Limits...
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.

Show MeSH

Related in: MedlinePlus

Simulated actual versus expected numbers of events and censorships. (a) one typical example simulated trial with decreasing hazard, 500 patients, no extra censoring, and (b) another typical example simulated trial with increasing hazard, 500 patients, with extra censoring. In (a) the curves for numbers of events are almost concurrent.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3198983&req=5

Figure 3: Simulated actual versus expected numbers of events and censorships. (a) one typical example simulated trial with decreasing hazard, 500 patients, no extra censoring, and (b) another typical example simulated trial with increasing hazard, 500 patients, with extra censoring. In (a) the curves for numbers of events are almost concurrent.

Mentions: First, the proposed method accurately predicts the numbers of events and censorships in each time interval. The method is particularly accurate when there is no extra censoring (additional non-informative censoring was modelled at a constant hazard) and when the hazard decreases over time (Figure 3a), and least accurate when there is extra censoring and when the hazard increases over time (Figure 3b): the typical overestimation of the total number of events and censorships is 0% and 0% respectively for decreasing hazard, no extra censorship; 3% and -2% for decreasing hazard, with extra censorship; 1% and -0.5% for constant hazard, no extra censorship; 6% and -2% for constant hazard, with extra censorship; 2% and -0.5% for increasing hazard, no extra censorship; 7% and -0.5% for increasing hazard, with extra censorship. We believe that the accuracy of the estimated numbers of events and censorships increases with the total number of events: for the scenario in Figure 3a, there are typically approximately 265 events, and for the scenario in Figure 3b, typically 45 events. Later in this section, it is shown that any slight errors in the estimated number of events and censorships have very little impact on the accuracy of the curve fits.


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

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

Simulated actual versus expected numbers of events and censorships. (a) one typical example simulated trial with decreasing hazard, 500 patients, no extra censoring, and (b) another typical example simulated trial with increasing hazard, 500 patients, with extra censoring. In (a) the curves for numbers of events are almost concurrent.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Simulated actual versus expected numbers of events and censorships. (a) one typical example simulated trial with decreasing hazard, 500 patients, no extra censoring, and (b) another typical example simulated trial with increasing hazard, 500 patients, with extra censoring. In (a) the curves for numbers of events are almost concurrent.
Mentions: First, the proposed method accurately predicts the numbers of events and censorships in each time interval. The method is particularly accurate when there is no extra censoring (additional non-informative censoring was modelled at a constant hazard) and when the hazard decreases over time (Figure 3a), and least accurate when there is extra censoring and when the hazard increases over time (Figure 3b): the typical overestimation of the total number of events and censorships is 0% and 0% respectively for decreasing hazard, no extra censorship; 3% and -2% for decreasing hazard, with extra censorship; 1% and -0.5% for constant hazard, no extra censorship; 6% and -2% for constant hazard, with extra censorship; 2% and -0.5% for increasing hazard, no extra censorship; 7% and -0.5% for increasing hazard, with extra censorship. We believe that the accuracy of the estimated numbers of events and censorships increases with the total number of events: for the scenario in Figure 3a, there are typically approximately 265 events, and for the scenario in Figure 3b, typically 45 events. Later in this section, it is shown that any slight errors in the estimated number of events and censorships have very little impact on the accuracy of the curve fits.

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