Mapping to estimate health state utility: a systematic review of development and limitations

Abstract

Background

Health utility measurement is critical for cost-utility analysis (CUA). However, clinical studies often lack direct utility data, and methods of measuring health utility vary across different periods and regions, resulting in missing utility information. Mapping, a method employed to infer utility when direct utility data is absent, has been widely applied in recent years but still faces challenges. This systematic review evaluates the current landscape, trends, and limitations of mapping studies and provides recommendations for improving study design and reporting standards.

Methods

A literature search was conducted in PubMed, Web of Science, and the HERC Database of Mapping Studies from 2018 to 2024. The study extracted information from the included studies and performed quality assessments based on existing mapping guidelines.

Results

One hundred thirty-one studies were included, 92 focused on Mapping as the primary objective, five were reviews, 13 focused on methodology, and 21 focused on economic evaluation. The source measure, target measure, and models in mapping functions development remain EORTC-QLQ-C30 (n = 13), EQ-5D (n = 79), and OLS (n = 93). Studies now use larger sample sizes and a higher proportion of response Mapping, and model applications have increased in diversity. However, 32 studies still lack conceptual overlap analysis, and only 16 studies with repeated measurements addressed its issue. Additionally, two studies did not report the region of the sample and value set, while 27 had inconsistencies between the two regions.

Conclusions

In the last seven years, mapping studies have improved sample size, model application, and result reporting. However, limitations remain in analysing conceptual overlap, ensuring alignment between the sample and value set regions, and processing repeated measurements. To advance the quality of mapping studies, it is necessary to update mapping guidelines and ensure that all mapping functions are developed in compliance with them.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12955-025-02426-3.

Introduction

The allocation of medical resources is often guided by Health Technology Assessment (HTA), where cost-effectiveness analysis (CUA) is a commonly used economic evaluation method. In CUA, utility is frequently measured through Quality Adjusted Life Years (QALY) [1]. QALY combines Health-Related Quality of Life (HRQoL) with life expectancy, calculated as the product of the Health State Utility Value (HSUV) and survival time. HSUV is determined using Preference-Based Measures (PBM), which assess HRQoL across dimensions such as physical function, pain, social function, and emotional well-being. PBM then calculates HSUV by applying a value set to the severity levels of each dimension [2]. Current PBM includes EuroQOL five dimensions questionnaire (EQ-5D), Short form 6 dimensions (SF-6D), Health utility index Mark 3 (HUI-3), and Child health utility nine dimensions (CHU-9D), with EQ-5D and SF-6D being the most widely used [3]. However, most clinical studies do not use PBM to measure HSUV [4–6]. Instead, they frequently rely on disease-specific, non-preference-based Patient-reported outcome measures (PROMs) to gather data on effectiveness and other non-economic indicators [7]. Incorporating PBM can increase administrative time and costs, burdening researchers and participants. Additionally, different HTA agencies recommend various PBM depending on the period and region [5, 8, 9], and results can vary among PBM [2, 10–15]. Even for the same PBM, results may not be directly comparable due to differences in versions or value sets [1, 16–19]. Furthermore, PBM inconsistency or absence issues often arise when CUA involves clinical data across different times or regions. These factors contribute to gaps in the utility data required for CUA.

Mapping is a method for establishing a connection between the source and target measure, using a mapping function to estimate the target measure value based on existing measurements. This approach helps bridge the gap between available evidence and the information required for CUA [1, 5]. Mapping can also convert results from different PBMs into a single PBM, thus enhancing comparability [14]. This method, also known as "Cross-Walking" or "Transfer to Utility," is considered a suboptimal option when PBMs are missing in existing studies. It has recently been recommended by the Chinese Pharmaceutical Association [9] and the National Institute for Health and Care Excellence (NICE) [20]. Between 2000 and 2019, 28.85% of HTAs conducted through the single technology appraisal (STA) process derived utility values through mapping [21]. Mapping is divided into direct and indirect methods. Direct mapping estimates the HSUV of the target measure directly from the source measure. In contrast, indirect mapping is a two-step process: the first step estimates the HRQoL for each dimension of the target measure based on the source measure, and the second combines these HRQoL with a value set to calculate the HSUV [1, 5]. Direct mapping does not require HRQoL for each dimension of the target measure, making it simpler to implement. However, the HSUV produced is based on a region-specific value set and omits detailed information on each dimension of the target measure. Although indirect mapping requires more comprehensive data, it allows for responses to each dimension of the target measure and, in the second step, can calculate HSUV according to region-specific value sets, resulting in a mapping function with broader applicability [18].

NICE, the International Society for Pharmacoeconomics and Outcomes Research (ISPOR), Oxford University, and the University of Sheffield have all published mapping guidelines [4, 22–24] to provide comprehensive guidance on various aspects of mapping studies. In addition to these four guidelines, Oxford University's Health Economics Research Centre (HERC) developed a mapping study database targeting EQ-5D and produced a related review [25]. However, recent reviews mostly focus on specific aspects of mapping studies, such as rare diseases [20], data relevance [26], and mapping from PROMIS-29 to EQ-5D [2], while neglecting to examine conceptual overlap as well as the consistency between the sample region and the value set region. Furthermore, The most recent systematic review inclusion date was October 2018 [1], which no longer reflects the current mapping studies state and needs updating.

Recently, extensive discussion has emerged concerning using QALY [27–29]. If QALY were to be replaced by a new metric, the mapping would facilitate a transition between QALY and the new metric, thus supporting economic evaluations of pharmaceuticals across different periods. In summary, mapping plays a crucial role in health economic evaluations when health utility evidence is lacking, making high-quality mapping practices an immediate priority. This systematic review aims to review recent mapping studies and analyse the current landscape of mapping research. It investigates the conceptual overlap and regional consistency between the sample population and value set that have been neglected in previous studies. The review seeks to reveal the latest developments and limitations in mapping research, providing recommendations for advancing high-quality mapping studies.

Methods

This systematic review was registered in PROSPERO (ID: CRD420250651687). It complies with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 statement and will be reported based on the PRISMA 2020 checklist.

Data sources and search strategy

The review searched three databases: PubMed, Web of Science, and the HERC Database of Mapping Studies [30], with searches finalized by December 31, 2024. The search strategy included multiple terms related to mapping, such as “mapp*,” “map,” “cross walk,” “crosswalk*,” and “transfer to utility,” combined with health preference-related keywords like “healthutilit*,” “QALY,” “quality of life,” “qol,” “health state utilit*,” “health state value,” “utility score,” “utility index,” “PBM,” “preference-based,” and “preference based.” PubMed and Web of Science searches were limited to subject headings and the Social Sciences index. The results from PubMed and Web of Science were merged with those collected from the HERC Database of Mapping Studies. Further details on the search strategy are provided in Additional file 1.

