PROGRAM FEES
ARTIFICIAL INTELLIGENCE LARGE LANGUAGE MODEL INTERROGATION
REPRESENTATIONAL MEASUREMENT FAILURE IN HEALTH TECHNOLOGY ASSESSMENT
RECONSTRUCTING HTA PROGRAMS
9-UNIT OVERVIEW
MEASUREMENT BEFORE ARITHMETIC
Paul C Langley PhD Adjunct Professor, College of Pharmacy,
University of Minnesota, Minneapolis, MN
LOGIT WORKING PAPER No 1600 JUNE 2026
Tucson AZ
RECONSTRUCTING HTA PROGRAMS: MEASUREMENT BEFORE ARITHMETIC
Meeting the Standards of Representational Measurement for Therapy Claims: A 9-Unit Program
OVERVIEW
The implication is uncomfortable but increasingly difficult to avoid: the global extent of measurement inversion within health technology assessment (HTA) effectively strips the field of recognition as a credible quantitative science. When arithmetic routinely precedes measurement, numerical outputs become detached from measurable attributes and quantitative claims degenerate into numerical storytelling. The consequence is unavoidable. A framework that applies arithmetic operations without first establishing lawful measurement structures cannot sustain a claim to quantify therapy impact.
This outcome should not be surprising. It was the predictable consequence of decades of reliance upon health-state descriptions, utilities, composite indices and ordinal scores while neglecting the axioms of representational measurement. Once these standards are recognized, the analytical landscape changes fundamentally. Only two forms of measurement remain permissible for therapy evaluation: linear ratio measures for manifest attributes and Rasch logit ratio measures for latent attributes. There are no exceptions and no alternative routes to lawful quantitative claims.
Recognition of this fact requires more than criticism of existing HTA practice. It demands transition to a framework capable of meeting the standards expected of quantitative science. The purpose of these nine Units is therefore practical rather than philosophical: to provide the skills necessary to construct, apply and evaluate the only two lawful forms of measurement available for assessing therapy impact. In both cases the objective is identical: creation of claims that are credible, evaluable, replicable and exposed to possible falsification.
The Units are designed to support this transition. Topics include the principle that measurement must precede arithmetic, the axioms of representational measurement, the role of falsification, the impossibility of ordinal scores as measures, development of Rasch instruments for latent attributes, the concept of possession, protocol-driven claims assessment and formulary evaluation. Each Unit may be read independently, with the exception of the three linked Rasch Units which, for the first time, provide a detailed account of development of the Rasch logit ratio scale, construction of the latent ruler and the central concept of possession of a latent attribute.
The objective throughout is straightforward: rebuild HTA around the standards required for lawful measurement and scientific accountability.
A detailed abstract for all Units is given below.
| FEE STRUCTURE AND OPTIONS The fees are set to cover production and distribution costs. Unit 1 is seen as introductory and is priced accordingly (US$49). All other units are US$85. If Units 2 to 9 are purchased together the fee is US $575. |
UNIT 1
WHY MEASUREMENT MUST PRECEDE ARITHMETIC
This Unit introduces the foundational proposition underlying all quantitative inquiry: measurement must precede arithmetic. The objective is to establish the conditions required for meaningful quantitative claims and to demonstrate why numerical operations cannot substitute for lawful measurement structures. The distinction between numbers and measures is central. Numbers may function as labels, rankings, or counts, but measurement requires that numerical values be linked to attributes through scales possessing defined properties. Arithmetic operations derive their legitimacy not from mathematics itself but from the measurement characteristics of the scales to which they are applied.
The Unit begins by examining claims and attributes, emphasizing that every evaluable claim presupposes a clearly defined attribute with specified measurement properties. A distinction is developed between manifest and latent attributes. Manifest attributes may support conventional linear ratio measures, whereas latent attributes require transformation from observed responses to lawful measurement structures. Rasch measurement is introduced as the only admissible framework for constructing invariant logit ratio measures of latent constructs capable of supporting meaningful arithmetic and quantitative claims.
