Signature
QALY = u_PF * A_PF + u_PD * (A_OS - A_PF)
| Inputs | Definition | Unit |
|---|---|---|
u_PF | Health state utility value for progression-free time | utility on the scale where 1 is full health and 0 is dead |
A_PF | Area under the PFS curve from model entry to the horizon, the mean progression-free time per person | years |
u_PD | Health state utility value for progressed time, usually below u_PF | utility on the same scale |
A_OS | Area under the OS curve from model entry to the horizon, the mean time alive per person and the life expectancy when the horizon is lifetime | years |
QALY | Expected quality-adjusted life years per person entering the model, over the time horizon | QALYs |
|---|
Function
Partitioned survival state occupancy and area-under-the-curve QALY function
Maps a set of survival curves that are not mutually exclusive, usually progression-free survival (PFS) and overall survival (OS) for each treatment arm, to the share of the cohort in each health state over time, and then to mean time in each state and QALYs as utility-weighted areas under the curves. State membership is read from the curves rather than built from transition probabilities, which is what separates a partitioned survival model from a state transition model. Linked records cover the parts this package does not repeat: the restricted mean from a Kaplan-Meier curve (HE-FM-ADMC-003), QALYs summed over periods (HE-FM-QALY-001), discounted totals (HE-FM-DR-002), a treatment curve from a baseline curve and a hazard ratio (HE-FM-HR-003) and the continuous discount rate (HE-FM-CONT-003).
Try this function
Implementations
Excel
Partitioned survival QALYs from two areas
With the areas in named cells AreaPFS and AreaOS and the utilities in UtilPF and UtilPD, the formula returns QALYs per person.
=UtilPF*AreaPFS+UtilPD*(AreaOS-AreaPFS)
Assumptions
One utility for all time in each partitioned survival state
Each alive state has one utility for all time spent in it, whatever the time since entry or the time to death. Over long horizons PMG36 (section 4.3.7) asks for utilities to be adjusted so that they do not exceed general population values at a given age; utilities then vary with time and the areas are weighted cycle by cycle instead.
PFS and OS areas from the same curves and horizon
A_PF and A_OS come from the pair of curves used for state occupancy and cover the same horizon, so A_PF is no larger than A_OS.
Worked examples
Standard care QALYs in the partitioned survival example
Mean PFS of 1.0 year and mean OS of 2.0 years leave 1.0 year progressed. At utilities of 0.75 and 0.60 the arm accrues 1.35 QALYs, undiscounted, as in the article.
u_PF = 0.75; u_PD = 0.60; A_PF = 1.0; A_OS = 2.0; QALY = 1.35
New treatment QALYs in the partitioned survival example
Mean PFS of 1.5 years and mean OS of 2.5 years also leave 1.0 year progressed, giving 1.725 QALYs. The gain of 0.375 QALYs comes entirely from progression-free time valued at 0.75.
u_PF = 0.75; u_PD = 0.60; A_PF = 1.5; A_OS = 2.5; QALY = 1.725
Common errors
Valuing the whole OS area at the progressed utility
Adding u_PD times the whole area under OS to u_PF times the PFS area counts progression-free time twice. In the standard-care example it gives 0.75 × 1.0 + 0.60 × 2.0 = 1.95 QALYs instead of 1.35.
Post-progression survival gain created by extrapolated OS alone
When extrapolated OS curves separate more than PFS curves, the model credits treatment with longer survival after progression whether or not evidence supports it. In the example, an OS hazard of 0.3 instead of 0.4 for the new treatment would raise its progressed time from 1.0 to about 1.83 years and its QALYs from 1.725 to 2.225. TSD 19 reports that reviewers criticised such differences in five appraisals for lack of supporting evidence.
Sources
Areas under PFS and OS curves and post-progression concerns in DSU TSD 19
Woods B, Sideris E, Palmer S, Latimer N, Soares M. NICE DSU Technical Support Document 19: partitioned survival analysis for decision modelling in health care: a critical review. Sheffield: Decision Support Unit, ScHARR, University of Sheffield; 2017. Section 2.2: health states carry state values, and the area under the extrapolated OS curve estimates mean life expectancy; section 3.2.10: differences in post-progression survival predicted by partitioned survival models were criticised in five appraisals.
Progression-based utilities in three-state area under the curve oncology models
Hatswell AJ, Pennington B, Pericleous L, Rowen D, Lebmeier M, Lee D. Patient-reported utilities in advanced or metastatic melanoma, including analysis of utilities by time to death. Health and Quality of Life Outcomes. 2014;12:140. Background and Discussion: health-state classifications for economic modelling are frequently based on progression status, and oncology models are frequently area under the curve models with pre-progression, post-progression and death states.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0