Inclusion criteria

The latest systematic review of Mapping included studies up to October 2018 [1]. This review only includes studies published after this date to analyse development trends in mapping studies and enable comparative analysis. After merging the results from the three databases and removing duplicates, three rounds of screening were conducted: title, abstract, and full text. At the title screening stage, studies were excluded if they were unrelated to quality of life, focused solely on analysing factors influencing quality of life, examined the structure or application of patient-reported outcome measures, or were scoping reviews. At the abstract screening stage, studies were excluded if they merely compared the structures of scales, investigated preferences, reported utility statistics, or presented outcomes that were not preference-based. Finally, at the full-text screening stage, outside the designated study period, CEA that did not derive utility values through mapping and studies solely seeking HSUV evidence was excluded. In order to offer a thorough analysis of mapping research, we include not only original studies on developing mapping algorithms but also relevant reviews, methodological studies, and economic evaluation applications.

Study selection

The studies screening process involved three reviewers. two reviewers (Q. S., Y. Z.) independently screened the studies, and after both completed their screenings, a third reviewer (L. S.) consolidated the results. Any discrepancies in the consolidated results were discussed with the other reviewers to reach a final consensus.

Data extraction and quality assessment

Data was extracted from studies that focused on mapping as the primary objective. The research team extracted data from all eligible publications using a standardized extraction table, and two reviewers (Q. S., Y. Z.) independently extracted information from the included records. Three checklists and one technical support document guided the development of the extraction table and served as quality assessment criteria. These resources included the MAPS checklist [23], the ISPOR Good Practices for Outcomes Research report on “Mapping to Estimate Health-State Utility from Non-Preference-Based Outcome Measures” [4], the University of Sheffield’s mapping practice recommendations [24], and NICE’s mapping technical support document [31].

To comprehensively evaluate the reporting quality of Mapping studies, a set of 27 quality assessment criteria was developed based on the checklists and technical support documents. These criteria cover various aspects of mapping research, including the content of the title and abstract, sample characteristics, country, source and target measures, value sets, data processing, models, variables, validation, and external generalizability. Detailed quality assessment information is provided in Additional file 2. On this basis, to reflect the current state of mapping research, data was extracted on bibliographic details, source measures, target measures, sample size, the countries of the sample and value set, methods for assessing conceptual overlap, data processing methods, mapping approaches and models, covariates, and validation methods. Detailed extraction information is provided in Additional file 3.

Results

Studies included

Figure 1 illustrates an overview of the search and selection processes. A total of 2962 studies were considered for this systematic review. After excluding 707 duplicates, 2255 studies remained. Following title screening, 1521 studies were excluded, leaving 734 studies. Subsequently, 347 studies were excluded based on abstract screening, resulting in 387 studies for full-text screening. After full-text assessment and chronological filtering, 131 studies were included in the final analysis [1, 2, 5, 7, 8, 10, 12, 14, 19, 20, 26, 32–151].

Fig. 1.

Study selection flowchart

Among the 131 studies, 92 focused on Mapping as the primary objective, 21 on economic evaluation, 13 on methodology, and five reviews. Among the reviews, one study examined the impact of repeated measurements on mapping and found that repeated measurements can lead to underestimating standard errors. Another review focused on mapping in rare diseases, revealing that such studies generally have small sample sizes, and the floor effect associated with the severity of rare diseases may compromise prediction accuracy. Three additional reviews were conducted, one analysing the mapping from PROMIS-29 to EQ-5D, one Summarizing Mapping studies of PROMs used in hip, knee, and shoulder replacement Surgeries, and another reviewing Mapping studies published between January 2007 and October 2018.

Among the 13 studies focused on methodology, six examined Mapping models, two focused on the selection and application of value sets, two addressed issues related to sample size and data processing, and the remaining 3 validated the reliability of Mapping. The 21 economic evaluation studies covered disease areas including nervous system diseases (n = 5), musculoskeletal and connective tissue diseases (n = 6), male reproductive system diseases (n = 3), respiratory diseases (n = 1), endocrine, nutritional, and metabolic diseases (n = 1), and complications and related care during pregnancy, childbirth, and the puerperium (n = 1).

Source and target measure

In a review of 92 studies focused on Mapping as the primary objective, 13 studies (14.13%) utilized multiple source measures, while 17 studies (18.48%) employed various target measures. By treating each target measure individually as a separate Mapping function, there are 113 mapping functions in total (Table 2).

Table 2.

Mapping functions information statistics

Target Measure	Sample			Mapping methods			Average application quantity of model		Average application quantity of covariate	Validation methods			Average application quantity of performance evaluation indicators	Average application quantity of prediction ability charts	Subgroup analysis
	Min	Mean	Max	Direct	Response	Both	Direct	Response		Internal	External	Both			Yes	No
EQ-5D-5L (53,46.90%)	71	741.20	5708	32 (60.38%)	0 (0%)	21 (39.62%)	3.47	1.36	2.08	47 (88.68%)	1 (1.89%)	5 (9.43%)	3.58	0.94	25 (47.17%)	28 (52.83%)
EQ-5D-3L (26,23.01%)	172	7917.94	49,999	11 (42.31%)	3 (11.54%)	12 (46.15%)	3.30	1.53	1.46	24 (92.31%)	0 (0%)	2 (7.69%)	3.35	0.92	14 (53.85%)	12 (46.15%)
SF-6D (11,9.73%)	239	3968.45	36,706	6 (54.55%)	0 (0%)	5 (45.45%)	2.82	1.00	2.81	10 (90.91%)	0 (0%)	1 (9.09%)	4.36	0.55	5 (45.45%)	6 (54.55%)
HUI-3 (6,5.31%)	209	1346.83	6348	5 (83.33%)	0 (0%)	1 (16.67%)	2.33	1.00	0.67	6 (100%)	0 (0%)	0 (0%)	4.00	0.83	2 (33.33%)	4 (66.67%)
SF-6Dv2 (6,5.31%)	389	1173.50	3320	6 (10.00%)	0 (0%)	0 (0%)	4.00	NA	2.17	5 (83.33%)	0 (0%)	1 (16.67%)	4.33	1.00	3 (50.00%)	3 (50.00%)
CHU9D (3,2.65%)	108	2913.67	6898	2 (66.67%)	0 (0%)	1 (33.33%)	4.67	1.00	2.33	2 (66.67%)	0 (0%)	1 (33.33%)	2.67	0.33	2 (66.67%)	1 (33.33%)
ReQoL-UI (2,1.77%)	1340	1956.50	2573	1 (50.00%)	0 (0%)	1 (0.5)	2.50	1.00	2.00	2 (100%)	0 (0%)	0 (0%)	5.00	1.50	0 (0%)	2 (100%)
15D (1,0.88%)	228	228.00	228	0 (0%)	0 (0%)	1 (100%)	3.00	1.00	2.00	1 (100%)	0 (0%)	0 (0%)	3.00	0.00	0 (0%)	1 (100%)
AQoL-8D (1,0.88%)	61	61.00	61	1 (100%)	0 (0%)	0 (0%)	3.00	NA	2.00	1 (100%)	0 (0%)	0 (0%)	2.00	1.00	0 (0%)	1 (100%)
AQoL-4D (1,0.88%)	3376	3376.00	3376	1 (100%)	0 (0%)	0 (0%)	7.00	NA	2.00	1 (100%)	0 (0%)	0 (0%)	3.00	1.00	1 (100%)	0 (0%)
MSIS-8D (1,0.88%)	1056	1056.00	1056	1 (100%)	0 (0%)	0 (0%)	2.00	NA	2.00	1 (100%)	0 (0%)	0 (0%)	2.00	1.00	1 (100%)	0 (0%)
CHU-9D (1,0.88%)	2152	2152.00	2152	0 (0%)	0 (0%)	1 (100%)	5.00	1.00	2.00	1 (100%)	0 (0%)	0 (0%)	4.00	1.00	0 (0%)	1 (100%)
VFQ-UI (1,0.88%)	2778	2778.00	2778	1 (100%)	0 (0%)	0 (0%)	1.00	NA	2.00	1 (100%)	0 (0%)	0 (0%)	5.00	2.00	0 (0%)	1 (100%)
Total (113)	61	2282.24	49,999	67 (59.29%)	3 (2.65%)	43 (38.05%)	3.39	1.11	1.96	102 (90.27%)	1 (0.88%)	10 (8.85%)	3.56	0.93	53 (46.9%)	60 (53.1%)

