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<h2 id="toc-title">Table of contents</h2>
<ul>
<li><a href="#sec-introduction" id="toc-sec-introduction" class="nav-link active" data-scroll-target="#sec-introduction">Introduction</a>
<ul class="collapse">
<li><a href="#compositional-preference-elicitation-methods" id="toc-compositional-preference-elicitation-methods" class="nav-link" data-scroll-target="#compositional-preference-elicitation-methods">Compositional preference elicitation methods</a></li>
<li><a href="#from-puf-to-opuf" id="toc-from-puf-to-opuf" class="nav-link" data-scroll-target="#from-puf-to-opuf">From PUF to OPUF</a></li>
<li><a href="#an-overview-of-the-opuf-structure" id="toc-an-overview-of-the-opuf-structure" class="nav-link" data-scroll-target="#an-overview-of-the-opuf-structure">An overview of the OPUF structure</a>
<ul class="collapse">
<li><a href="#attribute-weighting" id="toc-attribute-weighting" class="nav-link" data-scroll-target="#attribute-weighting">Attribute weighting</a></li>
<li><a href="#level-ratings" id="toc-level-ratings" class="nav-link" data-scroll-target="#level-ratings">Level ratings</a></li>
<li><a href="#anchoring-factor" id="toc-anchoring-factor" class="nav-link" data-scroll-target="#anchoring-factor">Anchoring factor</a></li>
</ul></li>
<li><a href="#sec-OPUF_methods" id="toc-sec-OPUF_methods" class="nav-link" data-scroll-target="#sec-OPUF_methods">OPUF logic and mathematics</a>
<ul class="collapse">
<li><a href="#example-responses" id="toc-example-responses" class="nav-link" data-scroll-target="#example-responses">Example responses</a></li>
</ul></li>
<li><a href="#aggregation-to-social-utility-function" id="toc-aggregation-to-social-utility-function" class="nav-link" data-scroll-target="#aggregation-to-social-utility-function">Aggregation to social utility function</a></li>
</ul></li>
<li><a href="#methods" id="toc-methods" class="nav-link" data-scroll-target="#methods">Methods</a>
<ul class="collapse">
<li><a href="#recruitment" id="toc-recruitment" class="nav-link" data-scroll-target="#recruitment">Recruitment</a></li>
<li><a href="#sec-surveystructure" id="toc-sec-surveystructure" class="nav-link" data-scroll-target="#sec-surveystructure">Survey structure</a></li>
<li><a href="#sec-livesurvey" id="toc-sec-livesurvey" class="nav-link" data-scroll-target="#sec-livesurvey">Live survey</a></li>
<li><a href="#missing-data" id="toc-missing-data" class="nav-link" data-scroll-target="#missing-data">Missing data</a></li>
<li><a href="#preference-heterogeneity" id="toc-preference-heterogeneity" class="nav-link" data-scroll-target="#preference-heterogeneity">Preference heterogeneity</a></li>
<li><a href="#permutational-analysis-of-variance" id="toc-permutational-analysis-of-variance" class="nav-link" data-scroll-target="#permutational-analysis-of-variance">Permutational analysis of variance</a></li>
<li><a href="#sensitivity-analysis" id="toc-sensitivity-analysis" class="nav-link" data-scroll-target="#sensitivity-analysis">Sensitivity analysis</a></li>
</ul></li>
<li><a href="#results" id="toc-results" class="nav-link" data-scroll-target="#results">Results</a>
<ul class="collapse">
<li><a href="#study-participants" id="toc-study-participants" class="nav-link" data-scroll-target="#study-participants">Study participants</a></li>
<li><a href="#survey-duration" id="toc-survey-duration" class="nav-link" data-scroll-target="#survey-duration">Survey duration</a></li>
<li><a href="#waite-descriptive-system" id="toc-waite-descriptive-system" class="nav-link" data-scroll-target="#waite-descriptive-system">WAItE descriptive system</a></li>
<li><a href="#level-ratings-1" id="toc-level-ratings-1" class="nav-link" data-scroll-target="#level-ratings-1">Level ratings</a></li>
<li><a href="#attribute-weights" id="toc-attribute-weights" class="nav-link" data-scroll-target="#attribute-weights">Attribute weights</a></li>
<li><a href="#anchoring" id="toc-anchoring" class="nav-link" data-scroll-target="#anchoring">Anchoring</a></li>
<li><a href="#social-utility-function-estimation" id="toc-social-utility-function-estimation" class="nav-link" data-scroll-target="#social-utility-function-estimation">Social utility function estimation</a></li>
<li><a href="#preference-heterogeneity-1" id="toc-preference-heterogeneity-1" class="nav-link" data-scroll-target="#preference-heterogeneity-1">Preference heterogeneity</a></li>
<li><a href="#permanova" id="toc-permanova" class="nav-link" data-scroll-target="#permanova">PERMANOVA</a></li>
<li><a href="#sensitivity-analysis-1" id="toc-sensitivity-analysis-1" class="nav-link" data-scroll-target="#sensitivity-analysis-1">Sensitivity analysis</a>
<ul class="collapse">
<li><a href="#attribute-weighting-and-level-rating-preference-heterogeneity" id="toc-attribute-weighting-and-level-rating-preference-heterogeneity" class="nav-link" data-scroll-target="#attribute-weighting-and-level-rating-preference-heterogeneity">Attribute weighting and level rating preference heterogeneity</a></li>
<li><a href="#anchoring-preference-heterogeneity" id="toc-anchoring-preference-heterogeneity" class="nav-link" data-scroll-target="#anchoring-preference-heterogeneity">Anchoring preference heterogeneity</a></li>
</ul></li>
</ul></li>
<li><a href="#discussion" id="toc-discussion" class="nav-link" data-scroll-target="#discussion">Discussion</a>
<ul class="collapse">
</ul></li>
</ul>
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<main class="content" id="quarto-document-content">
<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title">Development of a value-based scoring system for the WAItE using the OPUF in a sample of adults</h1>
</div>
<div class="quarto-title-meta-author">
<div class="quarto-title-meta-heading">Authors</div>
<div class="quarto-title-meta-heading">Affiliations</div>
<div class="quarto-title-meta-contents">
<p class="author">William King* <a href="mailto:w.king2@newcastle.ac.uk" class="quarto-title-author-email"><i class="bi bi-envelope"></i></a> </p>
</div>
<div class="quarto-title-meta-contents">
<p class="affiliation">
Newcastle University
</p>
</div>
<div class="quarto-title-meta-contents">
<p class="author">Tomos Robinson </p>
</div>
<div class="quarto-title-meta-contents">
<p class="affiliation">
Newcastle University
</p>
</div>
<div class="quarto-title-meta-contents">
<p class="author">Angela Bate </p>
</div>
<div class="quarto-title-meta-contents">
<p class="affiliation">
Northumbria University
</p>
</div>
<div class="quarto-title-meta-contents">
<p class="author">Laura Ternent </p>
</div>
<div class="quarto-title-meta-contents">
<p class="affiliation">
Newcastle University
</p>
</div>
</div>
<div class="quarto-title-meta">
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">December 4, 2024</p>
</div>
</div>
</div>
<div>
<div class="abstract">
<div class="block-title">Abstract</div>
<p><strong>Background:</strong> Online personal utility functions (OPUF) present a new method for eliciting preferences. In this study we used the OPUF to elicit a health state utility value set for the Weight-specific Adolescent Instrument for Economic-evaluation (WAItE) with a representative sample of the UK adult population.</p>
