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Improved curve fits to summary survival data: application to economic evaluation of health technologies.

Hoyle MW, Henley W - BMC Med Res Methodol (2011)

Bottom Line: Mean costs and quality-adjusted-life-years are central to the cost-effectiveness of health technologies.They are often calculated from time to event curves such as for overall survival and progression-free survival.However, such data are usually not available to independent researchers.

View Article: PubMed Central - HTML - PubMed

Affiliation: Peninsula College of Medicine and Dentistry, Veysey Building, Salmon Pool Lane, Exeter, EX2 4SG, UK. martin.hoyle@pms.ac.uk

ABSTRACT

Background: Mean costs and quality-adjusted-life-years are central to the cost-effectiveness of health technologies. They are often calculated from time to event curves such as for overall survival and progression-free survival. Ideally, estimates should be obtained from fitting an appropriate parametric model to individual patient data. However, such data are usually not available to independent researchers. Instead, it is common to fit curves to summary Kaplan-Meier graphs, either by regression or by least squares. Here, a more accurate method of fitting survival curves to summary survival data is described.

Methods: First, the underlying individual patient data are estimated from the numbers of patients at risk (or other published information) and from the Kaplan-Meier graph. The survival curve can then be fit by maximum likelihood estimation or other suitable approach applied to the estimated individual patient data. The accuracy of the proposed method was compared against that of the regression and least squares methods and the use of the actual individual patient data by simulating the survival of patients in many thousands of trials. The cost-effectiveness of sunitinib versus interferon-alpha for metastatic renal cell carcinoma, as recently calculated for NICE in the UK, is reassessed under several methods, including the proposed method.

Results: Simulation shows that the proposed method gives more accurate curve fits than the traditional methods under realistic scenarios. Furthermore, the proposed method achieves similar bias and mean square error when estimating the mean survival time to that achieved by analysis of the complete underlying individual patient data. The proposed method also naturally yields estimates of the uncertainty in curve fits, which are not available using the traditional methods. The cost-effectiveness of sunitinib versus interferon-alpha is substantially altered when the proposed method is used.

Conclusions: The method is recommended for cost-effectiveness analysis when only summary survival data are available. An easy-to-use Excel spreadsheet to implement the method is provided.

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Related in: MedlinePlus

Curve fits to progression free survival for (a) sunitinib, (b) interferon-alpha for renal cell carcinoma. Kaplan-Meier graphs are represented by continuous stepped lines joined by dots, curves fit by the proposed method are shown by thick continuous lines, fits used in the original economic evaluation by thin continuous lines, and curves fit by least squares by dotted lines. In (b) the last two curves are almost coincident.
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Figure 10: Curve fits to progression free survival for (a) sunitinib, (b) interferon-alpha for renal cell carcinoma. Kaplan-Meier graphs are represented by continuous stepped lines joined by dots, curves fit by the proposed method are shown by thick continuous lines, fits used in the original economic evaluation by thin continuous lines, and curves fit by least squares by dotted lines. In (b) the last two curves are almost coincident.

Mentions: (a) In one of the sensitivity analyses of the original economic evaluation, a Weibull curve was fit to the Kaplan-Meier graph of progression-free survival for interferon-alpha from the Motzer et al. [14] randomised controlled trial of sunitinib versus interferon-alpha, by regressing ln(-ln(S(t)) against ln(t). Survival probabilities were taken at monthly intervals from the Kaplan-Meier graph. This yielded Weibull parameters λ = 0.16 and γ = 0.88 (Figure 10). Next, λ for sunitinib was calculated as λ for interferon-alpha multiplied by the hazard ratio of 0.42, reported in the trial [14]. γ for sunitinib was set equal to γ for interferon-alpha (Figure 10). This gave a mean progression-free survival of 8.6 months for interferon-alpha and 23.0 months for sunitinib, and an ICER of £62,000 per quality-adjusted life year (QALY) [2].