The assumptions underlying arithmetic operations are then examined in detail. Addition requires equal intervals, unidimensionality and commensurability, while multiplication imposes stricter conditions including meaningful zeros, proportional interpretation and dimensional homogeneity. Examples illustrate why arithmetic involving ordinal scores, interval scales or preference-based utility structures frequently violates these requirements. Particular attention is given to the QALY, demonstrating how multiplication of utility values and time fails dimensional homogeneity and therefore lacks lawful measurement foundations.
The Unit concludes by introducing the concept of measurement inversion: the reversal of the scientific sequence whereby arithmetic proceeds before measurement has been established. Large language model interrogations suggest that measurement inversion has become institutionalized within HTA knowledge bases. The implication is that numerical sophistication cannot compensate for absent measurement foundations. Arithmetic creates numbers; measurement establishes meaning.
UNIT 2
THE AXIOMS OF REPRESENTATIONAL MEASUREMENT
This Unit examines the foundations of representational measurement and argues that lawful quantitative claims require adherence to explicit measurement axioms before arithmetic operations can occur. Beginning with the historical development of measurement theory, the discussion traces the evolution from nineteenth-century physical measurement through the contributions of Stanley Smith Stevens and the later formalization of representational measurement by Krantz, Luce, Suppes and Tversky. Central attention is given to the proposition that numbers do not create quantities; numerical systems acquire meaning only when they preserve empirical relationships present within the attributes being measured.
The Unit reviews the principal axioms underlying representational measurement, including unidimensionality, ordering, transitivity, additivity, equal intervals, ratio properties, invariance and falsifiability. These axioms are examined for both manifest and latent attributes and linked to Rasch measurement as the only framework capable of establishing lawful ratio structures for latent traits. Evidence from recent knowledge-base interrogations, including assessment of the ISPOR environment, demonstrates a recurring pattern of measurement inversion in which arithmetic operations are routinely endorsed before measurement requirements have been satisfied. The conclusion is direct: measurement precedes arithmetic. Without representational measurement, quantitative claims become numerical constructions detached from scientific foundations and the evolution of objective knowledge itself.
UNIT 3
THE DENIAL OF OBJECTIVE KNOWLEDGE
This Unit examines the scientific foundations necessary for lawful quantitative claims and argues that representational measurement and falsifiability are indispensable conditions for the evolution of objective knowledge. Beginning with the scientific revolution and the emergence of empirical inquiry, the Unit traces the development of the principle that scientific claims must expose themselves to possible failure. Drawing upon Karl Popper’s concept of falsification, it argues that scientific progress depends not upon confirmation but upon the elimination of error through empirical challenge. Measurement occupies a central role in this process because arithmetic operations and quantitative comparisons acquire legitimacy only when they preserve the structure of measurable attributes.
The Unit then considers the implications for health technology assessment (HTA), where increasingly sophisticated numerical frameworks often proceed without lawful measurement foundations. Particular attention is given to CHEERS 2022, ICER, reference-case methodologies and utility-based simulations that substitute transparency and validation for falsifiable claims. Through analyses of utilities, QALYs and assumption-driven simulation models, a common pattern emerges: arithmetic repeatedly assumes legitimacy before measurement has been established. Recent large language model interrogations demonstrate that these assumptions have become institutionalized within a broader HTA memeplex reproducing measurement inversion across agencies, journals and educational environments. The conclusion is straightforward: scientific inquiry requires falsifiable claims and lawful measurement. Without representational measurement, quantitative outputs become numerical constructions detached from the evolution of objective knowledge.
