Cited by 404Statistical Methods and Bayesian InferenceHealth Systems, Economic Evaluations, Quality of LifeStatistical Methods in Clinical Trials

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Multiple regression of cost data: use of generalised linear models

Barber, Julie, Thompson, Simon·2004·Journal of Health Services Research & Policy

DOI 10.1258/1355819042250249

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Abstract

Objective: Choosing an appropriate method for regression analyses of cost data is problematic because it must focus on population means while taking into account the typically skewed distribution of the data. In this paper we illustrate the use of generalised linear models for regression analysis of cost data. Methods: We consider generalised linear models with either an identity link function (providing additive covariate effects) or log link function (providing multiplicative effects), and with gaussian (normal), overdispersed poisson, gamma, or inverse gaussian distributions. These are applied to estimate the treatment effects in two randomised trials adjusted for baseline covariates. Criteria for choosing an appropriate model are presented. Results: In both examples considered, the gaussian model fits poorly and other distributions are to be preferred. When there are variables of prognostic importance in the model, using different distributions can materially affect the estimates obtained; it may also be possible to discriminate between additive and multiplicative covariate effects. Conclusions: Generalised linear models are attractive for the regression of cost data because they provide parametric methods of analysis where a variety of non-normal distributions can be specified and the way covariates act can be altered. Unlike the use of data transformation in ordinary least-squares regression, generalised linear models make inferences about the mean cost directly.

