelihood = -535.89226Iteration 3: log likelihood = -535.89227Iteration 2: log likelihood = -535.94519Iteration 1: log likelihood = -541.68367Iteration 0: log likelihood = -593.47212

id: patid analysis time _t: t2 failure _d: status == 1

. stcox Early history_tb baseline_bmi cd4_count

last observed exit t = 329 earliest observed entry t = 0 148364 total analysis time at risk, at risk from t = 0 92 failures in single failure-per-subject data 760 subjects 5411 obs. remaining, representing 36 overlapping records (t2[_n-1]>t1) PROBABLE ERROR 212 entry on or after exit (t1>t2) PROBABLE ERROR 5659 total obs.

exit on or before: failureobs. time interval: (t1, t2] failure event: status == 1 id: patid

. stset t2, id(patid) failure(status==1) time0(t1)

. rename grp1 Early

. quietly tabulate rxcode, generate(grp)

. use "C:\Documents and Settings\ald2018\Desktop\STATA Conference 2013\JSM Abstract\STATA Abstract Data.dta"

Results – Cox Regression with time-dependent covariates

cd4_count .9911868 .0010495 -8.36 0.000 .9891321 .9932458baseline_bmi .9376221 .0327094 -1.85 0.065 .8756554 1.003974 history_tb 1.991573 .4914993 2.79 0.005 1.227803 3.230456 Early .8041764 .1881104 -0.93 0.351 .5084414 1.271926 _t Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval]

Log likelihood = -535.89226 Prob > chi2 = 0.0000 LR chi2(4) = 115.16Time at risk = 148364No. of failures = 92No. of subjects = 760 Number of obs = 5411

Cox regression -- Breslow method for ties

Iteration 0: log likelihood = -535.89226Refining estimates:Iteration 4: log likelihood = -535.89226Iteration 3: log likelihood = -535.89227Iteration 2: log likelihood = -535.94519Iteration 1: log likelihood = -541.68367Iteration 0: log likelihood = -593.47212

id: patid analysis time _t: t2 failure _d: status == 1

. stcox Early history_tb baseline_bmi cd4_count

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