UNIT 4
ORDINAL SCORES AND THE GREAT MEASUREMENT ILLUSION
This Unit examines one of the most persistent and least recognized failures within health technology assessment (HTA): the confusion of ordinal observations with lawful quantitative measures. Across agencies, journals, educational institutions and professional organizations, recent knowledge-base interrogations reveal a stable pattern of measurement inversion in which arithmetic operations proceed before measurement properties have been established. Numbers assigned to questionnaire responses, preference judgments and health-state descriptions are repeatedly treated as though they represent quantities suitable for mathematical manipulation. Ordinal observations become summed scores; summed scores become transformed scales; transformed scales become utilities; utilities become QALYs; and QALYs ultimately become inputs to cost-effectiveness claims and policy decisions.
The Unit argues that this process reflects an institutionalized ordinal obsession where numerical labels create an illusion of measurement. Through analyses of summed questionnaire scores, the EORTC QLQ-C30, Time Trade-Off procedures, EQ-5D utility construction, CHEERS 2022 and the COSMIN–Cochrane evidence pathway, a common theme emerges: arithmetic repeatedly assumes legitimacy independently of representational measurement. Particular attention is given to the distinction between observations and measures, the inadmissibility of arithmetic operations on ordinal structures and the failure to distinguish manifest from latent attributes. The conclusion is straightforward: ordinal scores are not ratio measures. Without lawful quantitative structures, increasingly sophisticated mathematical procedures do not create science; they create numerical storytelling. Unit 4 therefore positions the ordinal misconception as one of the principal pathways through which HTA moved from representational measurement toward institutionalized measurement inversion.
UNIT 5
RASCH MEASUREMENT: FROM ITEM RESPONSE TO A PROVISIONAL RASCH RULER
Unit 5 introduces the Rasch framework as the only operational approach capable of transforming observations of latent attributes into lawful measures. Unlike manifest attributes such as hospital days, prescription counts or time, latent constructs including symptom burden, treatment satisfaction, need fulfilment and quality of life cannot be observed directly. They are inferred from patterns of item responses. The central challenge is therefore not data collection but determining whether these observations can support a measurement structure consistent with the requirements of representational measurement.
The Unit begins by introducing the conjoint person–item structure proposed by Rasch. Responses are interpreted not as isolated observations but as outcomes determined jointly by respondent possession of an attribute and item difficulty. This relationship is the basis for specific objectivity and the creation of an invariant latent measurement ruler. Rasch is presented not as one psychometric option among many, but as the operationalization of the axioms of measurement for latent constructs.
A key theme is the rejection of summed scores. The Unit explains why arithmetic applied to ordinal responses cannot manufacture measurement properties absent from the original observations. Rasch takes a fundamentally different position by asking whether responses conform to the conditions necessary for lawful measurement. Central to this framework is the concept of possession of a latent attribute, where therapy impact is assessed as movement on a latent continuum rather than change in descriptive scores.
The Unit also provides a detailed account of instrument development. Beginning with patient interviews, candidate statements are refined and ordered into a provisional item hierarchy. Construction of the Rasch ruler is described as a two-step process. Iterative parameter estimation generates a draft logit continuum from the response matrix, followed by testing of fit requirements to determine whether the structure satisfies invariance, unidimensionality and specific objectivity.
A worked example demonstrates movement from a fixed response matrix to an expected probability matrix and then to iterative revision of respondent and item locations. The Unit concludes by emphasizing that Rasch does not simply model observations; it creates the conditions under which latent measurement becomes possible.
UNIT 6
RASCH MEASUREMENT: FINALIZING THE RASCH LOGIT RATIO SCALE
Unit 6 addresses the critical second stage in Rasch measurement: the transformation of a provisional logit continuum into the final Rasch logit ratio scale. Unit 5 demonstrated how respondent and item locations could be iteratively estimated from an observed response matrix to create a draft latent continuum. Yet construction of a provisional ruler does not itself establish measurement. The question addressed in this Unit is whether the developing continuum satisfies the conditions necessary for lawful measurement and therefore conforms to the requirements of representational measurement.