<p><strong>Methods:</strong> WAItE OPUF survey design was informed by prior qualitative work. The survey consisted of the WAItE descriptive system, attribute weighting, level rating (per attribute) and a VAS anchoring task. Personal utility functions were estimated on the individual level for all participants. Personal utility functions were aggregated and combined with the anchoring factor to give the social utility function and utility value set. Preference heterogeneity was assessed using Euclidean distance and PERMANOVA to explore preference variation within the sample. An experimental sensitivity analysis dichotomised preference heterogeneity into anchoring variation and attribute weighting/level rating variation.</p>
<p><strong>Results:</strong> A total of 300 participants completed the WAItE OPUF survey. The sample was broadly representative of the UK adult population. Participants, on average, took less than 10 minutes to complete the survey. The most important attributes were tiredness and unhappiness, while least important attributes were sports and embarrassment. Social utility values and the anchoring utility value estimated were comparable to previous studies. Preferences generally were heterogeneous, especially among different ages. Younger participants assigned lower utility values to WAItE health states and provided significantly lower scores on the VAS anchoring task compared to older participants.</p>
<p><strong>Conclusion:</strong> This study successfully elicited health state utility values for the WAItE using the OPUF. Preference heterogeneity analysis identified differences in preferences for different age groups and a further valuation study is ongoing to explore whether this heterogeneity exists between adults and adolescents.</p>
</div>
</div>
<div>
<div class="keywords">
<div class="block-title">Keywords</div>
<p>Health state valuation, preference elicitation, quality of life</p>
</div>
</div>
</header>
<p><em>Disclaimer:</em> This is a work-in-progress, please do not redistribute or cite without the authors permission. This work was supported by the NIHR-ARC and Newcastle University.</p>
<p><em>Acknowledgements:</em> We would like to thank Paul Schneider and Valorem Health for collaborating on this project.</p>
<p><em>Code availability:</em> An interactive document (HTML) which includes the live survey is available <a href="https://willking98.github.io/opuf-adult/">here</a>. Source code for the analysis and this Quarto generated PDF are available <a href="https://github.com/willking98/opuf-adult">here</a>.</p>
<section id="sec-introduction" class="level1">
<h1>Introduction</h1>
<section id="compositional-preference-elicitation-methods" class="level2">
<h2 class="anchored" data-anchor-id="compositional-preference-elicitation-methods">Compositional preference elicitation methods</h2>
<p>Preference elicitation methods typically, fall into two categories: compositional and decompositional <span class="citation" data-cites="Keeney1979DecisionsTrade-Offs Marsh2016MultipleForce Belton2002MultipleAnalysis">(<a href="#ref-Keeney1979DecisionsTrade-Offs" role="doc-biblioref">1</a>–<a href="#ref-Belton2002MultipleAnalysis" role="doc-biblioref">3</a>)</span>. That is, methods such as DCE, BWS and TTO elicit preference orderings from individuals for an entire health state (composed of a combination of attributes and levels) and then responses are decomposed to identify marginal contributions of each attribute and level in each health state. Models like multinomial logit, mixed logit and latent class are frequently used to decompose responses to decompositional preference elicitation tasks <span class="citation" data-cites="Hauber2016StatisticalForce">(<a href="#ref-Hauber2016StatisticalForce" role="doc-biblioref">4</a>)</span>. Coefficients estimated in these models form the basis of dis/utility values for each attribute and level in a descriptive system.</p>
<p>Conversely, compositional methods seek to identify preferences for each attribute weighting and level rating individually for the number of attributes and levels in a given descriptive system. Therefore, statistical models to elicit coefficients for each individual attribute and level are not required and responses to each attribute weighting and level rating are combined (in addition to an anchoring factor) to yield dis/utility values for each attribute and level in the descriptive system. Compositional approaches can take many forms from simple VAS scores to using semantic categories and ranking methods <span class="citation" data-cites="BanaECosta1999TheApplication Danner2011IntegratingPreferences Oliveira2018ValuingStates">(<a href="#ref-BanaECosta1999TheApplication" role="doc-biblioref">5</a>–<a href="#ref-Oliveira2018ValuingStates" role="doc-biblioref">7</a>)</span>. These approaches have previously been used successfully in multi-criteria decision analysis (MCDA), but have been used less extensively in the preference elicitation space. Since the development of the OPUF, compositional approaches to elicit preferences have become more commonplace and a number of countries are using the OPUF to elicit value sets specific to their population <span class="citation" data-cites="Brodszky2023PCR108States">(<a href="#ref-Brodszky2023PCR108States" role="doc-biblioref">8</a>)</span>.</p>
</section>
<section id="from-puf-to-opuf" class="level2">
<h2 class="anchored" data-anchor-id="from-puf-to-opuf">From PUF to OPUF</h2>
<p>Personal utility functions (PUF) were first used in the context of preference elicitation by Devlin et al. (2019) <span class="citation" data-cites="Devlin2019AFunctions">(<a href="#ref-Devlin2019AFunctions" role="doc-biblioref">9</a>)</span> to estimate the feasibility for using this approach to estimate a value set for the EQ-5D-5L. Since the feasibility for the underlying PUF methods were established, the approach has been expanded by Schneider and colleagues <span class="citation" data-cites="Schneider2022TheStates">(<a href="#ref-Schneider2022TheStates" role="doc-biblioref">10</a>)</span> and converted into an online personal utility functions (OPUF) survey built initially using RShiny and subsequently using Javascript (available <a href="https://eq5d5l.me">here</a>). Since the development of the OPUF, a number of descriptive systems and different research teams have begun using this method to elicit value sets <span class="citation" data-cites="Bray2024DevelopmentImpairment Brodszky2023PCR108States">(<a href="#ref-Brodszky2023PCR108States" role="doc-biblioref">8</a>,<a href="#ref-Bray2024DevelopmentImpairment" role="doc-biblioref">11</a>)</span>.</p>
</section>
<section id="an-overview-of-the-opuf-structure" class="level2">
<h2 class="anchored" data-anchor-id="an-overview-of-the-opuf-structure">An overview of the OPUF structure</h2>
<section id="attribute-weighting" class="level3">
<h3 class="anchored" data-anchor-id="attribute-weighting">Attribute weighting</h3>
<p>This section is composed of two parts. First, attribute ranking is completed where participants identify their most important attribute (<a href="#fig-importantattribute" class="quarto-xref">Figure 1 (a)</a>). Second, respondents complete the attribute weighting (swing weighting) where the relative importance of other attributes is ascertained using their most important attribute as a reference point (<a href="#fig-swing" class="quarto-xref">Figure 1 (b)</a>). These questions are presented in <a href="#fig-attribute" class="quarto-xref">Figure 1</a>.</p>