In the parentheses following each target measure, the number and percentage represent the count of studies utilizing that specific target measure and its proportion relative to the total number of target measures. Abbreviation definitions are provided in the List of Abbreviations

The frequency of source measure utilization is presented in Table 1. The most prevalent instruments observed were the EORTC-QLQ series, including EORTC QLQ-C30 (n = 13), EORTC QLQ-H&N35 (n = 3), EORTC QLQ-CR29 (n = 1), and EORTC QLQ-BR53 (n = 1). This was followed by the FACT series, comprising FACT-B (n = 3), FACT-G (n = 3), and FACT-L (n = 1). Notably, most source measures (n = 104) were identified as non-preference-based instruments. However, two studies applied the PBM, specifically the EQ-5D-5L (n = 2) mapped to SF-6Dv2 and EQ-5D-3L. As illustrated in Table 2, the most frequently applied target measure was EQ-5D-5L (n = 53, 46.90%), followed by EQ-5D-3L (n = 26, 23.01%) and SF-6D (n = 11,9.73%).

Table 1.

Frequency of source measure application

n > 3	3 ≥ n > 1	n = 1
EORTC QLQ-C30 (13)	EORTC QLQ-H&N35 (3)	5-D itch scale (1)	EPIC (1)	IWQOL-Lite (1)	OP (1)	QOLIE-31-P2 (1)	WHODAS 2.0–12 (1)
	FACT-B (3)	AcroQoL (1)	ESAS-r: Renal (1)	KOOS (1)	OSS (1)	RAND-12 (1)	WHOQOL-BREF (1)
	FACT-G (3)	ADCS-ADL (1)	FAACT (1)	Lequesne Functional Index (1)	PANSS (1)	SAQ (1)	WHOQOL-HIV Bref (1)
	MLHFQ (3)	ALSFRS-R (1)	FACIT-F (1)	LTCQ-8 (1)	PCI (1)	SBI (1)	WI-NRS (1)
	BASDAI (2)	BCVA (1)	FACT-L (1)	MacNew (1)	PDI (1)	SDQ (1)	WOMAC (1)
	BASFI (2)	CH-QLQ2 (1)	FAQLQ-PF (1)	MAX-PC (1)	PDQ-8 (1)	SF-36 (1)
	CAT (2)	CLDQ-NASH (1)	FSS (1)	MENQOL (1)	PedsQL 4.0 (1)	Spanish National Health Survey functional disability scale (1)
	EQ-5D-5L (2)	CPCHILD (1)	GAD-7 (1)	MOS-HIV (1)	PedsQL GCS (1)	SQLS (1)
	FACT-H&N (2)	DLQI (1)	GHQ-12 (1)	MSQ (1)	PedsQL (1)	SWEMWBS (1)
	HAQ-DI (2)	EORTC QLQ-BR53 (1)	Haem-A-QoL (1)	ODI (1)	PHQ-9 (1)	TCM-HSS (1)
	HIT-6 (2)	EORTC QLQ-CR29 (1)	HeartQoL (1)	OHS (1)	PROMIS-GH10 (1)	UWQoL (1)
	PROMIS-29 (2)	EPDS (1)	IBS-QoL (1)	OKS (1)	QoL-AD (1)	WHODAS 2.0 (1)

The values in parentheses following each source measure indicate the number of studies that applied that source measure. Abbreviation definitions are provided in the List of Abbreviations

Sample and estimation methods

The reported sample sizes varied significantly, with the smallest being 61 [108] and the largest being 49999 [12] (Table 2). Only three studies (3.26%) had a sample size below 100. Among target measures with multiple Mapping functions, 38.05% of the mapping functions considered both direct and response mapping. For less frequently applied target measures, such as HUI-3 and CHU9D, a higher proportion of mapping functions only employed direct mapping (83.33% and 66.67%). In contrast, among the more commonly used target measures, studies using EQ-5D-3L and SF-6D showed the highest proportions of adopting both mapping methods (39.62% and 45.45%). However, the proportion for EQ-5D-5L was comparatively lower (39.62%), and all studies employing SF-6Dv2 adopted only direct mapping.

Most mapping functions used more than one regression method (n =94, 83.19%), among studies employing direct Mapping, the average number of models used exceeded 3 (Table 2), although 17 studies employed only one model. 36 distinct Mapping model types were employed in total Mapping functions, comprising 369 models (Table 3). The most frequently applied model for direct mapping was OLS (n = 93, 25.20%), followed by Tobit regression (n = 56, 15.18%), GLM (n = 40, 10.84%), and CLAD (n = 37, 10.03%). Additionally, ALDVMM (n = 27, 7.32%), BETAMIX (n = 25, 6.78%), and TPM (n = 21, 5.69%) were also used to some extent (Table 3). In contrast, response Mapping utilized 17 distinct model types, comprising 61 models (Table 3). Mapping functions employing response mapping used an average of only one model, predominantly OLM (n = 19, 31.15%) and ML (n = 12, 19.67%).

Table 3.