The Unit begins by clarifying the unique position of Rasch measurement within health technology assessment. Rasch is presented not as one psychometric option among many but as a framework developed specifically to solve the problem of measurement for latent attributes. Contrasts are drawn with conventional item response theory and PROMIS approaches, emphasizing that Rasch begins with a measurement requirement and asks whether observations support that requirement, whereas alternative approaches frequently seek models that best accommodate observed data.
A central theme concerns the historical recognition that latent variable estimation alone could not establish measurement. The Unit explains how, during the 1970s, Rasch procedures increasingly became associated with evaluating whether observations satisfied conditions necessary for lawful measurement. This distinction elevated Rasch beyond a statistical modeling exercise and established its potential role as one of only two acceptable approaches to ratio measurement in therapy impact assessment.
The remainder of the Unit presents a structured framework for endorsement of the Rasch logit ratio scale. Criteria including unidimensionality, item fit, specific objectivity, differential item functioning, local independence, response category functioning, targeting, item hierarchy stability, person and item separation and overall ruler stability are examined. These requirements are discussed not as isolated statistics but as collective evidence supporting an invariant measurement structure.
The Unit concludes by emphasizing the broader implications for health technology assessment. Rasch measurement challenges long-standing reliance upon summed scores and composite indices and establishes a framework in which measurement precedes arithmetic. Completion of the measurement structure also prepares the way for Unit 7, where attention turns to the central outcome of Rasch measurement: possession of a latent attribute.
UNIT 7
RASCH MEASUREMENT: THE POSSESSION OF LATENT ATTRIBUTES
Unit 7 introduces the concept of possession of a latent attribute, a concept unique to Rasch measurement and central to understanding therapy impact in health technology assessment. Previous Units established how ordinal observations can be transformed into a lawful Rasch logit ratio scale through item calibration, iterative estimation and endorsement of measurement requirements. This Unit addresses the next and critical question: once a stable ruler exists, what exactly is being measured?
The answer proposed is possession. Unlike traditional patient-reported outcome approaches, which rely on summed scores or composite indices, Rasch does not treat responses as quantities. Responses are viewed as evidence concerning an individual’s location on a latent continuum. Through the interaction of item difficulty and respondent location, individuals are assigned positions representing the extent to which they possess the underlying attribute. Therapy impact therefore becomes interpretable as movement in possession rather than movement in scores.
The Unit explains how possession is estimated for both individuals and target populations. The iterative estimation process is described, showing how person locations are repeatedly adjusted until observed response patterns become maximally consistent with calibrated item difficulties. Particular emphasis is placed on the distinction between possession and raw score totals. Possession emerges from the complete pattern of responses rather than from summation.
The implications for population-level assessment are then explored. Aggregate possession is presented as a mean logit location for the target population, with associated measures of variability and precision supporting inference regarding therapy impact. Worked examples demonstrate how changes in possession can be translated into changes in odds and how prospective therapy claims may be formulated and evaluated.
The broader significance of possession is then considered. Rasch measurement provides a framework where latent attribute claims become measurable, falsifiable and replicable. Therapy claims can be specified in advance, evaluated against observed data and either supported or rejected. Unit 7 therefore presents possession not simply as a technical consequence of Rasch estimation, but as a solution to one of the longest-standing problems in outcomes research: how latent attributes can be measured in a scientifically credible manner.
UNIT 8
ATTRIBUTE CLAIMS AND PROTOCOLS
This Unit proposes a new framework for health technology assessment (HTA) founded on a simple principle: measurement alone is insufficient; all claims must be linked to explicit protocols capable of empirical assessment. Earlier Units established that measurement must precede arithmetic and that only two lawful measurement structures support therapy evaluation: linear ratio measures for manifest attributes and Rasch logit ratio measures for latent attributes. This Unit addresses the next question: how should measurable attributes be translated into scientific claims regarding therapy impact? The answer proposed is a protocol-driven claims framework grounded in prospective evaluation and falsification.