<div id="fig-attribute" class="quarto-layout-panel">
<figure class="quarto-float quarto-float-fig figure">
<div aria-describedby="fig-attribute-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="quarto-layout-row">
<div class="quarto-layout-cell-subref quarto-layout-cell" data-ref-parent="fig-attribute" style="flex-basis: 50.0%;justify-content: flex-start;">
<div id="fig-importantattribute" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-subfloat-fig figure">
<div aria-describedby="fig-importantattribute-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/relative_importance.png" class="img-fluid figure-img" data-ref-parent="fig-attribute">
</div>
<figcaption class="quarto-float-caption-bottom quarto-subfloat-caption quarto-subfloat-fig" id="fig-importantattribute-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
(a) Most important attribute
</figcaption>
</figure>
</div>
</div>
<div class="quarto-layout-cell-subref quarto-layout-cell" data-ref-parent="fig-attribute" style="flex-basis: 50.0%;justify-content: flex-start;">
<div id="fig-swing" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-subfloat-fig figure">
<div aria-describedby="fig-swing-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/swing_rating.png" class="img-fluid figure-img" data-ref-parent="fig-attribute">
</div>
<figcaption class="quarto-float-caption-bottom quarto-subfloat-caption quarto-subfloat-fig" id="fig-swing-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
(b) Swing rating
</figcaption>
</figure>
</div>
</div>
</div>
</div>
<figcaption class="quarto-float-caption-bottom quarto-float-caption quarto-float-fig" id="fig-attribute-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Figure 1: Attribute weighting
</figcaption>
</figure>
</div>
</section>
<section id="level-ratings" class="level3">
<h3 class="anchored" data-anchor-id="level-ratings">Level ratings</h3>
<p>This element of the OPUF has varied across different iterations of the survey. Schnieder et al. (2022) <span class="citation" data-cites="Schneider2022TheStates">(<a href="#ref-Schneider2022TheStates" role="doc-biblioref">10</a>)</span> asked participants to rank the levels within the descriptive system generally (i.e. for any given attribute), while other iterations have administered separate level rating questions for each attribute in the descriptive system <span class="citation" data-cites="Bray2024DevelopmentImpairment">(<a href="#ref-Bray2024DevelopmentImpairment" role="doc-biblioref">11</a>)</span>. Selection of method requires a trade-off between participant burden and sensitivity of level ratings to each attribute. <a href="#fig-level" class="quarto-xref">Figure 2</a> presents the level rating question for the tiredness and treated differently attributes of the WAItE.</p>
<div id="fig-level" class="quarto-layout-panel">
<figure class="quarto-float quarto-float-fig figure">
<div aria-describedby="fig-level-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="quarto-layout-row">
<div class="quarto-layout-cell-subref quarto-layout-cell" data-ref-parent="fig-level" style="flex-basis: 50.0%;justify-content: flex-start;">
<div id="fig-levelrating" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-subfloat-fig figure">
<div aria-describedby="fig-levelrating-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/level_rating.png" class="img-fluid figure-img" data-ref-parent="fig-level">
</div>
<figcaption class="quarto-float-caption-bottom quarto-subfloat-caption quarto-subfloat-fig" id="fig-levelrating-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
(a) Level rating: Tiredness
</figcaption>
</figure>
</div>
</div>
<div class="quarto-layout-cell-subref quarto-layout-cell" data-ref-parent="fig-level" style="flex-basis: 50.0%;justify-content: flex-start;">
<div id="fig-levelrating2" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-subfloat-fig figure">
<div aria-describedby="fig-levelrating2-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/level_rating2.png" class="img-fluid figure-img" data-ref-parent="fig-level">
</div>
<figcaption class="quarto-float-caption-bottom quarto-subfloat-caption quarto-subfloat-fig" id="fig-levelrating2-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
(b) Level rating: Treated differently
</figcaption>
</figure>
</div>
</div>
</div>
</div>
<figcaption class="quarto-float-caption-bottom quarto-float-caption quarto-float-fig" id="fig-level-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Figure 2: Level rating
</figcaption>
</figure>
</div>
<div style="page-break-after: always;"></div>
</section>
<section id="anchoring-factor" class="level3">
<h3 class="anchored" data-anchor-id="anchoring-factor">Anchoring factor</h3>
<p>A task is required to rescale the latent coefficients estimated via combining level ratings and attribute weights onto the QALY scale. Participants are presented with a binary choice between the PITS state (or another state) of a given descriptive system and “being dead” (<a href="#fig-anchor1" class="quarto-xref">Figure 3 (a)</a>). If the PITS state is chosen, participants are asked to rank the PITS state on a VAS from 1 (full health) to 0 (dead). If “being dead” is chosen, participants are asked to rank “being dead” on a VAS from 1 (full health) to 0 (PITS state) (<a href="#fig-anchor2" class="quarto-xref">Figure 3 (b)</a>). Responses to these respective questions provide the anchoring factor. Anchoring questions, such that PITS is preferred to dead, are presented in <a href="#fig-anchoring" class="quarto-xref">Figure 3</a>.</p>
<div id="fig-anchoring" class="quarto-layout-panel">
<figure class="quarto-float quarto-float-fig figure">
<div aria-describedby="fig-anchoring-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="quarto-layout-row">
<div class="quarto-layout-cell-subref quarto-layout-cell" data-ref-parent="fig-anchoring" style="flex-basis: 50.0%;justify-content: flex-start;">
<div id="fig-anchor1" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-subfloat-fig figure">
<div aria-describedby="fig-anchor1-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/anchor1.png" class="img-fluid figure-img" data-ref-parent="fig-anchoring">
</div>
<figcaption class="quarto-float-caption-bottom quarto-subfloat-caption quarto-subfloat-fig" id="fig-anchor1-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
(a) PITS-dead
</figcaption>
</figure>
</div>
</div>
<div class="quarto-layout-cell-subref quarto-layout-cell" data-ref-parent="fig-anchoring" style="flex-basis: 50.0%;justify-content: flex-start;">
<div id="fig-anchor2" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-subfloat-fig figure">
<div aria-describedby="fig-anchor2-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/anchor2.png" class="img-fluid figure-img" data-ref-parent="fig-anchoring">
</div>
<figcaption class="quarto-float-caption-bottom quarto-subfloat-caption quarto-subfloat-fig" id="fig-anchor2-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
(b) PITS-VAS
</figcaption>
</figure>
</div>
</div>
</div>
</div>
<figcaption class="quarto-float-caption-bottom quarto-float-caption quarto-float-fig" id="fig-anchoring-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Figure 3: Anchoring factor