Mapping functions information extraction

Target measure	Models		Covariate	Internal validation methods	Predictive performance metrics	Predictive assessment plots
	Direct	Response
EQ-5D-5L (53,46.90%)	OLS (45,84.91%)	OLM (10,18.87%)	Age (39,73.58%)	Sample splitting (15,28.3%)	MAE (45,84.91%)	Scatter Plot Comparing Observed and Predicted Values (25,47.17%)
	Tobit regression (28,52.83%)	ML (5,9.43%)	Gender (33,62.26%)	tenfold cross-validation (14,26.42%)	RMSE (38,71.7%)	Bland–Altman Plot (13,24.53%)
	GLM (19,35.85%)	GLOGIT (2,3.77%)	BMI (4,7.55%)	Full-sample resubstitution validation (11,20.75%)	AIC (17,32.08%)	Error Histogram (7,13.21%)
	CLAD (17,32.08%)	OPM (2,3.77%)	Treatment and clinical management factors (15,28.3%)	fivefold cross-validation (7,13.21%)	MSE (14,26.42%)	CDF Plot (4,7.55%)
	ALDVMM (16,30.19%)	MVP (1,1.89%)	Other disease characteristics/health status factors (11,20.75%)	Validation in temporally distinct datasets (2,3.77%)	BIC (13,24.53%)	Histogram Comparing Observed and Predicted Values (1,1.89%)
	BETAMIX (15,28.3%)	SUR-OPM (1,1.89%)	Other demographic/socioeconomic factors (6,11.32%)	Bootstrap validation (2,3.77%)	Adj R2 (12,22.64%)	Failure to account for predictive assessment plots (12,22.64%)
	TPM (13,24.53%)	GEE (1,1.89%)	Failure to account for covariate (10,18.87%)	ninefold cross-validation (2,3.77%)	ICC (11,20.75%)
	MM (7,13.21%)	OLR (1,1.89%)		Leave-one-out cross-validation (1,1.89%)	R2 (10,18.87%)
	Beta regression (6,11.32%)	GOPM (1,1.89%)		threefold cross-validation (1,1.89%)	CCC (6,11.32%)
	FLOGIT (3,5.66%)	GBT (1,1.89%)			Spearman's ρ (4,7.55%)
	GEE (2,3.77%)	MVOPR (1,1.89%)			ME (3,5.66%)
	Mixed-effects linear regression (2,3.77%)	BN (1,1.89%)			AE (3,5.66%)
	RMM (1,1.89%)	MLR (1,1.89%)			nRMSE (2,3.77%)
	MFP (1,1.89%)	Failure to account for response mapping (32,60.38%)			Pred R2 (2,3.77%)
	FEM (1,1.89%)				nMAE (2,3.77%)
	FRM (1,1.89%)				Pearson's r (1,1.89%)
	REM (1,1.89%)				Lin’s CCC (1,1.89%)
	Mixed-effects Tobit regression (1,1.89%)				MID (1,1.89%)
	Three part models (1,1.89%)				GMSE (1,1.89%)
	GBT (1,1.89%)				AICC (1,1.89%)
	Beta regression-inflated GAMLSS (1,1.89%)				GMAE (1,1.89%)
	OIB (1,1.89%)				LL (1,1.89%)
	LASSO (1,1.89%)				MAD (1,1.89%)
	Median regression (1,1.89%)
EQ-5D-3L (26,23.01%)	OLS (18,69.23%)	OLM (7,26.92%)	Age (18,69.23%)	Sample splitting (11,42.31%)	MAE (24,92.31%)
	Tobit regression (12,46.15%)	ML (4,15.38%)	Gender (13,50%)	Full-sample resubstitution validation (9,34.62%)	RMSE (23,88.46%)
	GLM (8,30.77%)	SUR-OPM (3,11.54%)	Zubrod Performance Status (1,3.85%)	fivefold cross-validation (3,11.54%)	BIC (9,34.62%)
	ALDVMM (8,30.77%)	OLR (2,7.69%)	Viral load(log—viral load) (1,3.85%)	Bootstrap validation (2,7.69%)	AIC (7,26.92%)
	TPM (7,26.92%)	NP (2,7.69%)	Race (1,3.85%)	tenfold cross-validation (2,7.69%)	R2 (5,19.23%)
	CLAD (7,26.92%)	MLR (1,3.85%)	BMI (1,3.85%)	Leave-one-out cross-validation (1,3.85%)	MSE (4,15.38%)
	Beta regression (4,15.38%)	NP-LM (1,3.85%)	Diabetes status (1,3.85%)		ICC (4,15.38%)
	BETAMIX (3,11.54%)	GLOGIT (1,3.85%)	Failure to account for covariate (7,26.92%)		ME (4,15.38%)
	ZOIB (1,3.85%)	LASSO (1,3.85%)			Spearman's ρ (3,11.54%)
	EPM (1,3.85%)	GOPM (1,3.85%)			CCC (1,3.85%)
	MM (1,3.85%)	Failure to account for response mapping (11,42.31%)			MID (1,3.85%)
	Mixed-effects linear regression (1,3.85%)				QIC (1,3.85%)
	MRM (1,3.85%)				Adj R2 (1,3.85%)
	FLOGIT (1,3.85%)
	Cox regression (1,3.85%)
	PWL (1,3.85%)
	NMIX (1,3.85%)
	Failure to account for direct mapping (3,11.54%)
SF-6D (11,9.73%)	OLS (10,90.91%)	OPM (2,18.18%)	Gender (10,90.91%)	Sample splitting (6,54.55%)	MAE (11,100%)	Scatter Plot Comparing Observed and Predicted Values (3,27.27%)
	Tobit regression (6,54.55%)	OLM (1,9.09%)	Age (8,72.73%)	fivefold cross-validation (4,36.36%)	RMSE (8,72.73%)	Bland–Altman Plot (2,18.18%)
	BETAMIX (5,45.45%)	ML (1,9.09%)	Race (1,9.09%)	Full-sample resubstitution validation (2,18.18%)	AIC (7,63.64%)	CDF Plot (1,9.09%)
	CLAD (5,45.45%)	MLR (1,9.09%)	Seizure-free status (1,9.09%)	Validation in temporally distinct datasets (1,9.09%)	BIC (6,54.55%)	Failure to account for predictive assessment plots (5,54.55%)
	GLM (2,18.18%)	Failure to account for response mapping (5,45.46%)	Health insurance status (1,9.09%)	Leave-one-out cross-validation (1,9.09%)	MSE (3,27.27%)
	MM (1,9.09%)		Marital status (1,9.09%)	tenfold cross-validation (1,9.09%)	Adj R2 (3,27.27%)
	ALDVMM (1,9.09%)		Employment status (1,9.09%)		R2 (2,18.18%)
	FLOGIT (1,9.09%)		Income level (1,9.09%)		ICC (2,18.18%)
			NCCN risk category (1,9.09%)		CCC (2,18.18%)
			Relapse Frequency (1,9.09%)		AE (1,9.09%)
			Obesity-related comorbidities (1,9.09%)		Spearman's ρ (1,9.09%)
			Prostate cancer treatment type (1,9.09%)		ME (1,9.09%)
			Year of prostate cancer diagnosis (1,9.09%)		Pred R2 (1,9.09%)
			Failure to account for covariate (1,9.09%)
HUI-3 (6,5.31%)	OLS (5,83.33%)	ML (1,16.67%)	Age (1,33.33%)	Full-sample resubstitution validation (2,33.33%)	MAE (5,83.33%)	Error Histogram (2,33.33%)
