The Secret of Immortal Time Bias in Epidemiologic Studies
Salimah Z. Shariff*,,
Meaghan S. Cuerden*,
Arsh K. Jain*, and
Amit X. Garg*,
* Division of Nephrology and Department of Epidemiology and Biostatistics, University of Western Ontario, London, Ontario, Canada
Correspondence: Dr. Amit X. Garg, Medicine & Epidemiology, University of Western Ontario, Kidney Clinical Research Unit, Room ELL-101, Westminster Tower, London Health Sciences Centre, 800 Commissioners Road East, London, Ontario N6A 4G5, Canada. Phone: 519-685-8502; Fax: 519-685-8072; E-mail: amit.garg{at}lhsc.on.ca
In the March 2007 issue of JASN, Hemmelgarn et al.1 reporteda 50% reduction in the risk for all-cause mortality for patientswho had chronic kidney disease (CKD) and attended multidisciplinarycare (MDC) clinics compared with those who received usual care.Their survival curves showed a clear divergence in rates ofdeath between the two groups in the first 6 mo of follow-up.We suggest that it is less plausible from a biologic perspectivethat use of MDC clinics immediately reduces the short-term riskfor death. Rather, much of the early observed effect may bedue to survivor treatment selection bias, also known as immortaltime bias. Here we consider this issue.
In the Hemmelgarn study, a retrospective cohort of 187 clinicpatients who were exposed to a MDC clinic were matched to 187non-MDC clinic control patients to examine the association betweenMDC and survival.1 Control subjects were chosen on the basisof propensity matching, whereby individuals in the control grouphad a similar likelihood of being referred to a MDC clinic asthose in the MDC clinic group. Figure 1 shows a schematic ofhow patients with CKD entered the cohort. All patients wererequired to have an outpatient serum creatinine test performedbetween July 1 and December 31, 2001. Patients in the MDC clinicgroup were also required to have attended a MDC clinic betweenJuly 1, 2001, and December 31, 2002.
Figure 1. Schematic of cohort entry. SCr, serum creatinine.
The primary analysis for the study was the association betweenMDC clinic visits and survival, modeled using a Cox regressionanalysis. Survival time was measured starting from each patient'sserum creatinine test date. In other words, the date of eachpatient's serum creatinine represented the date they enteredthe cohort, or time 0. Patients were followed until the endof the assessment (December 31, 2004) or death, whichever camefirst. A difference in survival between the two groups was illustratedusing Kaplan-Meier survival curves (Figure 2). In this analysis,censoring occurred only at the end of assessment; therefore,the curves essentially represent the proportion of patientswho were still alive at each time during follow-up. The curveswere step-like in shape, and a dip in the curve occurred whena patient in that group died.2 As can be seen from Figure 2,the curves diverged almost immediately, with the non-MDC cliniccurve dipping below the MDC clinic curve, signifying an increaseddeath rate for the non-MDC control group. The difference inthe proportion of individuals alive between the two groups steadilyincreased until about 1.5 yrs, after which point the rate ofdecline was similar between the groups. The difference in curveswas tested using a log-rank test and found to be highly significant(P = 0.008). The Cox model yielded a risk reduction of 50% with95% confidence limits ranging from 29 to 65%.
Figure 2. Kaplan-Meier survival curve, presented by Hemmelgarn et al.1
Is this result biologically plausible? From a mechanistic perspective,we suggest that it is less plausible that attending MDC clinicsconfers an immediate survival advantage over regular care forelderly patients with CKD. These clinics concentrate on bettereducation, lifestyle modification, and medical management overthat provided in routine care. Although better efforts at smokingcessation, weight management, dietary protein restriction, glycemiccontrol, renin-angiotensin blockade, BP lowering, and statinuse all could improve survival in this high-risk population,practical experience suggests that such a benefit would likelytake longer to manifest.3–6 It is also improbable thatbetter potassium control explains the large early survival benefit.
Much of the early observed beneficial effect may be due to survivortreatment selection bias,7 more recently described as immortaltime bias.8 First noted in 1885,9 the bias explains the suggestionthat Popes seem to live longer than artists10 or Oscar winnerslonger than nonwinners.11 In general, such individuals mustsurvive long enough to become Pope or to win Oscars, whereastheir peers have no minimum survival requirements.
Taking the methods used by Hemmelgarn et al.1 to enter MDC clinicpatients into the cohort, the MDC clinic visit could have occurredeither before or after the serum creatinine test (Figure 3).In cases in which the MDC clinic visit occurred after the creatininetest, we know that patients were alive to attend their MDC clinicvisit; otherwise, they would not have met inclusion criteriafor cohort entry. Such time between cohort entry and exposure,whereby a patient is guaranteed to be alive because of the waythey were entered into the cohort, is known as "immortal time."Unlike patients who were exposed to MDC clinics, patients inthe control group could have died in the immortal time window,contributing to a bias and early separation between the MDCclinic and non-MDC clinic survival curves (Figures 2 and 3).
Figure 3. Immortal time bias. Situation in which MDC clinic visit occurred after serum creatinine test. Exposed patient was guaranteed to be alive between the test date and the clinic visit, resulting in a period of "immortal time." Control patient died within the immortal time window, resulting in an immortal time bias.
To strengthen the assertion that immortal time is present, considerthe additional analysis performed by Hemmelgarn et al.,1 wherebyboth the serum creatinine test and the MDC clinic visit forthe exposed group had to occur in the 6 mo between July 1 andDecember 31, 2001. In this setting, the maximum immortal timewas 6 mo. The analysis showed a risk reduction of 31% (downfrom 50%) with the 95% confidence interval now spanning unity.This analysis reduces the MDC clinic sample from 187 individualsto 105 individuals. Thus, 82 patients must have visited a MDCclinic after the initial 6-mo window, suggesting that the primaryanalysis included at least 82 MDC clinic patients with immortaltime. The true impact of this bias would be best determinedby reexamination of the data.
How can one prevent or fix immortal time bias? We focus on twopossible methods to account for immortal time. These solutionseliminate it from the design or provide a fix at the time ofanalysis. Other ways of accounting for immortal time have alsobeen described.11,12
The first solution is matching. At the design stage, an extracriterion is added to the matching procedure; a non-MDC clinicpatient must be alive at the time when their matched patientattends the MDC clinic. In this situation, cohort entry becomesthe date of the MDC clinic visit, and any time between the serumcreatinine test and the MDC clinic visit is not counted foreither group.13
The other solution is to perform an analysis using time-dependentcovariates. A time-dependent covariate is a predictor whosevalue may change over time. Immortal time bias can be avoidedby acknowledging a change in exposure status using a time-dependentcovariate.14 For example, a MDC clinic patient would be consideredunexposed from the date of study entry until he or she visitsthe MDC clinic and exposed from that point forward. Many statisticalsoftware packages can incorporate time-dependent covariatesinto survival analysis.
Immortal time has been described in other fields but, to ourknowledge, never with a clear example in nephrology. In theirdiscussion, Hemmelgarn et al.1 clearly acknowledged the potentialfor bias in the manner by which patients were selected for theprimary analysis. Here we outline the issues more completely,providing a context for other studies that may not be appreciatedby some readers.
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