Letters

Parametric survival models may be more accurate than Kaplan-Meier estimates

BMJ 2003; 326 doi: https://doi.org/10.1136/bmj.326.7393.822 (Published 12 April 2003) Cite this as: BMJ 2003;326:822
  1. Margaret May, statistician,
  2. Jonathan Sterne, reader in medical statistics and epidemiology,
  3. Matthias Egger, professor of epidemiology
  1. Department of Social Medicine, University of Bristol, Bristol BS6 2PR
  2. Department of Social and Preventive Medicine, University of Bern, Switzerland

    EDITOR—Lundin et al use Kaplan-Meier estimates of survival probabilities in their system for survival estimation in breast cancer (Finprog study, http://finprog.primed.info).1 They claim that researchers can obtain survival estimates based on actual data, rather than inferential estimates generated by a regression formula. However, any regression formula is based on actual data. More importantly, survival estimates from a regression model may be substantially more precise than Kaplan-Meier estimates when there are few patients in particular strata.

    We have modelled prognosis of HIV positive patients starting treatment by using data from the Antiretroviral Cohort Collaboration (http://www.art-cohort-collaboration.org).2 Patients are allocated to 80 strata by using five prognostic factors: CD4 cell count, viral load, AIDS at start of treatment, age, and transmission group. In some strata few events were noted, and no deaths at all, so that estimation of survival probabilities by using Kaplan-Meier curves is impossible. In regression modelling, estimates for strata with few or no events borrow strength from the pattern of events across all categories of the prognostic variables.

    In each graph in our figure survival estimates from the parametric model are contrasted with those calculated by using the Kaplan-Meier method. The two curves agree quite closely in (a) and (b), but the confidence interval for the parametric model is narrower. In (c) the estimates do not agree; moreover, the Kaplan-Meier curve peters out by two years due to lack of follow up, and the confidence interval is too broad to be a useful predictor of survival at one year, ranging from 5-95%. Figure (d) shows a similar sized group to (c) but by chance there were no events in (d) despite having a worse risk profile (lower CD4), giving a completely misleading prediction of 100% survival.

    The Kaplan-Meier estimates are less precise than parametric survival model estimates and may also be very inaccurate.

    Figure1

    Survival curves predicted from parametric model with corresponding Kaplan-Meier estimates (with 95% confidence intervals) for different groups of patients who were injecting drug users, had AIDS at start of treatment, and had log viral load >5

    Footnotes

    • Competing interests None declared.

    References

    1. 1.
    2. 2.
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