Background
Cost-utility analysis is an important part of the rational development of health care policy and evaluation of medical interventions. It quantifies the cost required for a gain in quality-adjusted life years (QALY) [
1] The quality adjustment factor in the estimation of QALY may be obtained from preference-based measures of patient outcomes, such as the EuroQoL 5 Dimensions Questionnaire (EQ-5D) [
2] and Health Utilities Index Mark III (HUI3) [
3]. Health state valuation studies have provided algorithms to convert the responses to these measures to health utility values, where 1 indicates full health, 0 indicates a state that is not better than death, and negative values indicate health states worse than death [
4]. Combining the utility values and patients’ survival duration result in estimates of QALY, which is needed for cost-utility analysis. Availability of utility information is a prerequisite for QALY and cost-utility analyses, but this information is not always available.
Clinical studies often employed quality of life measures that are descriptive, in the sense that they indicate better or worse quality of life but they do not provide a utility value that has a quantitative interpretation for adjusting survival duration to QALY. These descriptive measures are often conceptually overlapping with preference-based measures and empirically correlated with the utility values. In this context, there has been strong interest in developing functions to map descriptive measures to utility values using data from prior studies that included both types of measures [
5,
6]. Mapping functions capitalize on descriptive quality of life data and make cost-utility analysis possible when utility data is otherwise not available. Mapping is accepted by the National Institute of Health and Care Excellence Technology Appraisal [
7].
Quality of life is an important issue in the care of people living with human immunodeficiency virus (HIV). The EuroQoL Group’s 5 Dimensions 3-level instrument (EQ-5D-3 L) is a commonly used preference-based measure [
8]. Its validity and reliability have been demonstrated in various conditions, including in HIV [
9]. The responses can be converted to health utility values [
4]. The Medical Outcomes Study HIV Health Survey (MOS-HIV) [
10,
11] is a descriptive quality of life measures. Both the MOS-HIV and EQ-5D covered multiple health dimensions. The MOS-HIV includes 10 dimensions: general health perceptions, physical functioning, role functioning, pain, social functioning, mental health, energy, health distress, cognitive functioning, and quality of life [
11]. The EQ-5D covers five dimensions: mobility, self-care, usual activities, pain/discomfort and anxiety/depression [
4,
8]. Despite the more limited scope of the latter, the two measures have sufficient overlap for a conceptual basis for mapping one to the other. A previous study mapped the MOS-HIV to the EQ-5D-3 L utility index [
12]. However, the study was oriented towards methodological comparison about the handling of ceiling effects; the functions presented used only one or two significant digits, which is a serious limitation for utility mapping. Availability of an accurate mapping function can make cost-utility analysis in HIV studies become possible even when only MOS-HIV is available.
The ordinary least squares (OLS) is the most commonly used method for mapping a descriptive health measure to a health utility measure [
13,
14]. Alternative regression-based methods have been proposed, but there has been no consistent evidence that they performed better than OLS [
7,
12,
15‐
18]. It is well known that OLS mapping under-estimates variability and therefore inflates type 1 errors [
5]. Furthermore, OLS mapping tends to under-estimate the health utility of people in good health states and over-estimate it among people in bad health states, which leads to under-estimates of the incremental cost-utility ratio [
15,
19‐
21].
Mapping by the equi-percentile method (EPM) has been successful and popular in education research [
5,
22]. It does not suffer from the aforementioned problems. There has been a strong interest in the use of EPM to improve mapping in the health care context [
5,
22]. However, EPM is usable only if the cumulative distribution functions (CDF) of the source and target measures are both continuously increasing. Quality of life and health utility measures are often discrete in their distributions, giving CDFs that are step functions. In this situation, Kernel smoothing is required before EPM can be applied [
5]. Smoothing health utility and patient reported outcome data is not a simple task. In particular, these measures often have a substantial ceiling effect, which is known to create extra difficulties for smoothing [
19‐
21,
23].