	TPM (2,33.33%)	Failure to account for response mapping (5,83.33%)	Gender (1,33.33%)	tenfold cross-validation (3,50.00%)	RMSE (4,66.67%)	Scatter Plot Comparing Observed and Predicted Values (2,33.33%)
	Tobit regression (2,33.33%)		Disease severity (1,33.33%)	Sample splitting (1,16.67%)	AIC (3,50%)	Bland–Altman Plot (1,16.67%)
	MRM (1,16.67%)		Mini-mental state examination (1,33.33%)		R2 (3,50%)	Failure to account for predictive assessment plots (3,50.00%)
	CLAD (1,16.67%)		Failure to account for covariate (3,50.00%)		ICC (3,50%)
	Equipercentile linking (1,16.67%)				Adj R2 (2,33.33%)
	BETAMIX (1,16.67%)				MSE (1,16.67%)
	IRT model (1,16.67%)				BIC (1,16.67%)
					Pearson's r (1,16.67%)
					ME (1,16.67%)
SF-6Dv2 (6,5.31%)	OLS (6,100%)	Failure to account for response mapping (6,100%)	Age (6,100%)	tenfold cross-validation (3,50.50%)	RMSE (6,100%)	Bland–Altman Plot (5,83.33%)
	Tobit regression (5,83.33%)		Gender (3,50%)	Sample splitting (33.33%)	MAE (6,100%)	Scatter Plot Comparing Observed and Predicted Values (1,16.67%)
	CLAD (4,66.67%)		Cancer type (1,16.67%)	Full-sample resubstitution validation (1,16.67%)	AIC (3,50%)
	MM (3,50%)		Negative utility values (1,16.67%)		BIC (3,50%)
	GLM (3,50%)		BMI (1,16.67%)		CCC (2,33.33%)
	TPM (1,16.67%)		Worst-dimension attainment (1,16.67%)		Spearman's ρ (2,33.33%)
	CATREG (1,16.67%)				ICC (2,33.33%)
	MFP (1,16.67%)				Pred R2 (1,16.67%)
					Adj R2 (1,16.67%)
CHU9D (3,2.65%)	OLS (3,100%)	MLOGIT (1,33.33%)	Gender (3,100%)	Sample splitting (1,33.33%)	MAE (3,100%)	Scatter Plot Comparing Observed and Predicted Values (1,33.33%)
	GLM (3,100%)	Failure to account for response mapping (2,66.67%)	Age (2,66.67%)	fivefold cross-validation (1,33.33%)	MSE (2,66.67%)	Failure to account for predictive assessment plots (2,66.67%%)
	CLAD (2,66.67%)		Economic status (1,33.33%)	tenfold cross-validation (1,33.33%)	CCC (1,33.33%)
	Tobit regression (1,33.33%)		GMFCS level (1,33.33%)	Bootstrap validation (1,33.33%)	RMSE (1,33.33%)
	EEE (1,33.33%)				R2 (1,33.33%)
	FMM (1,33.33%)
	ZOIB (1,33.33%)
	Beta regression (1,33.33%)
	MM (1,33.33%)
ReQoL-UI (2,1.77%)	ALDVMM (1,50.00%)	SUR-OPM (1,50.00%)	Gender (2,100%)	Full-sample resubstitution validation (2,100%)	RMSE (2,100%)	CDF Plot (2,100%)
	BETAMIX (1,50.00%)	Failure to account for response mapping (1,50.00%)	Age (2,100%)		MAE (2,100%)	Bland–Altman Plot (1,50.00%)
	GLM (1,50.00%)				AIC (2,100%)
	OLS (1,50.00%)				BIC (2,100%)
	Tobit regression (1,50.00%)				LL (1,50%)
					AE (1,50%)
15D (1,0.88%)	OLS (1,100%)	OLM (1,100%)	Gender (1,100%)	Sample splitting (1,100%)	RMSE (1,100%)	Failure to account for predictive assessment plots (1,100%)
	GLM (1,100%)		Age (1,100%)		MAE (1,100%)
	MM (1,100%)				ICC (1,100%)
AQoL-8D (1,0.88%)	OLS (1,100%)	Failure to account for response mapping (1,100%)	Gender (1,100%)	Sample splitting (1,100%)	RMSE (1,100%)	Scatter Plot Comparing Observed and Predicted Values (1,100%)
	GLM (1,100%)		Age (1,100%)		MAE (1,100%)
	MM (1,100%)
AQoL-4D (1,0.88%)	OLS (1,100%)	Failure to account for response mapping (1,100%)	Gender (1,100%)	fivefold cross-validation (1,100%)	RMSE (1,100%)	Error Histogram (1,100%)
	MM (1,100%)		Age (1,100%)		MAE (1,100%)
	GLM (1,100%)				ICC (1,100%)
	BETAMIX (1,100%)
	LASSO (1,100%)
	GBT (1,100%)
	SVR (1,100%)
MSIS-8D (1,0.88%)	OLS (1,100%)	Failure to account for response mapping (1,100%)	Gender (1,100%)	Sample splitting (1,100%)	RMSE (1,100%)	Scatter Plot Comparing Observed and Predicted Values (1,100%)
	CLAD (1,100%)		Age (1,100%)		MAE (1,100%)
CHU-9D (1,0.88%)	OLS (1,100%)	ML (1,100%)	Gender (1,100%)	tenfold cross-validation (1,100%)	RMSE (1,100%)	Scatter Plot Comparing Observed and Predicted Values (1,100%)
	GLM (1,100%)		Age (1,100%)		MAE (1,100%)
	MM (1,100%)				CCC (1,100%)
	Tobit regression (1,100%)				Adj R2 (1,100%)
	Beta regression (1,100%)
VFQ-UI (1,0.88%)	ALDVMM (1,100%)	Failure to account for response mapping (1,100%)	Gender (1,100%)	Full-sample resubstitution validation (1,100%)	ME (1,100%)	Scatter Plot Comparing Observed and Predicted Values (1,100%)
			Age (1,100%)		MAE (1,100%)	CDF Plot (2,100%)
					RMSE (1,100%)
					AIC (1,100%)
					BIC (1,100%)

The values in parentheses represent the frequency with which each category appears in the corresponding target measure. At the same time, the percentages indicate the proportion of these occurrences relative to the total for that target measure. Abbreviation definitions are provided in the List of Abbreviations

Twenty-one mapping functions (18.58%) did not consider any covariates, while the remaining functions employed fewer than two covariates on average (Table 2). The most frequently used covariates were age (n = 82, 72.57%) and gender (n = 71, 62.83%), followed by BMI (n = 6, 5.31%). Additionally, supplementary covariates were included in studies involving different disease domains related to various source measures, such as treatment type for prostate cancer (n = 1) and diabetic status (n = 1).

