Conceived and designed the experiments: KK JJL. Performed the experiments: KK KM LGB RW. Analyzed the data: KK JJL RGW. Contributed reagents/materials/analysis tools: RW LGB KM SDL KK JJL RGW JRG. Wrote the paper: KK JJL RDW SDL RGW.
The authors have declared that no competing interests exist.
Survival analysis using time-updated CD4+ counts during antiretroviral therapy is frequently employed to determine risk of clinical events. The time-point when the CD4+ count is assumed to change potentially biases effect estimates but methods used to estimate this are infrequently reported.
This study examined the effect of three different estimation methods: assuming i) a constant CD4+ count from date of measurement until the date of next measurement, ii) a constant CD4+ count from the midpoint of the preceding interval until the midpoint of the subsequent interval and iii) a linear interpolation between consecutive CD4+ measurements to provide additional midpoint measurements. Person-time, tuberculosis rates and hazard ratios by CD4+ stratum were compared using all available CD4+ counts (measurement frequency 1–3 months) and 6 monthly measurements from a clinical cohort. Simulated data were used to compare the extent of bias introduced by these methods.
The midpoint method gave the closest fit to person-time spent with low CD4+ counts and for hazard ratios for outcomes both in the clinical dataset and the simulated data.
The midpoint method presents a simple option to reduce bias in time-updated CD4+ analysis, particularly at low CD4 cell counts and rapidly increasing counts after ART initiation.
Observational prospective cohort data of patients on antiretroviral therapy (ART) are often used to estimate the relationship between time-varying CD4+ counts and incident clinical events such as tuberculosis (TB), death, opportunistic infections and malignancies. These studies aim to investigate the effect of actual CD4+ count on morbidity and mortality by using time-varying measures. While within-subject CD4+ count variability
Differences in measurement frequency between two exposure groups have been shown to introduce bias when time to a specific biomarker level is used as a surrogate outcome
Author | Journal | Outcome | CD4+ count | Description of how time-updated CD4+ counts were determined. |
Dunn |
JID | AIDS or death | exposure | Follow-up time from the time that each measurement was obtained was censored at the date of the next measurement. |
Guiguet |
Open AIDS J | AIDS or death | exposure | CD4+ counts were modeled using linear interpolation between two measurements. |
Lawn |
AIDS | Death | exposure | Person time was divided into intervals each of which was defined by the CD4+ count measurement at the start of the interval. |
Lawn |
AIDS | Tuberculosis | exposure | Person-time was subdivided into 4-month intervals for analysis. Each interval was defined by theCD4 cell count measurement at the start of the interval. |
Reekie |
Cancer | non-AIDS-defining malignancies | exposure | |
d'Arminio Monforte |
AIDS | death from malignancies | exposure | Each person's follow-up was divided into a series of consecutive 1-months periods, and the individual's status (most recent CD4+ count) was determined. |
Lodi |
J Natl Cancer Inst | Kaposi sarcoma | exposure | |
Engels |
JAIDS | Non-Hodgkin Lymphoma | exposure | We considered the most recent laboratory result “current” until the next measurement. |
Crum-Cianflone |
Arch Intern Med | Cutaneous malignancy | exposure | |
Guiguet |
Lancet Oncology | Malignancies | exposure | Follow-up was divided into consecutive 1-month periods, and time-varying covariables were updated at the beginning of every month. The CD4+ count was linearly interpolated unless ART was started between 2 measurements. |
Podlekareva |
Sand J Infec Dis | Fungal infections | exposure | |
Prosperi |
CID | Malignancies | exposure | |
Seyler |
AIDS Res Human Retroviruses | Severe morbidity | exposure | |
Sogaard |
PLoS one | Death from pneumonia | confounder | CD4+ counts were estimated between measurements by carrying forward the value from the most recent measurement |
Walker |
Lancet | Effect of Co-trimoxazole | confounder | |
Crum-Cianflone |
AIDS | Malignancies | exposure | |
Phillips |
AIDS | Death | exposure | Person time was counted from the time of each qualifying CD4+ count until the next CD4+ count. |
Beaudrap |
BMC Infect Dis | AIDS defining illness | exposure | |
Mocroft |
AIDS | Clinical disease progression | exposure | |
Bohlius |
Antivir Ther | Non-Hodgkin Lymphoma | exposure | |
Bruyand |
CID | Malignancies | exposure | We assumed that the value of the measurement reported at a given follow-up visit remained stable until the next follow-up visit |
We aimed to assess how different methods of dealing with time points influence effect estimates and rates using data from a clinical ART cohort with frequent measurements. We used the two methods most frequently used in the literature and investigated the effect of a third method assuming that the CD4+ count remains constant from the midpoint of the preceding interval until the midpoint of the subsequent interval.