</figcaption>
</figure>
</div>
</section>
</section>
<section id="sec-OPUF_methods" class="level2">
<h2 class="anchored" data-anchor-id="sec-OPUF_methods">OPUF logic and mathematics</h2>
<p>This section presents the logic and underlying mathematics required to convert the raw OPUF responses from one person into an anchored value set for the WAItE descriptive system. This example assumes that level ratings are obtained for each attribute separately, therefore the mathematics presented here differs to those presented elsewhere <span class="citation" data-cites="Schneider2022TheStates">(<a href="#ref-Schneider2022TheStates" role="doc-biblioref">10</a>)</span>. Example response data are used for demonstration in this section and are presented in <a href="#tbl-exampledata" class="quarto-xref">Table 1</a>.</p>
<div style="page-break-after: always;"></div>
<section id="example-responses" class="level3">
<h3 class="anchored" data-anchor-id="example-responses">Example responses</h3>
<div class="cell">
<div id="tbl-exampledata" class="cell quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-float-tbl figure">
<figcaption class="quarto-float-caption-top quarto-float-caption quarto-float-tbl" id="tbl-exampledata-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Table 1: Example individual responses to the OPUF
</figcaption>
<div aria-describedby="tbl-exampledata-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="cell-output-display">
<table class="do-not-create-environment cell caption-top table table-sm table-striped small">
<colgroup>
<col style="width: 28%">
<col style="width: 6%">
<col style="width: 8%">
<col style="width: 7%">
<col style="width: 14%">
<col style="width: 12%">
<col style="width: 12%">
<col style="width: 8%">
</colgroup>
<thead>
<tr class="header">
<th style="text-align: left;">Response</th>
<th style="text-align: right;">Tired</th>
<th style="text-align: right;">Walking</th>
<th style="text-align: right;">Sports</th>
<th style="text-align: right;">Concentration</th>
<th style="text-align: right;">Embarrassed</th>
<th style="text-align: right;">Unhappiness</th>
<th style="text-align: right;">Treated</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">Level rating: Never</td>
<td style="text-align: right;">0</td>
<td style="text-align: right;">0</td>
<td style="text-align: right;">0</td>
<td style="text-align: right;">0</td>
<td style="text-align: right;">0</td>
<td style="text-align: right;">0</td>
<td style="text-align: right;">0</td>
</tr>
<tr class="even">
<td style="text-align: left;">Level rating: Almost Never</td>
<td style="text-align: right;">14</td>
<td style="text-align: right;">26</td>
<td style="text-align: right;">21</td>
<td style="text-align: right;">15</td>
<td style="text-align: right;">16</td>
<td style="text-align: right;">12</td>
<td style="text-align: right;">19</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Level rating: Sometimes</td>
<td style="text-align: right;">57</td>
<td style="text-align: right;">55</td>
<td style="text-align: right;">63</td>
<td style="text-align: right;">54</td>
<td style="text-align: right;">38</td>
<td style="text-align: right;">26</td>
<td style="text-align: right;">66</td>
</tr>
<tr class="even">
<td style="text-align: left;">Level rating: Often</td>
<td style="text-align: right;">83</td>
<td style="text-align: right;">82</td>
<td style="text-align: right;">85</td>
<td style="text-align: right;">86</td>
<td style="text-align: right;">64</td>
<td style="text-align: right;">38</td>
<td style="text-align: right;">91</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Level rating: Always</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">100</td>
</tr>
<tr class="even">
<td style="text-align: left;">Attribute Weighting</td>
<td style="text-align: right;">28</td>
<td style="text-align: right;">33</td>
<td style="text-align: right;">36</td>
<td style="text-align: right;">45</td>
<td style="text-align: right;">100</td>
<td style="text-align: right;">34</td>
<td style="text-align: right;">56</td>
</tr>
</tbody>
</table>
</div>
</div>
</figure>
</div>
</div>
<p>Level ratings (presented in <a href="#tbl-exampledata" class="quarto-xref">Table 1</a>) are converted to coefficients bounded between 0-1 (shown in <a href="#eq-level-rescale" class="quarto-xref">Equation 1</a>). Level rating coefficients are presented in <a href="#eq-level-matrix" class="quarto-xref">Equation 2</a>. Attribute weights (presented in <a href="#tbl-exampledata" class="quarto-xref">Table 1</a>) are then normalised to sum to the value of 1 by dividing each weight by the sum of all weights (shown in <a href="#eq-weight-normalise" class="quarto-xref">Equation 3</a>). Normalised attribute weights are presented in <a href="#eq-weight-vector" class="quarto-xref">Equation 4</a>.</p>
<p><span id="eq-level-rescale"><span class="math display">\[
L_{ij} \cdot 0.01
\tag{1}\]</span></span></p>
<p><span id="eq-level-matrix"><span class="math display">\[
L_{ij} =
\begin{bmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0.14 & 0.26 & 0.21 & 0.15 & 0.16 & 0.12 & 0.19 \\
0.57 & 0.55 & 0.63 & 0.54 & 0.38 & 0.26 & 0.66 \\
0.83 & 0.82 & 0.85 & 0.86 & 0.64 & 0.38 & 0.91 \\
1 & 1 & 1 & 1 & 1 & 1 & 1 \\
\end{bmatrix}
\tag{2}\]</span></span></p>
<p><span id="eq-weight-normalise"><span class="math display">\[
\frac{w_{j}}{\sum{w_j}}
\tag{3}\]</span></span></p>
<p><span id="eq-weight-vector"><span class="math display">\[
w_j = \begin{bmatrix}
0.08& 0.10& 0.11& 0.14& 0.30& 0.10& 0.17
\end{bmatrix}
\tag{4}\]</span></span></p>
<p>Combining the attribute weights (<a href="#eq-weight-vector" class="quarto-xref">Equation 4</a>) with the level coefficients (<a href="#eq-level-matrix" class="quarto-xref">Equation 2</a>) via element-wise multiplication (shown in <a href="#eq-element-wise-multiplication" class="quarto-xref">Equation 5</a> gives the coefficient matrix presented in <a href="#eq-coeff-matrix" class="quarto-xref">Equation 6</a>. Once the coefficient matrix has been estimated, preference values can be estimated on the 0-1 QALY scale where the worst health state (PITS state denoted 5555555) is zero and the best health state (denoted 1111111) is one. These latent coefficients must now be rescaled to incorporate the results from the PITS anchoring task so that the minimum utility value possible is equal to the PITS value.</p>
<p><span id="eq-element-wise-multiplication"><span class="math display">\[
L_{ij} \cdot w_{j} = {M}_{ij}
\tag{5}\]</span></span></p>
<p><span id="eq-coeff-matrix"><span class="math display">\[
M_{ij} =
\begin{bmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0.01 & 0.03 & 0.02 & 0.02 & 0.05 & 0.01 & 0.03 \\
0.05 & 0.05 & 0.07 & 0.07 & 0.11 & 0.03 & 0.11 \\
0.07 & 0.08 & 0.09 & 0.12 & 0.19 & 0.04 & 0.15 \\
0.08 & 0.10 & 0.11 & 0.14 & 0.30 & 0.10 & 0.17
\end{bmatrix}
\tag{6}\]</span></span></p>
<p>To rescale the latent coefficient matrix to incorporate the anchoring task, the coefficient matrix is multiplied by the compliment of the PITS value (shown in <a href="#eq-anchoring" class="quarto-xref">Equation 7</a>) to give the anchored coefficient matrix presented in <a href="#eq-anchored-matrix" class="quarto-xref">Equation 8</a>.</p>
<p><span id="eq-anchoring"><span class="math display">\[