A new mapping method called the Mean Rank Method (MRM) has been recently proposed [
21]. Its core idea is similar to EPM and thus it should have similar strengths. However, it does not require smoothing and therefore is much simpler to use than the EPM. One study has mapped the World Health Organization Quality of Life – Brief to the EQ-5D-5 L [
21] and another study has mapped the Functional Assessment of Cancer Therapy – Breast (FACT-B) to the EQ-5D-5 L [
20] using MRM. Furthermore, the Alzheimer’s Disease Cooperative Study-Activities of Daily Living Inventory (ADCS-ADL) has also been mapped to the Health Utility Index Mark III by the MRM [
19]. All three studies demonstrated good performance properties of the MRM at the group level. But the MRM did not out-perform the OLS at the individual level in the FACT-B and ADCS-ADL studies. Further empirical evaluation of the properties of MRM will help to improve understanding of its potentials.
This study therefore aims to map the MOS-HIV to the EQ-5D-3 L utility index, using MRM, OLS and EPM, and to examine the performance of the three mapping functions.
Discussion
We employed the OLS, EPM and the recently proposed MRM to map the MOS-HIV quality of life scores to EQ-5D-3 L utilities. The OLS is the most commonly used method in the health care context so far [
13,
14], but it suffers shrinkage of variance and inaccurate estimation in relation to covariates [
5,
15,
21]. There are other regression-based methods, such as the Tobit regression and indirect mapping by multinomial logistic regression [
7,
18]. These regression methods do not consistently perform better than the OLS [
7,
17,
19].
The applicability of the EPM in the health care context has received a lot of attention. But actual implementation of it has been limited in health research. Two reviews in this field recorded no mapping study that used EPM [
13,
14]. This may be related to the nature of CDFs of health utility and descriptive health measures often being step functions, sometimes with a sizeable mass at the ceiling, which makes EPM difficult to implement. The MRM overcomes this complexity by equating mean ranks to handle tied values, instead of smoothing.
One relative strength of OLS is that, unlike the MRM and EPM, it can use multiple predictor variables. In the present study, we used both the PHS and MHS instead of an overall summary score as the OLS predictors. In contrast, we used the mean of PHS and MHS to generate a single predictor variable as the input for MRM and EPM. In this regard, the accuracy of the mapping functions derived may be affected by two factors. Firstly, the association between the observed utilities and PHS and MHS should be approximately equal. As shown earlier, we assessed the equality and found this condition plausible. Secondly, a large deviation of the PHS/MHS ratio from unity (one) may exacerbate the impact of the aforementioned difference, if any. As shown in Table
1, the mean PHS and MHS scores were similar in this study. The mean PHS/MHS ratio was 0.97 in the training dataset. The number of participants who had PHS/MHS ratio < 0.7 or > 1.3 were 40 and 24, respectively. With such small sub-group sample sizes, we refrained from further analyses by sub-groups. While the MRM-derived MOS-HIV to EQ-5D utility mapping function performed well in this study, its performance in other populations will need further assessment in relation to the two conditions aforementioned. Another potential relative strength of the OLS is that the application of an OLS mapping formula does not require rounding of the predictor scores. Unlike many other patient reported outcomes like WHOQOL-BREF or FACT-B which generate integer values, the weighted average procedure in MOS-HIV generates non-integers. For easy utilization of the MRM and EPM mapping results, we rounded the predictor values to integers so that the results can be presented as a simple look-up table. Nevertheless, in this study the OLS did not perform better than the MRM. A previous simulation study has shown that the MRM had mean absolute errors smaller than or equal to OLS even if predictor scores were coarsened to only 10 levels [
21]. As such, we expected the rounding to integers to have minimal impact on the accuracy of MRM. Our findings on EPM in this study refer to EPM as applied with MOS-HIV scores rounded to integers.
We have reservations about including demographic and clinical variables in mapping, a practice that has been seen in the health and quality of life literature. This practice changes the research purpose from “mapping a descriptive health measure to a utility measure” to “mapping multiple measures to a utility measure”. The implication of the practice is that the mapping function is not usable unless all the demographic and clinical variables involved in the mapping algorithm are also available.
In the present study, MRM generated a utility distribution that closely reflected the features of the observed utility distribution, including the mean, SD, various percentiles, and the level of ceiling effect. The OLS accurately reproduced the observed mean utility values in the training dataset but under-estimated the mean in the validation dataset. Neither OLS nor EPM were accurate in describing the variability and percentiles at the lower and upper ends of the utility distribution.
