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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

Simulation results for variations on proposed method. The mean, over 1,000 simulations, of the mean time and the error in the mean time for trials with (a) 100 and (b) 500 patients for the proposed method and variations on the proposed method. The population mean time is 10, as indicated by the horizontal lines. 1,000 simulations are sufficiently large that the 95% error bars (not shown) are virtually indistinguishable from the mean/median values in Figures 4, 5 and 6.
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Figure 4: Simulation results for variations on proposed method. The mean, over 1,000 simulations, of the mean time and the error in the mean time for trials with (a) 100 and (b) 500 patients for the proposed method and variations on the proposed method. The population mean time is 10, as indicated by the horizontal lines. 1,000 simulations are sufficiently large that the 95% error bars (not shown) are virtually indistinguishable from the mean/median values in Figures 4, 5 and 6.

Mentions: Second, we consider the performance of the proposed method in isolation (black bars in Figure 4). There is virtually no bias in estimates of the mean time (the difference between the mean over all simulations of the mean times and the population mean of 10) assuming trials of 100 and 500 patients. This is consistent with the finding that the method accurately predicts the total number of events and censorships. Estimates of the mean error in the mean time (mean absolute error) are displayed because this indicates the approximate expected error in resulting estimates of cost-effectiveness due to uncertainty in the survival distribution. As expected, the mean error is greater with additional censoring and with 100 (Figure 4a) compared to 500 patients (Figure 4b).


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

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

Simulation results for variations on proposed method. The mean, over 1,000 simulations, of the mean time and the error in the mean time for trials with (a) 100 and (b) 500 patients for the proposed method and variations on the proposed method. The population mean time is 10, as indicated by the horizontal lines. 1,000 simulations are sufficiently large that the 95% error bars (not shown) are virtually indistinguishable from the mean/median values in Figures 4, 5 and 6.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Simulation results for variations on proposed method. The mean, over 1,000 simulations, of the mean time and the error in the mean time for trials with (a) 100 and (b) 500 patients for the proposed method and variations on the proposed method. The population mean time is 10, as indicated by the horizontal lines. 1,000 simulations are sufficiently large that the 95% error bars (not shown) are virtually indistinguishable from the mean/median values in Figures 4, 5 and 6.
Mentions: Second, we consider the performance of the proposed method in isolation (black bars in Figure 4). There is virtually no bias in estimates of the mean time (the difference between the mean over all simulations of the mean times and the population mean of 10) assuming trials of 100 and 500 patients. This is consistent with the finding that the method accurately predicts the total number of events and censorships. Estimates of the mean error in the mean time (mean absolute error) are displayed because this indicates the approximate expected error in resulting estimates of cost-effectiveness due to uncertainty in the survival distribution. As expected, the mean error is greater with additional censoring and with 100 (Figure 4a) compared to 500 patients (Figure 4b).

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