DISTANCE EDUCATION PROGRAM 1: NUMERICAL STORYTELLING: SYSTEMATIC MEASUREMENT FAILURE IN HEALTH TECHNOLOGY ASSESSMENT MODULES 1 – 5

MODULE 1: WHY STEVENS? THE CONTEXT OF 1946

Before 1946, measurement outside physics lacked a clear warrant. Campbell addressed additivity
for manifest quantities; psychophysics mapped sensations; operationalism equated meaning with
procedure. None guaranteed that numerals preserved empirical structure or justified arithmetic,
particularly for latent traits. Stevens resolved this by linking scale types—nominal, ordinal,
interval, ratio—to permissible arithmetic and statistics. He did not provide a method for
constructing invariant rulers for latent attributes. That gap was later filled by the axiomatic work
in Foundations of Measurement and by Rasch modeling as an operational solution.

MODULE 2: AXIOMS OF REPRESENTATIONAL MEASUREMENT THEORY

Between 1946 and 1971, measurement theory advanced from typology to formal axioms. Suppes
derived additivity from concatenation for extensive attributes. Luce and Tukey showed how
conjoint measurement yields additive representations without concatenation under conditions
such as cancellation and solvability. Krantz, Luce, Suppes, and Tversky unified these results,
proving representation and uniqueness theorems. In parallel, Rasch modeling provided a
probabilistic implementation for measuring latent traits when data conform to the model.

MODULE 3: SUSTAINED MEASUREMENT FAILURE—TTO, EQ-5D-3L, AND UTILITIES

Time trade-off entrenched measurement failure by valuing multiattribute health-state
descriptions. TTO outputs are regressed into preference algorithms to generate utilities,
producing numbers without satisfying unidimensionality, additivity, or invariance. Protocol
variation and country-specific tariffs further destroy invariance, while task artifacts generate
negative values. Because the axioms fail at inception, these utilities are non-measures and cannot
support arithmetic.

MODULE 4: SUSTAINED MEASUREMENT FAILURE—THE IMPOSSIBLE QALY AND THE CHIMERICAL REFERENCE CASE

The QALY multiplies time, a ratio measure, by utilities that are not measures. The resulting
construct lacks unidimensionality, equal units, invariance, and a true zero. Reference-case
modeling institutionalizes this error by mandating cost-per-QALY outputs and treating them as
evidence. Thresholds and sensitivity analyses add precision without meaning. The reference case
thus formalizes numerical storytelling while ignoring fundamental measurement requirements.

MODULE 5: THE IDENTITY CRISIS OF HTA—NOTHING WITHOUT THE REFERENCE CASE