M_{ij} \cdot (1-P) \quad \backepsilon \quad P = 0.2
\tag{7}\]</span></span></p>
<p><span id="eq-anchored-matrix"><span class="math display">\[
V_{ij} =
\begin{bmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0.01 & 0.02 & 0.02 & 0.02 & 0.04 & 0.01 & 0.02 \\
0.04 & 0.04 & 0.06 & 0.06 & 0.09 & 0.02 & 0.09 \\
0.06 & 0.06 & 0.07 & 0.10 & 0.15 & 0.03 & 0.12 \\
0.06 & 0.08 & 0.09 & 0.11 & 0.24 & 0.08 & 0.14 \\
\end{bmatrix}
\tag{8}\]</span></span></p>
<p>Once the attribute and level labels are reintroduced to the anchored coefficient matrix this forms the value set which presents the disutility corresponding to each attribute level combination presented in the WAItE. <a href="#tbl-example-valueset" class="quarto-xref">Table 2</a> presents the WAItE example PUF value set. <a href="#eq-HS123" class="quarto-xref">Equation 9</a> provides examples of how to estimate a utility value given a specific WAItE health state.</p>
<div class="cell">
<div id="tbl-example-valueset" class="cell quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-float-tbl figure">
<figcaption class="quarto-float-caption-top quarto-float-caption quarto-float-tbl" id="tbl-example-valueset-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Table 2: WAItE example PUF value set
</figcaption>
<div aria-describedby="tbl-example-valueset-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="cell-output-display">
<table class="do-not-create-environment cell caption-top table table-sm table-striped small">
<colgroup>
<col style="width: 19%">
<col style="width: 7%">
<col style="width: 9%">
<col style="width: 8%">
<col style="width: 16%">
<col style="width: 14%">
<col style="width: 14%">
<col style="width: 9%">
</colgroup>
<thead>
<tr class="header">
<th style="text-align: left;">Attribute level</th>
<th style="text-align: right;">Tired</th>
<th style="text-align: right;">Walking</th>
<th style="text-align: right;">Sports</th>
<th style="text-align: right;">Concentration</th>
<th style="text-align: right;">Embarrassed</th>
<th style="text-align: right;">Unhappiness</th>
<th style="text-align: right;">Treated</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">Never</td>
<td style="text-align: right;">0.00</td>
<td style="text-align: right;">0.00</td>
<td style="text-align: right;">0.00</td>
<td style="text-align: right;">0.00</td>
<td style="text-align: right;">0.00</td>
<td style="text-align: right;">0.00</td>
<td style="text-align: right;">0.00</td>
</tr>
<tr class="even">
<td style="text-align: left;">Almost Never</td>
<td style="text-align: right;">0.01</td>
<td style="text-align: right;">0.02</td>
<td style="text-align: right;">0.02</td>
<td style="text-align: right;">0.02</td>
<td style="text-align: right;">0.04</td>
<td style="text-align: right;">0.01</td>
<td style="text-align: right;">0.02</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Sometimes</td>
<td style="text-align: right;">0.04</td>
<td style="text-align: right;">0.04</td>
<td style="text-align: right;">0.06</td>
<td style="text-align: right;">0.06</td>
<td style="text-align: right;">0.09</td>
<td style="text-align: right;">0.02</td>
<td style="text-align: right;">0.09</td>
</tr>
<tr class="even">
<td style="text-align: left;">Often</td>
<td style="text-align: right;">0.06</td>
<td style="text-align: right;">0.06</td>
<td style="text-align: right;">0.07</td>
<td style="text-align: right;">0.10</td>
<td style="text-align: right;">0.15</td>
<td style="text-align: right;">0.03</td>
<td style="text-align: right;">0.12</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Always</td>
<td style="text-align: right;">0.06</td>
<td style="text-align: right;">0.08</td>
<td style="text-align: right;">0.09</td>
<td style="text-align: right;">0.11</td>
<td style="text-align: right;">0.24</td>
<td style="text-align: right;">0.08</td>
<td style="text-align: right;">0.14</td>
</tr>
</tbody>
</table>
</div>
</div>
</figure>
</div>
</div>
<p><span id="eq-HS123"><span class="math display">\[
\begin{aligned}
\text{Health State [5555555]} & \Rightarrow 1 - (0.06 + 0.08 + 0.09 + 0.11 + 0.24 + 0.08 + 0.14) = 0.20 \\
\text{Health State [5223445]} & \Rightarrow 1 - (0.06 + 0.02 + 0.02 + 0.06 + 0.15 + 0.03 + 0.14) = 0.52 \\
\text{Health State [2222222]} & \Rightarrow 1 - (0.03 + 0.02 + 0.01 + 0.01 + 0.02 + 0.02 + 0.04) = 0.85
\end{aligned}
\tag{9}\]</span></span></p>
</section>
</section>
<section id="aggregation-to-social-utility-function" class="level2">
<h2 class="anchored" data-anchor-id="aggregation-to-social-utility-function">Aggregation to social utility function</h2>
<p>The OPUF is designed to be able to estimate personal utility functions and so estimation occurs on an individual basis. Aggregating personal utility functions to a social utility function (SUF) takes place by taking a mean of all the individual personal utility functions from your sample. This operation is presented in <a href="#eq-meanvalueset" class="quarto-xref">Equation 10</a>.</p>
<p><span id="eq-meanvalueset"><span class="math display">\[
\bar{V}_{{ij}} = \frac{\sum_{V_{{ij}}}^{}}{N}
\tag{10}\]</span></span></p>
</section>
</section>
<section id="methods" class="level1">
<h1>Methods</h1>
<section id="recruitment" class="level2">
<h2 class="anchored" data-anchor-id="recruitment">Recruitment</h2>
<p>This study recruited 300 adults to respond to a quality-of-life survey hosted online. Study participants were recruited based on specific quotas (age, ethnicity and gender) to form a representative sample based on UK census data. The survey was hosted on the <a href="https://www.prolific.com">Prolific</a> platform which invited paid respondents to complete the WAItE version of the OPUF survey. A demonstration of the OPUF survey and questions is available <a href="https://survey.valorem.health/waite_opuf_adult2">here</a>. Informed consent was obtained at the outset of the survey and participants reserved the right to withdraw at any point without giving a reason. Participants who withdrew were not paid and their data deleted. Participation in this survey was estimated to take approximately fifteen minutes to complete and participants received £2.50 as a payment upon completion. This is in line with reimbursements rates from other OPUF studies <span class="citation" data-cites="Schneider2022TheStates Bray2024DevelopmentImpairment">(<a href="#ref-Schneider2022TheStates" role="doc-biblioref">10</a>,<a href="#ref-Bray2024DevelopmentImpairment" role="doc-biblioref">11</a>)</span> and is in line with recommended reimbursement rates from <a href="https://www.prolific.com">Prolific</a>. The survey was designed to be an unassisted survey administered online (no face-to-face contact) and no identifiable data was collected. Statistical analysis was conducted on the survey data. Newcastle University Medical School Ethics Committee approved this study (reference 49737/2023). The survey structure is detailed in <a href="#sec-surveystructure" class="quarto-xref">Section 2.2</a>.</p>
</section>
<section id="sec-surveystructure" class="level2">
<h2 class="anchored" data-anchor-id="sec-surveystructure">Survey structure</h2>
<ol type="1">
<li>Consent and Prolific ID: Participants were asked to consent to participate and enter their unique Prolific ID. This enables demographic information held by Prolific on their participants to be linked to each respondent.</li>
