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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

Mean times for methods vs. mean times from IPD. Mean times for each of the methods: least squares, proposed method, and regression, versus the mean time estimated from IPD for 1,000 simulated trials of 100 patients. Decreasing hazard is modelled (a) without and (b) with extra censoring. Some points extend outside the displayed range.
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Figure 8: Mean times for methods vs. mean times from IPD. Mean times for each of the methods: least squares, proposed method, and regression, versus the mean time estimated from IPD for 1,000 simulated trials of 100 patients. Decreasing hazard is modelled (a) without and (b) with extra censoring. Some points extend outside the displayed range.

Mentions: As expected, the method of fitting to the IPD performs well. However, the proposed method is about as accurate, and gives similar estimates of the mean for each simulated trial (see Figure 8, where the estimated mean for each trial based on the IPD method is closer to the estimated mean based on the proposed method than the least squares or regression methods: mean difference between proposed method and IPD = - 2% compared to corresponding mean differences of 12% and 7% for the least squares and regression methods in the absence of extra censoring). The IPD method appears to be preferable to the proposed method only when considering the median of the mean times, particularly for smaller trials, when the hazard decreases over time and with additional censoring (Figures 5).


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

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

Mean times for methods vs. mean times from IPD. Mean times for each of the methods: least squares, proposed method, and regression, versus the mean time estimated from IPD for 1,000 simulated trials of 100 patients. Decreasing hazard is modelled (a) without and (b) with extra censoring. Some points extend outside the displayed range.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Mean times for methods vs. mean times from IPD. Mean times for each of the methods: least squares, proposed method, and regression, versus the mean time estimated from IPD for 1,000 simulated trials of 100 patients. Decreasing hazard is modelled (a) without and (b) with extra censoring. Some points extend outside the displayed range.
Mentions: As expected, the method of fitting to the IPD performs well. However, the proposed method is about as accurate, and gives similar estimates of the mean for each simulated trial (see Figure 8, where the estimated mean for each trial based on the IPD method is closer to the estimated mean based on the proposed method than the least squares or regression methods: mean difference between proposed method and IPD = - 2% compared to corresponding mean differences of 12% and 7% for the least squares and regression methods in the absence of extra censoring). The IPD method appears to be preferable to the proposed method only when considering the median of the mean times, particularly for smaller trials, when the hazard decreases over time and with additional censoring (Figures 5).

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