Improved curve fits to summary survival data: application to economic evaluation of health technologies.

Hoyle MW, Henley W - BMC Med Res Methodol (2011)

Curve fits to progression free survival for (a) sunitinib, (b) interferon-alpha for renal cell carcinoma. Kaplan-Meier graphs are represented by continuous stepped lines joined by dots, curves fit by the proposed method are shown by thick continuous lines, fits used in the original economic evaluation by thin continuous lines, and curves fit by least squares by dotted lines. In (b) the last two curves are almost coincident.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3198983&req=5

Figure 10: Curve fits to progression free survival for (a) sunitinib, (b) interferon-alpha for renal cell carcinoma. Kaplan-Meier graphs are represented by continuous stepped lines joined by dots, curves fit by the proposed method are shown by thick continuous lines, fits used in the original economic evaluation by thin continuous lines, and curves fit by least squares by dotted lines. In (b) the last two curves are almost coincident.
Mentions: (a) In one of the sensitivity analyses of the original economic evaluation, a Weibull curve was fit to the Kaplan-Meier graph of progression-free survival for interferon-alpha from the Motzer et al. [14] randomised controlled trial of sunitinib versus interferon-alpha, by regressing ln(-ln(S(t)) against ln(t). Survival probabilities were taken at monthly intervals from the Kaplan-Meier graph. This yielded Weibull parameters λ = 0.16 and γ = 0.88 (Figure 10). Next, λ for sunitinib was calculated as λ for interferon-alpha multiplied by the hazard ratio of 0.42, reported in the trial [14]. γ for sunitinib was set equal to γ for interferon-alpha (Figure 10). This gave a mean progression-free survival of 8.6 months for interferon-alpha and 23.0 months for sunitinib, and an ICER of £62,000 per quality-adjusted life year (QALY) [2].

Bottom Line: Mean costs and quality-adjusted-life-years are central to the cost-effectiveness of health technologies.They are often calculated from time to event curves such as for overall survival and progression-free survival.However, such data are usually not available to independent researchers.

View Article: PubMed Central - HTML - PubMed

Affiliation: Peninsula College of Medicine and Dentistry, Veysey Building, Salmon Pool Lane, Exeter, EX2 4SG, UK. martin.hoyle@pms.ac.uk

ABSTRACT

Background: Mean costs and quality-adjusted-life-years are central to the cost-effectiveness of health technologies. They are often calculated from time to event curves such as for overall survival and progression-free survival. Ideally, estimates should be obtained from fitting an appropriate parametric model to individual patient data. However, such data are usually not available to independent researchers. Instead, it is common to fit curves to summary Kaplan-Meier graphs, either by regression or by least squares. Here, a more accurate method of fitting survival curves to summary survival data is described.

Methods: First, the underlying individual patient data are estimated from the numbers of patients at risk (or other published information) and from the Kaplan-Meier graph. The survival curve can then be fit by maximum likelihood estimation or other suitable approach applied to the estimated individual patient data. The accuracy of the proposed method was compared against that of the regression and least squares methods and the use of the actual individual patient data by simulating the survival of patients in many thousands of trials. The cost-effectiveness of sunitinib versus interferon-alpha for metastatic renal cell carcinoma, as recently calculated for NICE in the UK, is reassessed under several methods, including the proposed method.

Results: Simulation shows that the proposed method gives more accurate curve fits than the traditional methods under realistic scenarios. Furthermore, the proposed method achieves similar bias and mean square error when estimating the mean survival time to that achieved by analysis of the complete underlying individual patient data. The proposed method also naturally yields estimates of the uncertainty in curve fits, which are not available using the traditional methods. The cost-effectiveness of sunitinib versus interferon-alpha is substantially altered when the proposed method is used.

Conclusions: The method is recommended for cost-effectiveness analysis when only summary survival data are available. An easy-to-use Excel spreadsheet to implement the method is provided.

Show MeSH
Related in: MedlinePlus