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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

Excel spreadsheet to estimate the numbers of patients with events and censorships per time interval. The user needs only enter the survival probabilities from the Kaplan-Meier curve and the number of patients at risk. The R code to fit survival curves is also given in the spreadsheet.
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Figure 1: Excel spreadsheet to estimate the numbers of patients with events and censorships per time interval. The user needs only enter the survival probabilities from the Kaplan-Meier curve and the number of patients at risk. The R code to fit survival curves is also given in the spreadsheet.

Mentions: In Step A, the method estimates the underlying IPD. This is coded in an easy-to-use Microsoft Excel spreadsheet, which is available from several sources (see Conclusions) (Figure 1). In Step B, the fitted curve is estimated by maximisation of the likelihood function for the IPD. The relevant R statistics code to estimate the survival curves is also available in the spreadsheet.


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

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

Excel spreadsheet to estimate the numbers of patients with events and censorships per time interval. The user needs only enter the survival probabilities from the Kaplan-Meier curve and the number of patients at risk. The R code to fit survival curves is also given in the spreadsheet.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Excel spreadsheet to estimate the numbers of patients with events and censorships per time interval. The user needs only enter the survival probabilities from the Kaplan-Meier curve and the number of patients at risk. The R code to fit survival curves is also given in the spreadsheet.
Mentions: In Step A, the method estimates the underlying IPD. This is coded in an easy-to-use Microsoft Excel spreadsheet, which is available from several sources (see Conclusions) (Figure 1). In Step B, the fitted curve is estimated by maximisation of the likelihood function for the IPD. The relevant R statistics code to estimate the survival curves is also available in the spreadsheet.

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