Validation

All mapping functions were validated for performance (Table 2), typically through internal validation (n = 102, 90.27%). A total of 9 distinct validation methods were employed, amounting to 121 validation procedures (Table 3). The most frequently used method was cross-validation, which included 10-fold (n = 25, 20.66%), 5-fold (n = 16, 13.22%), 9-fold (n = 2, 1.65%), and 3-fold (n = 1, 0.83%), this was followed by sample splitting (n = 38, 31.40%) and full-sample resubstitution validation (n = 28, 23.14%).

Mapping functions employed more than three performance metrics (Table 2), with 22 types used across 274 (Table 3). The most frequently used metrics were MAE (n = 100, 36.50%) and RMSE (n = 89, 32.48%), followed by AIC (n = 42, 15.33%), BIC (n = 35, 12.77%), MSE (n = 26, 9.49%), R2 (n = 21, 7.66%), Adj R2 (n = 20, 7.30%), ICC (n = 19, 6.93%), and CCC (n = 15, 5.47%).

Moreover, 46.90% of the mapping functions conducted subgroup analyses (Table 2). Predictive assessment plots were provided for 90 mapping functions (79.65%), each employing fewer than one plot average. Six types of predictive assessment plots were utilized, amounting to 101 plots overall (Table 3). The most used plots were the Scatter Plot Comparing Observed and Predicted Values (n = 36, 35.64%) and the Bland–Altman Plot (n = 22, 21.78%).

Quality assessment

Figure 2 graphically demonstrates the distribution of the studies’ quality. Among the 92 studies focused on Mapping as the primary objective, each met more than 20 of the reporting quality criteria, 24 studies fully satisfied all quality standards, among the 27 quality criteria, deficiencies were observed in 8 items, including sample description (n = 39), conceptual overlap (n = 32), consistency between the sample population and the value set population (n = 29), regression variable description (n = 10), regression design description (n = 6), data integrity and missing data handling (n = 4), description of source and target measures (n = 2), and comparison with previous studies (n = 1).

Fig. 2.

Distribution of eligible items number

Regarding sample description, 37 studies did not report the appropriateness of the sample size, and seven studies failed to indicate whether repeated observations were present. Among the 19 studies that reported the presence of repeated observations, three did not address this issue, while the remaining 16 employed various methods to handle repeated observations. These methods included the use of robust standard errors (n = 3), cluster-robust standard errors (n = 3), random effects/mixed effects models (n = 3), generalized estimating equations (GEE) (n = 3), conducting separate regressions for different time points (n = 2), and averaging the score over two time periods (n = 1).

Thirty-two studies did not assess conceptual overlap before developing the mapping function. While the remaining studies, various methods were employed: Spearman correlation analysis (n = 42), qualitative evaluation of content overlap (n = 12), Pearson correlation analysis (n = 7), exploratory factor analysis (EFA) (n = 5), scatter plot (n =3), Bland–Altman plot (n = 1), intraclass correlation coefficient (n = 1), principal component analysis (PCA) (n = 1), literature review (n = 1), and multiple correspondence analysis (MCA) (n = 1).

Among the 29 studies where the region of the sample population did not match that of the target measure’s value set, two studies could not be compared due to missing region information for the value set. In 3 studies, partial consistency was observed. In 2 of these, the Hong Kong value set was used because mainland China did not have an SF-6D value set at the time, while in 1 study, the UK value set was adopted because the EQ‑5D‑5L and SF‑6D demonstrated good reliability and validity in Singapore. Of the remaining 24 studies, 15 explained that a corresponding value set was unavailable for the sample population at that time. One study (with a Canadian sample) employed the UK value set due to its widespread use. The remaining eight studies did not explain. Furthermore, in three studies, the regions of the sample population and the target measure’s value set were different regions within the same country, ten studies were located on the same continent, and the remaining 16 were from different continents.

In the section on data integrity and missing data handling, three studies did not specify the completeness of the data, and one study did not detail the method used to handle missing values. 56 studies removed missing values, one employed chained regression multiple imputation, and one used median imputation. Additionally, one study excluded questionnaires with more than 20% missing data, while in the SF-6Dv2, items that were missing or marked as “not applicable” were assigned a value of 1, and in the FAQLQ-PF, missing values were imputed using the median. Regarding regression variable descriptions, ten studies did not clarify whether covariates were used, and in the regression design descriptions, six studies did not outline the strategy for selecting model variables. Finally, concerning comparisons with previous studies, only one study did not consider comparing its results with those of previously published mapping algorithms that utilized the same source and target measures.

Discussion

This systematic review comprises 131 studies covering various aspects of Mapping research: 92 focused on Mapping as the primary objective, 21 on economic evaluation, 13 on methodology, and five reviews. Among the 113 mapping functions, the source measures are mostly non-preference-based, with the EORTC-QLQ-C30 being the most frequently used and the EQ-5D-5L being the primary target measure. Sample sizes varied considerably across studies, with only three studies having fewer than 100 participants. Of the Mapping functions, 59.29% employed only direct Mapping, while 38.05% considered both direct and response Mapping. Direct Mapping functions used an average of more than three models, most commonly OLS and Tobit regression. Whereas response mapping studies typically used about one model, predominantly OLM and ML. On average, each model incorporated fewer than two covariates, most frequently age and gender. All mapping functions assessed performance, with 90.27% using internal validation methods, most commonly cross-validation, and sample splitting. More than three performance metrics were reported per mapping function, with MAE and RMSE being the most common, and approximately one predictive performance plot was used on average, most frequently Scatter Plots Comparing Observed and Predicted Values and Bland–Altman Plots. Additionally, 46.9% of the mapping functions conducted subgroup analyses.

