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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

Survivor functions for three simulated distributions. Each distribution is parameterized by a Weibull distribution with mean time to event of 10: decreasing hazard over time (γ = 0.6, λ = 0.321), constant hazard (γ = 1, λ = 0.1), and increasing hazard (γ = 2, λ = 0.0079).
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Figure 2: Survivor functions for three simulated distributions. Each distribution is parameterized by a Weibull distribution with mean time to event of 10: decreasing hazard over time (γ = 0.6, λ = 0.321), constant hazard (γ = 1, λ = 0.1), and increasing hazard (γ = 2, λ = 0.0079).

Mentions: The accuracy of the proposed method was tested by simulation. Survival data were generated by simulating multiple independent trials by the Monte Carlo method in the statistics package R. Patient recruitment was modelled at a constant rate over a time period of 10 units, without loss of generality. This was also assumed to be the calendar time at maximum follow up. In this way, follow up varied from 0 to 10 time units. Patient survival was assumed to follow a Weibull distribution, S(t) = exp(-λtγ), and three shapes were independently modelled which were deemed to cover the great majority of cases experienced in practice (see Figure 2 for a plot of the survivor functions): (a): decreasing hazard over time (γ = 0.6, λ = 0.321) (e.g. patients recovering from surgery), (b) constant hazard (i.e. exponential distribution) (e.g. healthy people), (γ = 1, λ = 0.1), and (c) increasing hazard (γ = 2, λ = 0.0079) (e.g. leukaemia patients). The mean time to event was set to 10 in all three cases, corresponding to the maximum follow up time, which is typical for published survival data. The total number of patients was independently set at 100 and 500, as this covers the typical range from trials.


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

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

Survivor functions for three simulated distributions. Each distribution is parameterized by a Weibull distribution with mean time to event of 10: decreasing hazard over time (γ = 0.6, λ = 0.321), constant hazard (γ = 1, λ = 0.1), and increasing hazard (γ = 2, λ = 0.0079).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Survivor functions for three simulated distributions. Each distribution is parameterized by a Weibull distribution with mean time to event of 10: decreasing hazard over time (γ = 0.6, λ = 0.321), constant hazard (γ = 1, λ = 0.1), and increasing hazard (γ = 2, λ = 0.0079).
Mentions: The accuracy of the proposed method was tested by simulation. Survival data were generated by simulating multiple independent trials by the Monte Carlo method in the statistics package R. Patient recruitment was modelled at a constant rate over a time period of 10 units, without loss of generality. This was also assumed to be the calendar time at maximum follow up. In this way, follow up varied from 0 to 10 time units. Patient survival was assumed to follow a Weibull distribution, S(t) = exp(-λtγ), and three shapes were independently modelled which were deemed to cover the great majority of cases experienced in practice (see Figure 2 for a plot of the survivor functions): (a): decreasing hazard over time (γ = 0.6, λ = 0.321) (e.g. patients recovering from surgery), (b) constant hazard (i.e. exponential distribution) (e.g. healthy people), (γ = 1, λ = 0.1), and (c) increasing hazard (γ = 2, λ = 0.0079) (e.g. leukaemia patients). The mean time to event was set to 10 in all three cases, corresponding to the maximum follow up time, which is typical for published survival data. The total number of patients was independently set at 100 and 500, as this covers the typical range from trials.

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