The clinical ART cohort used for this study was based in Cape Town, South Africa and CD4+ counts were measured monthly for the first 3 months and 3 monthly thereafter. We also investigated the direction of bias using a simulated dataset.
Data collected in a peri-urban township in the greater area of Cape Town as part of the CIPRA-SA trial were used for this analysis
CD4+ counts were measured at weeks −4, 0, 4, 8, 12 (relative to the start of ART) and then every 12 weeks. Incident TB was used as the outcome of interest. Start and end of TB treatment were determined by merging the ART register with the electronic TB register on first name, surname, medical record number, date of birth, truncation of names and switching of first name and surname. This method was validated by clinical folder review in a similar dataset of 585 patients from a different study and revealed 96.1% sensitivity and 97.4% specificity. All identifiers were removed from the data after merging.
Individuals who did not live in the study community and individuals who were on TB treatment at ART initiation and died or were lost to follow-up before they completed treatment were excluded from the analysis.
The exposure was time-updated CD4+count and the outcome was incident TB defined as starting TB treatment. Person-time accrued from ART initiation to the date of TB disease, death, becoming lost to follow-up or the 31st December 2008 was calculated. Individuals who were on TB treatment at time of ART initiation were only included in the analysis after they had completed TB treatment. Individuals who developed incident TB were re-included in the analysis after completing TB treatment. Individuals only contributed time while they were on ART and person-time while defaulting care was excluded from the analysis, as neither the exposure (CD4+ count) not the outcome (TB) was known for these periods.
The data were analyzed in three different ways: the first analysis assumed that the CD4+ count changed at the date when the blood sample for CD4+ count measurement was drawn (
In the patient shown, we actually observed 11 CD4+ cell counts over the two years (grey line). We have illustrated what would have been modeled if only the results at 6 month intervals (black diamonds) had been available. Dotted and dashed lines (black) are the CD4+ counts assumed by the three different methods: data of measurement (A), midpoint (B) and linear interpolation (C).
A dataset including baseline CD4+ counts and 6-monthly CD4+ counts only was generated. From this dataset 15% of the follow-up CD4+ counts were randomly selected and removed to simulate the reality of missing data in clinical cohorts. A total of 100 datasets with 15% randomly missing follow-up CD4+ counts were generated.
The effect estimates and person-time using the newly generated dataset with 6-monthly CD4+ counts and different methods to estimate time-point of change were compared with results obtained when analysing the dataset using all available CD4+ counts (gold standard dataset). The gold standard dataset included CD4+ counts measured on a monthly bases from 0–3 months on ART, followed by 3-monthly CD4+ counts until death, loss-to-follow up, transfer out or censoring.
Months | All available CD4+ counts | 6 monthly CD4+ counts only | ||
Date of measurement | Midpoint | Linear interpolation | ||
0 | 191.5 (109–256) | 191.5 (109–256) | 191.5 (109–256) | 191.5 (109–256) |
1 | 265 (185.5–365.5) | 191.5 (109–256) | 191.5 (109–256) | 191.5 (109–256) |
2 | 296 (198–381) | 191.5 (109–256) | 191.5 (109–256) | 191.5 (109–256) |
3 | 291.5 (198–380) | 191.5 (109–256) | 307 (213.5–432.5) | 248 (158–324) |
6 | 307 (213.5–432.5) | 307 (213.5–432.5) | 307 (213.5–432.5) | 307 (213.5–432.5) |
9 | 313.5 (213.5–432.5) | 307 (213.5–432.5) | 333 (236–4447) | 318 (222–404) |
12 | 333 (236–4447) | 333 (236–4447) | 333 (236–4447) | 333 (236–4447) |
All analyses were carried out using Stata version 11.0 (Stata Corp. LP, College Station, TX, United States of America). The association between time-updated CD4+ count and TB was explored describing the rate of incident TB and using crude Kaplan-Meier curves. Cox proportional hazard regression was used to model the relationship between time-updated CD4+ count and TB. Hazard proportionality was assessed by analysis of scaled Schoenfeld residuals.