Compared to previous review findings [1], studies focused on mapping as the primary objective over the past seven years indicate that the EORTC QLQ-C30 and EQ-5D continue to be the most widely used source and target measures, respectively. Notably, within EQ-5D applications, the use of the EQ-5D-5L has increased from 14.97% to 67.09%, now surpassing the EQ-5D-3L. The incidence of studies with small sample sizes has decreased, with those having fewer than 100 participants dropping from 10 (4%) to 3 (3.26%). Additionally, the proportion of Mapping functions employing both direct and response Mapping increased by 22.05%, and the use of multiple models in Mapping rose by 22.19%. The inclusion of age and gender as covariates increased by 21.57% and 7.83%, respectively, and all recent studies now report model parameters. In predictive performance evaluation, MAE and RMSE remain the most frequently used metrics, while the proportion of Mapping functions reporting predictive performance plots has increased by 27.65%. These trends suggest that recent mapping research has adopted more rigorous sample size requirements, expanded model applications, and enhanced parameter reporting and predictive performance plotting standardization and comprehensiveness.

However, 32 (34.78%) of the studies did not conduct a conceptual overlap analysis. In many cases, the correlation between the dimensions of the EORTC QLQ-C30 and those of the EQ-5D-5L and EQ-5D-3L was only moderate to strong [36, 85, 133]. Due to cultural differences among populations in various regions, which may lead to different interpretations and perceptions of the scales, the observed correlations are uncertain. Conceptual overlap analysis evaluates whether the source measure is appropriate for mapping to the target measure by examining its content and structure, and it is considered a prerequisite for mapping [18]. Future mapping function development should incorporate this step to ensure mapping validity. Furthermore, Pearson correlation analysis, which tends to underestimate the relationship between ordered categorical data [152], was still used in 7 studies for assessing conceptual overlap.The MAPS statement recommends initially applying Spearman correlation to examine the source and target measures relationship, followed by exploratory or confirmatory principal components analysis (PCA) to further investigate and compare their structures [23]. Although Spearman correlation has been widely employed, only one study has used PCA. Future research should comprehensively and appropriately apply these testing methods.

Differences in cultural background, health perceptions, socioeconomic conditions, and healthcare environments across regions may lead to biases in utility estimation when the geographical origin of the sample population does not match that of the target measure’s value set [153, 154]. In studies exhibiting such geographical discrepancies, some cases involve different countries (n = 10, 34.48%), and in over half of the instances (n = 16, 55.17%), the regions do not belong to the same continent. The EQ-5D-3L user manual recommends using the value set from the nearest region when a region value set is unavailable [155]. However, cases remain where the closest available value set is not used. For example, when the EQ-5D-3L is the target measure, and the sample is from Canada, the nearest available value set is from the United States. Nonetheless, the UK value set is chosen because of its widespread use. Moreover, more than half of these studies did not consider response mapping (n = 17, 58.62%). Consequently, even if a value set from the sample's region is later developed, it cannot be substituted. Future research should carefully consider the selection of value sets and, if the data includes detailed information on the dimensions of the target measure, develop response mapping meanwhile.

Currently, direct Mapping functions employ an average of more than 3 models, whereas response mapping functions employ only one average. Since model predictive performance is affected by the type and distribution of data, it is advisable to use a wide variety of models when possible. Testing different combinations of covariates can help compare predictive performance, allowing the selection of the most effective application model. Most existing direct mapping functions employ linear models, with OLS being the most widely used. However, OLS requires the data to meet specific assumptions. Violations, such as repeated measurements and ceiling effects (most individuals achieved the maximum score), can lead to underestimated standard errors when using linear models directly [2, 5, 20, 26, 68]. Furthermore, seven studies did not indicate whether the data contained repeated observations, and three studies with repeated observations did not address this issue. Future studies should verify the presence of repeated measurements and ceiling effects before initiating mapping predictions and apply appropriate adjustments if necessary. For repeated observations, methods like cluster-robust standard errors can be used. In contrast, TPM, ALDVMM, or alternative methods like random forests, unaffected by repeated measurements and ceiling effects, may address it, ensuring estimation accuracy. Small sample sizes can compromise the stability of regression coefficients and increase prediction errors. Thus, studies should justify sample size selection, particularly for rare diseases where samples are often limited [20].

Nevertheless, it should be noted that this study had several potential limitations. Ideally, comparing the findings of the new review with the original review to identify trends would require that both reviews employ identical search strategy and inclusion/exclusion criteria. However, with mapping research progressing, this strategy and criteria of the new review would be refined and cannot remain unchanged. Although comparisons under these conditions may not be optimal, they still reveal overarching trends by enhancing comprehensiveness while preserving consistency. Secondly, the considerable heterogeneity in validation methods and performance metrics used across studies developing mapping algorithms significantly limits the feasibility of meaningful statistical comparisons. As a result, neither our study nor existing reviews have been able to conduct such analyses. Future research could categorize mapping algorithms by their source and target measures, then validate and compare them using the same datasets, validation methods, and performance metrics. Additionally, studies developing mapping algorithms could strive to reach consensus on the selection of validation methods and performance metrics.

Conclusion

The systematic review indicates that over the past 7 years, the content and format of mapping studies have become more standardized, with the most used source measure, target measure, and models remaining consistent. Sample sizes have generally increased, the proportion of studies employing response mapping has risen, and the type of models applied has diversified. In addition, our analysis finds aspects that previous reviews overlooked, including a lack of conceptual overlap analysis, inadequate handling of repeated measurements, and regional inconsistencies between the sample populations and the value sets. Mapping guidelines require continuous updates to address these limitations, and researchers should adopt more standardized and comprehensive practices in mapping development studies to advance the quality of mapping research collectively.

Abbreviations

HTA

Health Technology Assessment

CUA

Cost-Utility Analysis

QALY

Quality Adjusted Life Years

HRQoL

Health-Related Quality of Life

HSUV

Health State Utility Value

PBM

Preference-Based Measures

15D

15-Dimensional Health-Related Quality of Life Instrument

AQoL-8D

Assessment of Quality of Life – 8 Dimensions

CHU9D

Child Health Utility 9-Dimension

EQ-5D-3L

EuroQol 5-Dimension 3-Level Questionnaire

EQ-5D-5L

EuroQol 5-Dimension 5-Level Questionnaire

HUI-3

Health Utilities Index Mark 3

ReQoL-UI

Recovering Quality of Life Utility Index

SF-6D

Short Form 6-Dimension

SF-6Dv2

Short Form 6-Dimension Version 2

PROMs

Patient-reported outcome measures

AcroQoL

Acromegaly Quality of Life Questionnaire

ADCS-ADL

Alzheimer’s Disease Cooperative Study–Activities of Daily Living

ALSFRS-R

Amyotrophic Lateral Sclerosis Functional Rating Scale–Revised

BASDAI

Bath Ankylosing Spondylitis Disease Activity Index

BASFI

Bath Ankylosing Spondylitis Functional Index

BCVA

Best-Corrected Visual Acuity

CAT

COPD Assessment Test

CH-QLQ

Chronic Headache Questionnaire

CLDQ-NASH

Chronic Liver Disease Questionnaire for Non-Alcoholic Steatohepatitis

CPCHILD

Caregiver Priorities & Child Health Index of Life with Disabilities

DLQI

Dermatology Life Quality Index

EORTC QLQ-BR53

European Organisation for Research and Treatment of Cancer Breast Cancer Quality of Life Questionnaire (53 items)