As expected, in the training dataset the mean squared error was lowest in the OLS-based mapping. However, in the training dataset both the OLS and EPM had higher mean absolute errors and lower ICC than the MRM. Furthermore, in the validation dataset, the MRM had the same mean squared error as the OLS and better performance according to all other indicators. There was no strong and consistent pattern to indicate whether OLS or MRM was more accurate in making individual-level predictions, but EPM was consistently inferior.
MRM agreed with the observed data in reproducing observed association patterns with clinical covariates. OLS agreed with the observed data in the training dataset but not in the validation dataset. The EPM performed worst in this regard. This suggests that OLS and EPM mapping are less suitable for studies that wish to explore associations. Our study supports the use of MRM, but further validation of this is required.
The mapped values all showed a reasonable degree of accuracy in terms of R2 over 0.5 in the training dataset. This is comparable to a review of mapping studies which showed the R2 in the training datasets in the mapping of disease-specific health measures to utility indices was typically less than 0.5, while mapping of generic health measures typically had within training dataset R2 in the range of 0.4 to 0.6 [
13].
We acknowledge that this study has several limitations. Firstly, the MOS-score in the trial only covered the 18 to 65 range. Based on the MOS-HIV reference data [25], the mean and SD are 50 and 10, respectively. The present study covers the lower range quite well (to about − 3 SD) but not the upper range (to about 1.5 SD). This may limit the applicability of the mapping in populations with good health and quality of life. Secondly, the study included only people living with HIV in four African countries. The applicability of the mapping functions in other populations need further evaluation. This includes further evaluation of the relative strength of the association between EQ-5D utilities and PHS and MHS in other populations and the mapping functions’ performance in populations that have PHS/MHS ratio substantially different from unity. Thirdly, the study used the 3-level EQ-5D instead of the latest 5-level EQ-5D (EQ-5D-5 L). Currently there is no official valuation set for mapping the responses to the EQ-5D-5 L to a utility index. Until this is developed, the mapped or observed EQ-5D-3 L utilities will remain useful. In the longer term, updating of the mapping using the EQ-5D-5 L will be needed. Fourthly, our validation dataset was not a randomly selected sample independent of the training dataset, this could have increased the similarity of the training and validation results. However, this impact was minor in this data, because the correlation between EQ-5D-3 L utility at baseline and subsequent visits was weak, ranging from 0.18 (with week 144) to 0.25 (with week 48).
Acknowledgements
We thank all the participants and staff from all the centres participating in the EARNEST trial. Members of the EARNEST Trial Team are:
Participating Sites.
Uganda.
JCRC Kampala (African trial co-ordinating centre; 231) E Agweng, P Awio, G Bakeinyaga, C Isabirye, U Kabuga, S Kasuswa, M Katuramu, C Kityo, F Kiweewa, H Kyomugisha, E Lutalo, P Mugyenyi, D Mulima, H Musana, G Musitwa, V Musiime, M Ndigendawan, H Namata, J Nkalubo, P Ocitti Labejja, P Okello, P Olal, G Pimundu, P Segonga, F Ssali, Z Tamale, D Tumukunde, W Namala, R Byaruhanga, J Kayiwa, J Tukamushaba, S Abunyang, D Eram, O Denis, R Lwalanda, L Mugarura, J Namusanje, I Nankya, E Ndashimye, E Nabulime, D Mulima, O Senfuma.
IDI, Kampala (216): G Bihabwa, E Buluma, P Easterbrook, A Elbireer, A Kambugu, D Kamya, M Katwere, R Kiggundu, C Komujuni, E Laker, E Lubwama, I Mambule, J Matovu, A Nakajubi, J Nakku, R Nalumenya, L Namuyimbwa, F Semitala, B Wandera, J Wanyama.
JCRC, Mbarara (97): H Mugerwa, A Lugemwa, E Ninsiima, T Ssenkindu, S Mwebe, L Atwine, H William, C Katemba, S Abunyang, M Acaku, P Ssebutinde, H Kitizo, J Kukundakwe, M Naluguza, K Ssegawa, Namayanja, F Nsibuka, P Tuhirirwe, M Fortunate.
JCRC Fort Portal (66): J Acen, J Achidri, A Amone, M. Chamai, J Ditai, M Kemigisa, M Kiconco, C Matama, D Mbanza, F Nambaziira, M Owor Odoi, A Rweyora, G. Tumwebaze.