Events, person-time, rates, hazard ratios and standard errors were determined for the 100 datasets with 15% randomly missing follow-up data. The overall estimates were calculated according to the combination rules described by Rubin
Simulated CD4+ count data by time since treatment initiation and baseline CD4+ strata,
The areas under the CD4+ curve (AUC) were calculated using date of measurement, midpoint or linear interpolation methods with either 6 monthly or 3 monthly measurements. The AUC measures CD4 exposure. It is derived from the actual CD4+ values and the time spent with these values. Rates were calculated assuming constant rates within CD4+ count strata using TB rate estimates from published literature
All patients in the CIPRA-SA trial signed informed consent forms. The trial was approved by the University of Cape Town Ethics Committee and Partners Human Subjects Institutional Review Board. The London School of Hygiene and Tropical Medicine Ethics Committee and the University of Cape Town Ethics Committee and Partners Human Subjects Institutional Review Board gave approval for the analysis of the anonymised data.
Overall TB incidence was 4.9/100 person–years (PY) (95% confidence interval (CI) 3.6–6.8). TB incidence rates were 14.7 in the lowest CD4+ count stratum (≤200 cells/uL), 3.1 in the middle CD4+ count stratum (201–350 cells/uL) and 2.9 in the highest CD4+ count stratum (>350 cells/uL) when using all available CD4+ counts and performing a date of measurement analysis (
CD4+ strata (cells/uL) | Date of measurement analysis | Midpoint analysis | Linear interpolation analysis | |||||||||
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Events | PY | Rate | HR | Events | PY | Rate | HR | Not performed |
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≤200 | 19 | 128.9 | 14.7 | 1 | 19 | 119.0 | 16.0 | 1 | ||||
201–350 | 8 | 261.2 | 3.1 | 0.26 (0.11–0.61) | 8 | 255.4 | 3.1 | 0.25 (0.11–0.55) | ||||
>350 | 11 | 378.7 | 2.9 | 0.34 (0.15–0.75) | 11 | 394.5 | 2.8 | 0.29 (0.13–0.65) | ||||
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Events | PY | Rate | HR | Events | PY | Rate | HR | Events | PY | Rate | HR | |
≤200 | 22 | 176.6 | 12.5 | 1 | 18 | 140.2 | 12.8 | 1 | 20 | 152.1 | 13.2 | 1 |
201–350 | 10 | 256.4 | 3.9 | 0.41 (0.19–0.88) | 13 | 246.2 | 5.3 | 0.52 (0.25–1.08) | 12 | 261.9 | 4.6 | 0.45 (0.22–0.95) |
>350 | 6 | 335.7 | 1.8 | 0.25 (0.06–0.66) | 7 | 382.3 | 1.8 | 0.24 (0.09–0.62) | 6 | 354.7 | 1.7 | 0.22 (0.08–0.60) |
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Events | PY | Rate | HR | Events | PY | Rate | HR | Events | PY | Rate | HR | |
≤200 | 16.1 | 184.7 | 8.7 | 1 | 18.7 | 145.9 | 12.8 | 1 | 16.1 | 158.6 | 10.2 | 1 |
201–350 | 14.5 | 255.8 | 5.7 | 0.86 (0.42–1.77) | 12.7 | 245.9 | 5.2 | 0.51 (0.24–1.05) | 14.5 | 262.9 | 5.5 | 0.73 (0.35–1.510 |
>350 | 7.4 | 326.2 | 2.3 | 0.49 (0.19–1.25) | 6.6 | 374.5 | 1.8 | 0.23 (0.09–0.59) | 7.4 | 344.8 | 2.1 | 0.40 (0.15–1.02) |
*Linear interpolation analysis was not performed for the analysis using all available CD4+ counts, as the result was not expected to differ greatly compared to the date of measurement and midpoint analysis.