<li>WAItE descriptive system: Participants were asked to complete the WAItE descriptive system (presented in <a href="#fig-waite-descriptive" class="quarto-xref">Figure 4</a>) to describe their current health state.</li>
<li>Attribute selection: Participants were presented with the worst level for each WAItE attribute and asked to choose which health problem would have the most negative impact on their quality of life. The attribute chosen is then used in the subsequent attribute swing weighting task.</li>
<li>Attribute swing weighting: Participants were presented with each attribute in the WAItE and asked to consider an improvement from the worst level of that attribute to the best level of that attribute. Participants were asked to rank this improvement on a visual slider from 0-100 where the most important attribute (chosen in the previous task) is fixed at 100. Participants were reminded to use their most important attribute as a reference point.</li>
<li>Level rating: Participants were presented with a specific attribute of the WAItE and shown each level within that attribute. Levels best and worst (never and always) were fixed at 0 and 100 respectively. Participants were asked to rank the intermediate levels within each attribute using the fixed levels as a reference point.</li>
<li>Anchoring: Participants were presented with a binary choice asking whether they prefer the worst state of the WAItE (PITS state) or death. If participants choose the worst state of the WAItE, a second question is asked which asks them to rank the WAITE PITS state on a visual analogue scale where zero is labelled as being dead and one hundred is labelled as no health problems. If participants choose death in the binary choice, they were asked to rank being dead on a visual analogue scale where zero is labelled as the WAItE PITS state and one hundred is labelled as no health problems.</li>
<li>Survey feedback and demographic questions: Participants were asked about how difficult they found the task to complete and demographic information on age, gender, ethnicity, education, employment and weight status.</li>
</ol>
<div id="fig-waite-descriptive" class="quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-float-fig figure">
<div aria-describedby="fig-waite-descriptive-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<img src="https://willking98.github.io/opuf-adult/outputs/figures/WAItE%20descriptive.png" class="img-fluid figure-img" width="400">
</div>
<figcaption class="quarto-float-caption-bottom quarto-float-caption quarto-float-fig" id="fig-waite-descriptive-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Figure 4: WAItE descriptive system
</figcaption>
</figure>
</div>
</section>
<section id="sec-livesurvey" class="level2">
<h2 class="anchored" data-anchor-id="sec-livesurvey">Live survey</h2>
<div class="callout callout-style-default callout-note callout-titled">
<div class="callout-header d-flex align-content-center" data-bs-toggle="collapse" data-bs-target=".callout-1-contents" aria-controls="callout-1" aria-expanded="false" aria-label="Toggle callout">
<div class="callout-icon-container">
<i class="callout-icon"></i>
</div>
<div class="callout-title-container flex-fill">
Live Survey
</div>
<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div>
</div>
<div id="callout-1" class="callout-1-contents callout-collapse collapse">
<div class="callout-body-container callout-body">
<iframe width="800" height="600" src="https://survey.valorem.health/waite_opuf_adult2" title="Information">
</iframe>
</div>
</div>
</div>
</section>
<section id="missing-data" class="level2">
<h2 class="anchored" data-anchor-id="missing-data">Missing data</h2>
<p>Through the survey design process, the potential for large amounts of missing data was mitigated by ensuring responses were compulsory to certain questions. However for ethical reasons, we allowed participants to not answer the questions relating to death. For participants who do not provide responses to the anchoring questions, their responses were imputed using multiple imputation by chained equations (MICE) <span class="citation" data-cites="White2011MultiplePractice">(<a href="#ref-White2011MultiplePractice" role="doc-biblioref">12</a>)</span> which were informed by demographic information and attribute weighting responses.</p>
</section>
<section id="preference-heterogeneity" class="level2">
<h2 class="anchored" data-anchor-id="preference-heterogeneity">Preference heterogeneity</h2>
<p>As PUFs are estimated on an individual basis, exploring preference heterogeneity between individuals in the sample is straightforward. Investigating the heterogeneity of preferences between individuals, requires a measure of dis/similarity to quantify how far apart two PUFs are <span class="citation" data-cites="Schneider2024ExploringLevel">(<a href="#ref-Schneider2024ExploringLevel" role="doc-biblioref">13</a>)</span>. The measurement and estimation of preference heterogeneity in this section will follow methods detailed by Schneider et al. (2024) <span class="citation" data-cites="Schneider2024ExploringLevel">(<a href="#ref-Schneider2024ExploringLevel" role="doc-biblioref">13</a>)</span>. Each PUF estimated in this study was represented by a vector of 78,125 health state utility values for each respondent in the sample. In order to assess the dis/similarity between these PUFs, we used the euclidean difference measure (EUD). Analogous to a line between two points on a two dimensional plane, the EUD between two PUFs denotes the shortest path length in a 78,125 dimensional space. It is computed as the square root of the sum of the squared differences between the PUFs of individuals <span class="math inline">\(i\)</span> and <span class="math inline">\(j\)</span> (presented in <a href="#eq-EUD" class="quarto-xref">Equation 11</a>). Once PUFs have been estimated for all individuals in the sample, pairwise EUD was estimated for all possible pairwise combinations within the sample. Pairwise EUD was stored in an [N <span class="math inline">\(\times\)</span> N] distance matrix.</p>
<p><span id="eq-EUD"><span class="math display">\[
\begin{aligned}
d_{EUD}(i,j) & =\sqrt{\sum_{}^{}(u_{i}(s_{1})-u_{j}(s_{1}))^{2}+ ... +(u_{i}(s_{78125})-u_{j}(s_{78125}))^{2}}\\
& \backepsilon \quad \quad s = \{1111111, 2111111, ..., 5555555\}\\
\end{aligned}
\tag{11}\]</span></span></p>
</section>
<section id="permutational-analysis-of-variance" class="level2">
<h2 class="anchored" data-anchor-id="permutational-analysis-of-variance">Permutational analysis of variance</h2>
