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The Theoretical Relationship between Sample Size and Expected Predictive Precision for EQ-5D Valuation Studies: A

Kelvin K W Chan^1,2,3,4, Eleanor M Pullenayegum^5,4

¹Sunnybrook Odette Cancer Centre, University of Toronto, Toronto, ON, Canada.

Medical Decision Making : an International Journal of the Society for Medical Decision Making

|May 20, 2020

Summary

We developed a formula to estimate the mean square error (MSE) for multi-attribute utility instruments (MAUI) scoring algorithms. Increasing sample size improves accuracy up to 300-500 participants, after which adding more health states is more beneficial.

Area of Science:

Health Economics
Psychometrics
Biostatistics

Background:

Scoring algorithms for multi-attribute utility instruments (MAUI) are subject to uncertainty due to their development in valuation studies.
Designing valuation studies with adequate sample sizes is crucial for achieving reliable accuracy in MAUI scoring.
Existing methods do not fully account for the inherent uncertainty and model-fit limitations in MAUI valuation.

Purpose of the Study:

To derive the first closed-form mathematical formula for the mean square error (MSE) of additive MAUI scoring algorithms.
To express MSE as a function of sample size and the number of directly valued health states.
To provide a tool for optimizing the design of MAUI valuation studies for desired predictive precision.

Main Methods:

Derived a closed-form MSE formula based on the EQ-5D valuation study design.
Incorporated sample size and the number of valued health states (overall and per subject) into the formula.
Validated the formula using a simulation study on the US EQ-5D-3L dataset, assessing model fit and data characteristics (random-effects vs. OLS, heteroscedasticity).

Main Results:

The derived MSE formula was validated across different statistical models and assumptions (random-effects vs. OLS, heteroscedasticity vs. homoscedasticity).
Mean square error (MSE) plateaus asymptotically as sample size increases, rather than approaching zero.
Significant MSE improvement is observed with increasing sample size for smaller samples (up to 300-500); beyond this, increasing the number of health states offers greater precision gains.

Conclusions:

A closed-form formula for calculating the MSE of additive MAUI scoring algorithms has been successfully derived.
The formula quantifies the impact of sample size and the number of health states on predictive precision.
This provides MAUI valuation study developers with a method to determine optimal sample sizes for achieving specific accuracy targets.

Keywords:

EQ-5D mean square error prediction precision sample size valuation study

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