San Raphael of St Francis Hospital, Nsambya (48): H Kalanzi, J Katabaazi, A Kiyingi, M Mbidde, M. Mugenyi, R Mwebaze, P Okong, I Senoga.
JCRC Mbale (47): M Abwola, D Baliruno, J Bwomezi, A Kasede, M Mudoola, R Namisi, F Ssennono, S Tuhirwe.
JCRC Gulu (43): G Abongomera, G Amone, J Abach, I Aciro, B Arach, P Kidega, J Omongin, E Ocung, W Odong, A Philliam.
JCRC Kabale (33): H Alima, B Ahimbisibwe, E Atuhaire, F Atukunda, G Bekusike, A Bulegyeya, D. Kahatano, S Kamukama, J Kyoshabire, A Nassali, A Mbonye, T M Naturinda, Ndukukire, A Nshabohurira, H. Ntawiha, A Rogers, M Tibyasa;
JCRC Kakira (31): S. Kiirya, D. Atwongyeire, A. Nankya, C. Draleku, D. Nakiboneka, D. Odoch, L. Lakidi, R. Ruganda, R. Abiriga, M. Mulindwa, F. Balmoi, S. Kafuma, E. Moriku.
Zimbabwe.
University of Zimbabwe Clinical Research Centre, Harare (265): J Hakim, A Reid, E Chidziva, G Musoro, C Warambwa, G Tinago, S Mutsai, M Phiri, S Mudzingwa, T Bafana, V Masore, C Moyo, R Nhema, S Chitongo.
Malawi.
Department of Medicine, University of Malawi College of Medicine and the Malawi-Liverpool-Wellcome Trust Clinical Research Programme, University of Malawi College of Medicine (92): Robert Heyderman, Lucky Kabanga, Symon Kaunda, Aubrey Kudzala, Linly Lifa, Jane Mallewa, Mike Moore, Chrissie Mtali, George Musowa, Grace Mwimaniwa, Rosemary Sikwese, Joep van Oosterhout, Milton Ziwoya.
Mzuzu Central Hospital, Mzuzu (19): H Chimbaka. B Chitete, S Kamanga, T Kayinga E Makwakwa, R Mbiya, M Mlenga, T Mphande, C Mtika, G Mushani, O Ndhlovu, M Ngonga, I Nkhana, R Nyirenda.
Kenya.
Moi Teaching and Referral Hospital (52): P Cheruiyot, C Kwobah, W Lokitala Ekiru, M Mokaya, A Mudogo, A Nzioka, A Siika, M Tanui, S Wachira, K Wools-Kaloustian.
Zambia.
University Teaching Hospital (37): P Alipalli, E Chikatula, J Kipaila, I Kunda, S Lakhi, J Malama, W Mufwambi, L Mulenga, P Mwaba, E Mwamba, A Mweemba, M Namfukwe.
The Aids Support Organisation (TASO), Uganda: E Kerukadho, B Ngwatu, J Birungi.
MRC Clinical Trials Unit: N Paton, J Boles, A Burke, L Castle, S Ghuman, L Kendall, A Hoppe, S Tebbs, M Thomason, J Thompson, S Walker, J Whittle, H Wilkes, N Young.
Monitors: C Kapuya, F Kyomuhendo, D Kyakundi, N Mkandawire, S Mulambo, S Senyonjo.
Clinical Expert Review Committee: B Angus, A Arenas-Pinto, A Palfreeman, F Post, D Ishola.
European Collaborators:
J Arribas (Hospital La Paz, Madrid, Spain), R Colebunders (Institute of Tropical Medicine, Antwerp, Belgium), M Floridia (ISS, Italy), M Giuliano (ISS, Italy), P Mallon (University College Dublin, Ireland), P Walsh (University College Dublin, Ireland), M De Rosa (CINECA, Italy), E Rinaldi (CINECA, Italy).
Trial Steering Committee: I Weller (Chair), C Gilks, J Hakim, A Kangewende, S Lakhi, E Luyirika, F Miiro, P Mwamba, P Mugyenyi, S Ojoo, N Paton, S Phiri, J van Oosterhout, A Siika, S Walker, A Wapakabulo,
Data Monitoring Committee: T Peto (Chair), N French, J Matenga.
Pharmaceutical companies: G Cloherty, J van Wyk, M Norton, S Lehrman, P Lamba, K Malik, J Rooney, W Snowden, J Villacian.