<p>Permutational analysis of variance (PERMANOVA), analogous to analysis of variance, is a geometric partitioning of variation across a multivariate data cloud, defined in the space of any given dissimilarity measure, in response to one or more groups <span class="citation" data-cites="Anderson2017 Anderson2013PERMANOVATesting">(<a href="#ref-Anderson2017" role="doc-biblioref">14</a>,<a href="#ref-Anderson2013PERMANOVATesting" role="doc-biblioref">15</a>)</span>. This method of statistical testing has been used most commonly in ecological research to test for population dispersion among different subgroups <span class="citation" data-cites="Souza2013PopulationEstuary">(<a href="#ref-Souza2013PopulationEstuary" role="doc-biblioref">16</a>)</span>. PERMANOVA decomposes the total distances between observations (SS<span class="math inline">\(_T\)</span>) into within-groups (SS<span class="math inline">\(_W\)</span>) and between groups sum-of-squares (SS<span class="math inline">\(_B\)</span>). <a href="#eq-sumsquares" class="quarto-xref">Equation 12</a> details the estimation of total and within-groups sum-of-squares. Mathematical notation presented here is reproduced from Schneider et al. (2024) <span class="citation" data-cites="Schneider2024ExploringLevel">(<a href="#ref-Schneider2024ExploringLevel" role="doc-biblioref">13</a>)</span> for consistency.</p>
<p><span id="eq-sumsquares"><span class="math display">\[
SS_{T} = \frac{1}{N}\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}d(i,j)^{2}; \quad SS_{W} = \sum_{i=1}^{N-1}\sum_{j=i+1}^{N}d(i,j)^{2}\epsilon_{ij}^{\ell}/n_{\ell}
\tag{12}\]</span></span></p>
<p>where N is the total sample size (=300), <span class="math inline">\(d(i,j)^2\)</span> is the squared distance between the PUFs of participants <span class="math inline">\(i\)</span> and <span class="math inline">\(j\)</span>, <span class="math inline">\(\epsilon_{i,j}\)</span> indicator which is 1, if participants <span class="math inline">\(i\)</span> and <span class="math inline">\(j\)</span> belong to the same group, and 0 if they do not, and <span class="math inline">\(n_{\ell}\)</span> is the size for group <span class="math inline">\(\ell\)</span>. Then, SS<span class="math inline">\(_B\)</span> can then be calculated as SS<span class="math inline">\(_B\)</span> = SS<span class="math inline">\(_T\)</span> – SS<span class="math inline">\(_W\)</span>, which allows calculating the pseudo F statistic for <span class="math inline">\(p\)</span> groups:</p>
<p><span id="eq-ssb"><span class="math display">\[
F= \frac{(\frac{SS_B}{p-1})}{(\frac{SS_W}{N-p})}
\tag{13}\]</span></span></p>
<p>Further details about the mathematical and statistical properties of PERMANOVA are available elsewhere <span class="citation" data-cites="Schneider2024ExploringLevel Anderson2017 Anderson2013PERMANOVATesting">(<a href="#ref-Schneider2024ExploringLevel" role="doc-biblioref">13</a>–<a href="#ref-Anderson2013PERMANOVATesting" role="doc-biblioref">15</a>)</span>. In this study, we used PERMANOVA to explore the variability in WAItE health state preferences (individual value sets) between various subgroups. A multivariate PERMANOVA model was estimated with subgroups of: age, gender, self-reported weight status, education, employment status and ethnicity.</p>
</section>
<section id="sensitivity-analysis" class="level2">
<h2 class="anchored" data-anchor-id="sensitivity-analysis">Sensitivity analysis</h2>
<p>In an experimental sensitivity analysis, preference heterogeneity was assessed using EUD estimated based on individual’s personal utility functions anchored using the social PITS utility value (henceforth referred to as EUD2). This differed to prior preference heterogeneity estimation as individual variation in PITS utility values were not included in the EUD2 estimation. EUD2 was entirely composed by differences in level ratings and attribute weights. Further details on the derivation of EUD2 are presented in the online <a href="https://willking98.github.io/opuf-adult/">Appendix</a>.</p>
<p>An additional analysis of preference heterogeneity in anchoring values was conducted using a generalised linear model. A multivariate Gamma GLM (with log-link function) was constructed to explore the relationship between PITS utility values and demographic information. This facilitated exploration into how anchoring preferences differed among different demographic subgroups in our sample.</p>
</section>
</section>
<section id="results" class="level1">
<h1>Results</h1>
<section id="study-participants" class="level2">
<h2 class="anchored" data-anchor-id="study-participants">Study participants</h2>
<p>A sample of 334 individuals were approached to participate in the study via the survey company <a href="https://www.prolific.com">Prolific</a>. Individuals that successfully inputted their unique Prolific ID and obtained a correct completion code from the end of the study were included in the analysis sample and received a small payment (£2.50) for their participation. Seven participants were excluded from the study as they had an incorrect completion code and did not enter the correct unique Prolific ID. Therefore, no data was available on those seven participants and they were excluded from the analysis. An additional participant was excluded from the analysis due to completing the survey in eighteen seconds (well under the pre-specified minimum time limit of 2 minutes). Two respondents timed-out while completing the survey and were therefore not included. Twenty-four individuals chose not complete the study (referred to by Prolific as ‘returned’ participants). This left an analysis sample of N=300 participants who successfully completed the survey. The sample was representative of the UK based on age, gender and ethnicity. A summary of demographic information collected in the OPUF are presented in <a href="#tbl-demographic-html" class="quarto-xref">Table 4</a>.</p>
</section>
<section id="survey-duration" class="level2">
<h2 class="anchored" data-anchor-id="survey-duration">Survey duration</h2>
<p>The mean (SD) and median (IQR) survey completion time in minutes was 9.66 (5.85) and 8.15 (5.88; 11.89). <a href="#tbl-time" class="quarto-xref">Table 3</a> summarises how much time was spent completing each individual section of the survey.</p>
<div class="cell">
<div id="tbl-time" class="cell quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-float-tbl figure">
<figcaption class="quarto-float-caption-top quarto-float-caption quarto-float-tbl" id="tbl-time-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Table 3: Survey completion times (secs)
</figcaption>
<div aria-describedby="tbl-time-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="cell-output-display">
<table class="do-not-create-environment cell caption-top table table-sm table-striped small">
<colgroup>
<col style="width: 29%">
<col style="width: 20%">
<col style="width: 30%">
<col style="width: 8%">
<col style="width: 10%">
</colgroup>
<thead>
<tr class="header">
<th style="text-align: left;">Section</th>
<th style="text-align: right;">Mean (SD)</th>
<th style="text-align: right;">Median (Q1; Q3)</th>
<th style="text-align: right;">Min</th>
<th style="text-align: right;">Max</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">WAItE</td>
<td style="text-align: right;">73.0 (90.1)</td>
<td style="text-align: right;">53.0 (38.0; 77.0)</td>
<td style="text-align: right;">10.0</td>
<td style="text-align: right;">1066.0</td>
</tr>
<tr class="even">
<td style="text-align: left;">Attribute ranking</td>
<td style="text-align: right;">35.4 (50.6)</td>
<td style="text-align: right;">26.0 (16.0; 40.0)</td>
<td style="text-align: right;">2.0</td>
<td style="text-align: right;">741.0</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Attribute weighting</td>
<td style="text-align: right;">115.7 (94.9)</td>
<td style="text-align: right;">91.5 (69.8; 142.2)</td>
<td style="text-align: right;">18.0</td>