EORTC QLQ-C30

European Organisation for Research and Treatment of Cancer Core Quality of Life Questionnaire (30 items)

EQ-5D-5L

EuroQol 5-Dimension 5-Level Questionnaire

EPDS

Edinburgh Postnatal Depression Scale

EPIC

Expanded Prostate Cancer Index Composite

ESAS r: Renal

Edmonton Symptom Assessment System—revised for Renal patients

FAACT

Functional Assessment of Anorexia/Cachexia Therapy

FAQLQ-PF

Food Allergy Quality of Life Questionnaire–Parent Form

FACIT F

Functional Assessment of Chronic Illness Therapy–Fatigue

FACT B

Functional Assessment of Cancer Therapy–Breast

FACT G

Functional Assessment of Cancer Therapy–General

FACT H&N

Functional Assessment of Cancer Therapy–Head and Neck

FACT L

Functional Assessment of Cancer Therapy–Lung

GHQ 12

General Health Questionnaire 12

GAD 7

Generalized Anxiety Disorder 7

HAQ DI

Health Assessment Questionnaire Disability Index

HIT 6

Headache Impact Test 6

IBS QoL

Irritable Bowel Syndrome Quality of Life Questionnaire

IWQOL Lite

Impact of Weight on Quality of Life Lite

KOOS

Knee injury and Osteoarthritis Outcome Score

LTCQ 8

Long Term Conditions Questionnaire (8 items)

MacNew

MacNew Heart Disease Health Related Quality of Life Questionnaire

MAX PC

Memorial Anxiety Scale for Prostate Cancer

MENQOL

Menopause Specific Quality of Life Questionnaire

MLHFQ

Minnesota Living with Heart Failure Questionnaire

MOS HIV

Medical Outcomes Study HIV Health Survey

MSQ

Migraine Specific Quality of Life Questionnaire version 2.1

ODI

Oswestry Disability Index

OHS

Oxford Hip Score

OKS

Oxford Knee Score

PedsQL 4.0

Pediatric Quality of Life Inventory 4.0

PANSS

Positive and Negative Syndrome Scale

PCI

Head and Neck Patient Concerns Inventory

PDQ 8

Parkinson’s Disease Questionnaire 8

PHQ 9

Patient Health Questionnaire 9

PROMIS 29

Patient Reported Outcomes Measurement Information System 29

PROMIS GH10

Patient Reported Outcomes Measurement Information System Global Health 10

QLQ H&N35

European Organisation for Research and Treatment of Cancer Quality of Life Questionnaire Head and Neck 35

QOLIE 31 P

Quality of Life in Epilepsy Inventory 31 Patient Version

QoL AD

Quality of Life in Alzheimer’s Disease

RAND 12

RAND 12 Item Health Survey

SAQ

Seattle Angina Questionnaire

SBI

Shah modified Barthel Index

SDQ

Strengths and Difficulties Questionnaire

SWEMWBS

Short Warwick–Edinburgh Mental Wellbeing Scale

TCM HSS

Traditional Chinese Medicine Health Status Scale

UWQoL

University of Washington Quality of Life Questionnaire

WHODAS 2.0

World Health Organization Disability Assessment Schedule 2.0

WHODAS 2.0–12

World Health Organization Disability Assessment Schedule 2.0 12 item version

WHOQOL BREF

World Health Organization Quality of Life Brief Version

WHOQOL HIV Bref

World Health Organization Quality of Life HIV Brief

WINRS

Worst Itching Intensity Numerical Rating Scale

WOMAC

Western Ontario and McMaster Universities Osteoarthritis Index

ALDVMM

Adjusted Limited Dependent Variable Mixture Model

BETAMIX

Beta mixture model

CLAD

Censored Least Absolute Deviation

EEE

Extended Estimating Equations

EPM

Extended Probit Model

FEM

Fixed Effects Model

FLOGIT

Fractional Logit

FRM

Fractional Regression Model

GAMLSS

Generalized Additive Models for Location Scale and Shape

GBT

Gradient Boosted Tree

GEE

Generalized Estimating Equations

GLM

Generalized Linear Model

IRT

Item Response Theory

MM

Robust MM-estimator

MRM

Multivariate Regression Model

NMIX

Normal Mixture Model

OIB

One-Inflated Beta regression

OLS

Ordinary Least Squares

PWL

Piecewise Linear

REM

Random Effects Model

Tobit

Tobit regression

TPM

Two-Part Model

ZOIB

Zero-One-Inflated Beta regression

BN

Bayesian Network

GEE

Generalized Estimating Equations

GBT

Gradient Boosted Trees

GLOGIT

Generalized Logit Model

GOPM

Generalized Ordered Probit Model

LASSO

Least Absolute Shrinkage and Selection Operator

ML

Multinomial Logistic Model

MVP

Multivariate Probit Model

MVOPR

Multivariate Ordered Probit Regression

NP

Non–Parametric approach

NP-LM

Non-Parametric approach excluding Logical Inconsistencies

OLM

Ordered Logit Model

OPM

Ordered Probit Model

SUR–OPM

Seemingly Unrelated Regression Ordered Probit Models.

AIC

Akaike Information Criterion

Adj R2

Adjusted Coefficient of Determination

BIC

Bayesian Information Criterion

CCC

Concordance Correlation Coefficient

CDF

Cumulative Distribution Function

DIC

Deviance Information Criterion

GMSE

Gradient Mean Squared Error

GMAE

Gradient Mean Absolute Error

ICC

Intraclass Correlation Coefficient

LL

Log-likelihood

MAE

Mean Absolute Error

ME

Mean Error

MSE

Mean Squared Error

MID

Minimum Important Difference

nMAE

Normalized Mean Absolute Error

nRMSE

Normalized Root Mean Square Error

Pearson’s r

Pearson’s Correlation Coefficient

Pred R2

Predicted Coefficient of Determination

R2

Coefficient of Determination

RMSE

Root Mean Square Error

Spearman’s ρ

Spearman’s rank-correlation coefficient

Authors’ contributions

Conceptualization: Q.S., L.S.; Methodology: Q.S.; Data curation: Q.S., Y.Z.; Formal analysis and investigation: Q.S., Y.Z.; Writing—original draft preparation: Q.S., X.P.; Writing—review and editing: Q.S., X.P., L.S.; Supervision: L.S., X.P.

Funding

The authors did not receive support from any organization for the submitted work.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.