Sir,
Dr Dulku1 criticised the Kaplan–Meier analysis that Drs Anand and Wechsler2 used to assess failure and complications after deep sclerectomy with mitomycin C in eyes with failed glaucoma surgery, pseudophakia, or both. He pointed out that these events had occurred at unknown times before the visit at which they were recorded, making the survival curves too good, and recommended that interval censoring3 adjust for this bias. However, competing risk bias should additionally be considered.
Drs Anand and Wechsler operated on 82 patients,2 who were on average 76 years old. A total of 20 patients died during the over 5-year-long observation period.2 The authors do not mention how they dealt statistically with patients who died.2 We dare expect they were censored just like the patients who became too ill to attend their clinic.2 However, a fundamental difference exists between these two groups: only the latter group of patients remained at risk after censoring.
After censoring, the Kaplan–Meier curve will drop proportionately more with any subsequent event as compared with what it would have dropped had censoring not taken place. A key assumption is that censoring is independent of the risk of experiencing the event of interest, that is, the risk is equal before and after censoring.4 Clearly, this assumption is not met if any subjects die: the survival curve will become too pessimistic. Death is a competing risk event, which should be dealt with methods other than censoring,5, 6 such as cumulative incidence analysis,7 found both in the R package mentioned and in a number of commercial packages.
The paper of Drs Zhang and Sun,3 which Dr Dulku1 cites, briefly discusses interval censoring in face of competing risks. However, commercial software for this purpose is not yet marketed. Formal adjustment is available either for interval censoring1, 3, 6 or for competing risks.5, 7, 8, 9, 10 To address simultaneously both biases, one reasonable approach at present is to undertake cumulative incidence analysis and to plot two curves, the first modelling the event of interest as occurring when it was recorded, and the second assigning it to the immediately preceding visit. The former curve will exaggerate the probability of success and the latter the probability of failure. Alternatively, a cumulative incidence curve based on the midpoint of the review interval may be used as an approximation of interval censoring.9
Interval censoring and competing risks bias in survival analysis are ill known to authors, reviewers, and readers, risking misinterpretation of study results.
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Kivelä, T., Kujala, E., Forsman, E. et al. Interval censoring and competing risks when reporting results of glaucoma surgery. Eye 28, 362–363 (2014). https://doi.org/10.1038/eye.2013.288
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DOI: https://doi.org/10.1038/eye.2013.288
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