TB incidence rates and hazard ratios (HRs) were different when using a dataset with 6 monthly CD4+ counts as compared to analysis using all available CD4+ counts (
Analyses using a dataset with 6 monthly CD4+ counts and 15% randomly missing follow-up CD4+ counts revealed more extreme variations in rates, but with the same pattern of underestimation at low and high counts, and overestimation at moderate counts (
The midpoint analysis estimated the AUC most accurately for cohorts with low (25–50 cell/uL), high (151–200 cells/uL) and mixed baseline CD4+ counts (
Baseline CD4+ count of the cohort | Time | Cumulative area under the CD4+ count curve | ||||
True | Date of measurement method 6 monthly CD4+ counts | Date of measurement method 3 monthly CD4+ counts | Linear interpolation method 6 monthly CD4+ counts | Midpoint method 6 monthly CD4 counts | ||
25–50 cells/uL | 1 year | 145 | 99 | 123 | 120 | 142 |
5 years | 1348 | 1272 | 1311 | 1307 | 1342 | |
51–100 cells/uL | 1 year | 180 | 138 | 160 | 157 | 177 |
5 years | 1435 | 1368 | 1403 | 1399 | 1430 | |
101–150 cells/uL | 1 year | 228 | 186 | 208 | 205 | 225 |
5 years | 1662 | 1597 | 1631 | 1627 | 1657 | |
151–200 cells/uL | 1 year | 282 | 238 | 261 | 258 | 278 |
5 years | 1862 | 1801 | 1833 | 1829 | 1856 | |
201–300 cells/uL | 1 year | 345 | 305 | 326 | 323 | 342 |
5 years | 2180 | 2121 | 2152 | 2148 | 2274 | |
Mixed | 1 year | 237 | 194 | 216 | 213 | 233 |
5 years | 1704 | 1639 | 1673 | 1669 | 1699 |
Both the date of measurement and midpoint analysis underestimated TB rates for low CD4+ count strata (<200 cell/uL). Rates were less accurately estimated using the date of measurement analysis compared to the midpoint analysis (
CD4+ strata | True rates | Cohort with baseline CD4+ count 25–50 cells/uL | Cohort with baseline CD4+ count 51–100 cells/uL | Cohort with baseline CD4+ count 151–200 cells/uL | Mixed cohort | ||||
Date of measurement method | Midpoint method | Date of measurement method | Midpoint method | Date of measurement method | Midpoint method | Date of measurement method | Midpoint method | ||
≤50 | 21.7 | 11.25 | 13.2 | -- | -- | -- | -- | -- | -- |
51–100 | 12.8 | -- | -- | 9.69 | 10.12 | -- | -- | -- | -- |
101–200 | 9.27 | 6.65 | 9.27 | 6.24 | 8.13 | 5.93 | 6.39 | 7.38 | 9.27 |
201–300 | 5.48 | 5.42 | 5.73 | 5.39 | 5.48 | 4.75 | 5.18 | 5.48 | 5.48 |
301–400 | 4.61 | 4.61 | 4.61 | 4.61 | 4.65 | 4.51 | 4.59 | 4.61 | 4.66 |
401–500 | 4.23 | -- | -- | -- | -- | 4.23 | 4.23 | -- | -- |
This study shows that the time-point when a CD4+ count is assumed to change influences incidence rates of clinical events during ART and effect estimates in time-updated CD4+ count analysis. The analysis using modeled CD4+ count data showed that the midpoint method gives a better approximation of person-time spent at low CD4+ counts compared to the date of measurement method. The choice of time-point when a CD4+ count is assumed to change had the greatest impact in cohorts with low baseline CD4+ counts and during the first year after ART initiation. While the absolute difference in effect estimates was small when analyzing data with frequent measurements, the choice of time-point was important in data with less frequent and missing measurements. Thus the frequency of measurement and the method used to determine the time-point of change in CD4+ count need to be taken into account when comparing effect estimates from different studies. However, most studies performing survival or Cox regression analysis with time-updated CD4+ count as exposure or confounder variable fail to describe how the time-point of change in CD4+ count was determined
The rate of change in CD4+ count is highest in the first months after initiation of ART
Our study confirms and extends the findings of a study from Côte d’Ivoire
Most analyses investigating the effect of time-updated CD4+ counts on clinical outcomes use CD4+ count categories
Analysis using time-updated CD4+ counts as exposure or confounder should consider using the midpoint method as a simple way to reduce bias. In addition authors should be encouraged to clearly describe the assumption underlying the time-point of change in CD4+ count and researchers conducting meta-analyses should contact authors to determine the method used.