<td style="text-align: right;">1380.0</td>
</tr>
<tr class="even">
<td style="text-align: left;">Level rating</td>
<td style="text-align: right;">220.5 (206.4)</td>
<td style="text-align: right;">171.0 (119.0; 249.0)</td>
<td style="text-align: right;">34.0</td>
<td style="text-align: right;">2158.0</td>
</tr>
<tr class="odd">
<td style="text-align: left;">PITS vs death</td>
<td style="text-align: right;">25.5 (45.4)</td>
<td style="text-align: right;">16.5 (11.0; 25.2)</td>
<td style="text-align: right;">4.0</td>
<td style="text-align: right;">620.0</td>
</tr>
<tr class="even">
<td style="text-align: left;">PITS-VAS</td>
<td style="text-align: right;">37.3 (39.2)</td>
<td style="text-align: right;">29.0 (21.0; 45.0)</td>
<td style="text-align: right;">5.0</td>
<td style="text-align: right;">605.0</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Total (secs)</td>
<td style="text-align: right;">579.5 (351.1)</td>
<td style="text-align: right;">489.2 (352.5; 713.4)</td>
<td style="text-align: right;">126.7</td>
<td style="text-align: right;">3738.2</td>
</tr>
<tr class="even">
<td style="text-align: left;">Total (mins)</td>
<td style="text-align: right;">9.66 (5.85)</td>
<td style="text-align: right;">8.15 (5.88; 11.89)</td>
<td style="text-align: right;">2.11</td>
<td style="text-align: right;">62.30</td>
</tr>
</tbody>
</table>
</div>
</div>
</figure>
</div>
</div>
</section>
<section id="waite-descriptive-system" class="level2">
<h2 class="anchored" data-anchor-id="waite-descriptive-system">WAItE descriptive system</h2>
<p>Responses to the WAItE descriptive system are presented in <a href="#tbl-demographic-html" class="quarto-xref">Table 4</a>. Feeling tired and avoiding doing sport were the attributes that were most frequently experienced by participants in our analysis sample. WAItE summary statistics were in line with results from previous studies <span class="citation" data-cites="Robinson2019EstimatingEvaluation">(<a href="#ref-Robinson2019EstimatingEvaluation" role="doc-biblioref">17</a>)</span>.</p>
<div class="cell">
<div id="tbl-demographic-html" class="cell quarto-float quarto-figure quarto-figure-center anchored">
<figure class="quarto-float quarto-float-tbl figure">
<figcaption class="quarto-float-caption-top quarto-float-caption quarto-float-tbl" id="tbl-demographic-html-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
Table 4: Summary of demographic information collected in the OPUF
</figcaption>
<div aria-describedby="tbl-demographic-html-caption-0ceaefa1-69ba-4598-a22c-09a6ac19f8ca">
<div class="cell-output-display">
<table class="do-not-create-environment cell caption-top table table-sm table-striped small">
<thead>
<tr class="header">
<th style="text-align: left;">Participant Characteristics (N=300)</th>
<th style="text-align: right;">N (%)</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: left;">Age</td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;">18-24</td>
<td style="text-align: right;">32 (10.9%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">25-34</td>
<td style="text-align: right;">50 (17%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">35-44</td>
<td style="text-align: right;">48 (16.3%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">45-54</td>
<td style="text-align: right;">49 (16.7%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">55-64</td>
<td style="text-align: right;">81 (27.6%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">65-90</td>
<td style="text-align: right;">34 (11.6%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Not Stated</td>
<td style="text-align: right;">6 (2.0%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Gender</td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;">Female</td>
<td style="text-align: right;">154 (51%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Male</td>
<td style="text-align: right;">144 (48%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Non-binary</td>
<td style="text-align: right;">1 (0%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Ethnicity</td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;">White</td>
<td style="text-align: right;">251 (84%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Asian</td>
<td style="text-align: right;">23 (8%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Black</td>
<td style="text-align: right;">11 (4%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Mixed</td>
<td style="text-align: right;">10 (3%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Other</td>
<td style="text-align: right;">5 (2%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Weight Status</td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;">Normal</td>
<td style="text-align: right;">154 (51%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Overweight</td>
<td style="text-align: right;">104 (35%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Obese</td>
<td style="text-align: right;">30 (10%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Underweight</td>
<td style="text-align: right;">8 (3%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Prefer not to say</td>
<td style="text-align: right;">4 (1%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Education</td>
<td style="text-align: right;"></td>
</tr>
<tr class="even">
<td style="text-align: left;">Degree</td>
<td style="text-align: right;">147 (49%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">A Level</td>
<td style="text-align: right;">64 (21%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Higher Education</td>
<td style="text-align: right;">46 (15%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Other</td>
<td style="text-align: right;">20 (7%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">GCSE A-C</td>
<td style="text-align: right;">18 (6%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">GCSE D-G</td>
<td style="text-align: right;">5 (2%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Occupation</td>
<td style="text-align: right;"></td>
</tr>
<tr class="odd">
<td style="text-align: left;">Full-time</td>
<td style="text-align: right;">130 (43%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Part-time</td>
<td style="text-align: right;">62 (21%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Not Paid</td>
<td style="text-align: right;">30 (10%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Other</td>
<td style="text-align: right;">31 (10%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Student</td>
<td style="text-align: right;">17 (6%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Unemployed</td>
<td style="text-align: right;">18 (6%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Not Stated</td>
<td style="text-align: right;">9 (3%)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Starting a New Job</td>
<td style="text-align: right;">3 (1%)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">WAItE</td>
<td style="text-align: right;">Mean (SD)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Tiredness</td>
<td style="text-align: right;">3.4 (0.8)</td>
</tr>
<tr class="odd">
<td style="text-align: left;">Walking</td>
<td style="text-align: right;">2.1 (1.1)</td>
</tr>
<tr class="even">
<td style="text-align: left;">Sport</td>
<td style="text-align: right;">3.3 (1.3)</td>