The Unit contrasts this framework with traditional reference-case approaches. Under simulation-driven systems, assumptions concerning utilities, transition probabilities and disease progression generate internally coherent projections whose outputs become substitutes for evidence. In contrast, the protocol framework begins with explicit empirical propositions regarding anticipated therapy effects. Claims concerning hospital utilization, treatment persistence, symptom burden, compliance or possession of latent attributes are specified prospectively, linked to measurable attributes and exposed to possible failure. Evidence emerges through observation rather than through simulation.
Particular emphasis is given to compliance behavior. Compliance is presented not as a secondary outcome or background model parameter but as a foundational manifest attribute claim underwriting all subsequent therapy effects. Because treatment exposure conditions all downstream outcomes, compliance assumptions should become measurable, explicit and falsifiable propositions within every protocol. The Unit also explores the concept of protocol links, emphasizing that claims may form networks of related empirical expectations while preserving the independence of each measurable attribute.
Separate protocol requirements are then developed for manifest and latent claims. Manifest claims focus primarily on empirical justification and protocol design because measurement structures already exist. Latent claims require an additional layer of scientific discipline: demonstration that Rasch measurement requirements have been satisfied before therapy claims can proceed. Instrument development, unidimensionality, item fit, invariance and evidence supporting possession claims become essential components of latent protocols. The Unit concludes by arguing that protocol-driven claims reconnect HTA with the broader requirements of science by replacing false analytical assumptions with measurable propositions capable of challenge, replication and contribution to the evolution of objective knowledge.
UNIT 9
FORMULARY GUIDELINES
This unit proposes a reconstruction of formulary submission guidelines founded on a simple principle: measurement must precede arithmetic. For more than four decades, health technology assessment (HTA) has relied upon utilities, QALYs, composite indices and reference-case simulation models as the basis for claims regarding therapy value and cost-effectiveness. While these approaches generated increasingly sophisticated numerical outputs, they also institutionalized a fundamental methodological error: the routine application of arithmetic operations before establishing whether the underlying attributes possessed lawful measurement properties. The consequence has been measurement inversion, where numerical manipulation replaces measurement and increasingly elaborate analytical structures generate numbers rather than measures.
The paper makes clear that conventional formulary requirements are not compatible with the standards of representational measurement. Health-state descriptions, utility algorithms, QALYs and simulation outputs are treated as though they possess quantitative properties that have never been demonstrated. Once arithmetic is detached from lawful measurement, numerical complexity cannot compensate for the absence of measurement foundations. The result is a closed analytical framework in which internally coherent simulations substitute for empirical evaluation and assumptions are protected from falsification. The reference case is closed as a scientific framework for assessing therapy impact.
A new formulary framework is proposed in which manufacturers are required to present explicit attribute claims supported by lawful measurement structures and prospective evaluation protocols. Only two measurement pathways are recognized. Manifest attributes, such as hospital admissions, hospital days, treatment persistence and resource utilization, require linear ratio measures. Latent attributes, such as symptom burden, treatment satisfaction and need fulfilment, require Rasch logit ratio measures. All claims must be measurable, evaluable, replicable and vulnerable to failure. Each claim is linked to a protocol specifying the target population, comparator, endpoint, observation period, data source and criteria for success or failure.
The unit also details the implications for manufacturers, including responsibilities for attribute development, protocol design, staff training, recruitment, contracting and continuing evidence generation throughout the product lifecycle. Particular emphasis is placed on integrating attribute development into clinical development programs and creating continuity between regulatory evidence and formulary assessment. The conclusion is that HTA must move beyond simulation-driven numerical storytelling and return to the standards of quantitative science through lawful measurement, protocol-driven claims and empirical evaluation capable of supporting the continuing evolution of objective knowledge.
ACKNOWLEDGEMENT
I acknowledge that I have used OpenAI technologies, including the large language model, to assist in the development of this work. All final decisions, interpretations, and responsibilities for the content rest solely with me
REFERENCES