Sir,
Kivelä et al1 raise an important point regarding survival analysis in glaucoma surgery in that bias is caused when the competing risk of death is not taken into account. A glaucoma operation that does not fail in the patient’s lifetime can be considered a complete success (as long as the patient does not die before they could be expected to benefit from the procedure). The current implementation of survival analysis in glaucoma surgery does not account for this by considering such patients still at risk of failure even after they have died.
Kivelä et al1 note that current statistical packages do not yet allow for the routine analysis of competing risks data subject to interval censoring. While methods have been devised to deal with such data,2, 3 such techniques are considerably more difficult to apply than standard Kaplan–Meier survival analysis.
As the proportion of deaths in the population decreases, the effect of the competing risk of death will reduce. Studies with shorter follow-up are less likely to encounter bias than those with longer follow-up. However, death is a common outcome in studies with longer follow-up. The 20-year outcomes of trabeculectomy have been reported4 and in this study, 21% of patients were censored due to death. In the TVT study,5 13% of patients had died by 5 years. Surgical failure is, therefore, likely to have been overestimated in these studies.
Competing risks analysis in glaucoma studies could be extended to competing risks other than death. For trabeculectomy, an important competing risk is the requirement for needling. Current studies usually ignore needling as an event;5 competing risks analysis would provide a mechanism whereby this could be taken into account.
Given the above, it may be necessary to rethink the application of survival analysis to glaucoma surgery so that we can make more accurate predictions of survival and better use of the available data. A more sophisticated approach will ultimately allow us to more accurately describe the likely postoperative course when counseling patients regarding glaucoma surgery.
References
Kivelä T, Kujala E, Forsman E, Vesti E . Interval censoring and competing risks when reporting results of glaucoma surgery. Eye 2014; 28 (3): 362–363.
Hudgens MG, Satten GA, Longini IM Jr . Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation. Biometrics 2001; 57: 74–80.
Barrett JK, Siannis F, Farewell VT . A semi-competing risks model for data with interval-censoring and informative observation: an application to the MRC cognitive function and ageing study. Stat Med 2011; 30: 1–10.
Landers J, Martin K, Sarkies N, Bourne R, Watson P . A twenty-year follow-up study of trabeculectomy: risk factors and outcomes. Ophthalmology 2012; 119: 694–702.
Gedde SJ, Schiffman JC, Feuer WJ, Herndon LW, Brandt JD, Budenz DL . Treatment outcomes in the Tube Versus Trabeculectomy (TVT) study after five years of follow-up. Am J Ophthalmol 2012; 153 (5): 789–803 e2.
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Dulku, S. Reply to Kivelä et al. Eye 28, 363–364 (2014). https://doi.org/10.1038/eye.2013.291
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DOI: https://doi.org/10.1038/eye.2013.291