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“30 months: everyone No depression (n= 498), mean, £ (SD) Depression (n= 100), mean, £ (SD) Difference, mean, £ (95% CI) A&E attendances 10 (42) 14 (35) 4 (–5 to 13) Day hospital attendances 57 (636) 46 (161) –11 (–137 to 115) Inpatient stays 449 (2247) 1237 (5372) 788 (143 to 1434) Outpatient visits 268 (553) 434 (137…”
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Luo, H., Shrestha, S. S., Zhang, X., SAADDINE, J. B., Zeng, X., & Reeder, T. J. (2018) · Ophthalmic Epidemiology · doi:10.1080/09286586.2018.1441425 · Cited by 10
“with log link and gamma distribution to estimate the average costs examined in this study because expenditure data were highly skewed and right-tailed.(29) We compared the predicted expenditures between the first and other later periods using t test with unequal variance.”
Method
Healthcare Resource Uses and Out-of-Pocket Expenses Associated with Pulmonary TB Treatment in Thailand
Tanvejsilp, P., Loeb, M. B., Dushoff, J. G., & Xie, F. (2017) · PharmacoEconomics - Open · doi:10.1007/s41669-017-0053-0 · Cited by 9
“Smaller AIC values indicate better-fitting models; differences of ten or more in AIC indicate that the better-fitting model should be strongly preferred [14].”
BackgroundMethodInfluential
Triggering Factors of Primary Care Costs in the Years Following Type 2 Diabetes Diagnosis in Mexico
Castro‐Ríos, A., Nevárez-Sida, A., Tiro-Sánchez, M. T., & Wacher, N. H. (2014) · Archives of Medical Research · doi:10.1016/j.arcmed.2014.05.002 · Cited by 9
Does smoking status affect cost of hospitalization? Evidence from three main diseases associated with smoking in Iran
Sari, A. A., Rezaei, S., Arab, M., Matin, B. K., & Majdzadeh, R. (2017) · Medical Journal of the Islamic Republic of Iran · doi:10.14196/mjiri.31.63 · Cited by 9
Economic evaluation of a complex intervention (Engager) for prisoners with common mental health problems, near to and after release: a cost-utility and cost-consequences analysis
Hunter, R. M., Anderson, R., Kirkpatrick, T., Lennox, C., Warren, F. C., Taylor, R. S., Shaw, J. J., Haddad, M., Stirzaker, A., Maguire, M., et al. (2021) · The European Journal of Health Economics · doi:10.1007/s10198-021-01360-7 · Cited by 9
Adherence rates and health care costs in Crohn's disease patients receiving certolizumab pegol with and without home health nurse assistance: results from a retrospective analysis of patient claims and home health nurse data
Wolf, D. C., Jaganathan, S., Burudpakdee, C., Seetasith, A., Low, R., Lee, E. W., Gucky, J., Yassine, M., & Schwartz, D. A. (2018) · Patient Preference and Adherence · doi:10.2147/ppa.s148777 · Cited by 9
Comparing Manufacturer Submitted and Pan-Canadian Oncology Drug Review Reanalysed Incremental Cost-Effectiveness Ratios for Novel Oncology Drugs
Saluja, R., Jiao, T., Koshy, L., Cheung, M. C., & Chan, K. (2021) · Current Oncology · doi:10.3390/curroncol28010060 · Cited by 9
“Generalized linear regression models with Gamma distribution and log link were used to examine the changes in ICERs over time from 2012 to 2018, as costs have non-negative values and are right-skewed [14,15].”
Method
Economic and clinical outcomes of a physician-led continuous quality improvement intervention in the delivery of percutaneous coronary intervention.
Rihal, C. S., Kamath, C. C., Holmes, D. R., Reller, M. K., Anderson, S. S., McMurtry, E. K., & Long, K. H. (2006) · PubMed · Cited by 9
Early high-dose cryoprecipitate to reduce mortality in adult patients with traumatic haemorrhage: the CRYOSTAT-2 RCT with cost-effectiveness analysis
Curry, N. S., Davenport, R. A., Thomas, H., Fox, E. E., Lucas, J., Evans, A. L., Massou, E., Sharma, R., Shanmugaranjan, S., Rourke, C., et al. (2024) · Health Technology Assessment · doi:10.3310/jytr6938 · Cited by 8
A longitudinal, retrospective cohort study on the impact of roflumilast on exacerbations and economic burden among chronic obstructive pulmonary disease patients in the real world
Wan, Y., Sun, S. X., Corman, S. L., Huang, X., Gao, X., & Shorr, A. F. (2015) · International Journal of COPD · doi:10.2147/copd.s80106 · Cited by 8
“Wilcoxon rank-sum tests were used to compare the HCRU and cost data between study groups because they usually have a skewed distribution.(10) The differences between baseline and postindex exacerbation rates (PPPM), monthly HCRU, and monthly costs were calculated for each patient, and difference-in-difference (DID) li…”
Cost of illness of spinal muscular atrophy (SMA) in Italy
Marcellusi, A., Bini, C., Casiraghi, J. L., D’Ambrosio, F., Rotundo, M. A., Pallara, A., & Mennini, F. S. (2019) · Global & Regional Health Technology Assessment · doi:10.1177/2284240319867662 · Cited by 8
Clinical outcomes and health care costs combining metformin with sitagliptin or sulphonylureas or thiazolidinediones in uncontrolled type 2 diabetes patients
Esposti, L. D., Saragoni, S., Buda, S., & Esposti, E. D. (2014) · ClinicoEconomics and Outcomes Research · doi:10.2147/ceor.s63666 · Cited by 8
“A generalized linear model with an identity link function and a gamma distribution was used to estimate the association between health care costs and the type of OHD treatment.(20) Two-tailed P-values ,0.”
Economic Evaluation of the Protecting Teeth @ 3 Randomized Controlled Trial
Anopa, Y., Macpherson, L. M. D., McMahon, A. D., Wright, W., Conway, D. I., & McIntosh, E. (2022) · JDR Clinical & Translational Research · doi:10.1177/23800844221090444 · Cited by 8
“Differences in cost and QALYs between the intervention and control groups were estimated using generalized linear models (Barber and Thompson 2004).”
Method
The Importance of Proximity to Death in Modelling Community Medication Expenditures for Older People: Evidence From New Zealand
Moore, P., Bennett, K., & Normand, C. E. M. (2014) · Applied Health Economics and Health Policy · doi:10.1007/s40258-014-0121-x · Cited by 8
Computed tomographic coronary angiography for patients with heart failure (CTA-HF): a randomized controlled trial (IMAGE HF Project 1-C)
Chow, B. J. W., Green, R. E., Coyle, D., Laine, M., Hänninen, H., Leskinen, H., Rajda, M., Larose, É., Hartikainen, J. E. K., Hedman, M., et al. (2013) · Trials · doi:10.1186/1745-6215-14-443 · Cited by 8
“The modified Parks test can be used to determine the appropriate family while the novel technique of extended estimating equations has been developed, which allows identification of both the link function and family [18-20].”
BackgroundMethod
Medical Costs of Chronic Musculoskeletal Pain in Italy
Garattini, L., Koleva, D., Motterlini, N., & Cornago, D. (2007) · Clinical Drug Investigation · doi:10.2165/00044011-200727020-00007 · Cited by 8
Evaluation of costs, osteoporosis treatment, and re-fractures in German collaborative orthogeriatric care after fragility fractures
Konnopka, C., Büchele, G., Jaensch, A., Rothenbacher, D., Becker, C., Rapp, K., Henken, E., & König, H. (2023) · Osteoporosis International · doi:10.1007/s00198-023-06965-7 · Cited by 7
“Therefore, weighted generalized linear models with a gamma distribution and a log link function were applied to estimate the amount of costs [52].”
Method
Is ultra-hypo-fractionated radiotherapy more cost-effective relative to conventional fractionation in treatment of prostate cancer? A cost–utility analysis alongside a randomized HYPO-RT-PC trial
Sun, S., Jönsson, H., Salén, K.-G., Anden, M., Beckman, L., & Fransson, P. (2022) · The European Journal of Health Economics · doi:10.1007/s10198-022-01467-5 · Cited by 7
“In cost analysis, the Generalized linear models (GLM) assuming gamma distribution with log and identity links were commonly applied [22, 23].”
Method
Quality of life, out-of-pocket expenditures, and indirect costs among patients with the central nervous system tumors in Thailand
Tunthanathip, T., Sae-heng, S., Oearsakul, T., Kaewborisutsakul, A., Inkate, S., Madteng, S., & Tanvejsilp, P. (2022) · Journal of Neurosciences in Rural Practice · doi:10.25259/jnrp-2022-3-45 · Cited by 7
“The influence of disease severity and baseline characteristics on patient expenditures [Table 5] demonstrated results of GLM analyses for patient expenditures.”
MethodInfluential
An Economic Evaluation of the Relationship Between Glycemic Control and Total Healthcare Costs for Adults with Type 2 Diabetes: Retrospective Cohort Study
Boye, K. S., Bae, J. P., Thieu, V. T., & Lage, M. J. (2023) · Diabetes Therapy · doi:10.1007/s13300-023-01507-0 · Cited by 7
“Speciﬁcally, given the skewed nature of cost data, generalized linear models (GLM) with gamma distribution and log link [15] were used to examine all-cause total costs, outpatient costs, and drug costs, while all-cause acute care costs were examined using a two-part model.”
Using statistical models to assess medical cost of hepatitis C virus.
Vahedi, M., Pourhoseingholi, A., Ashtari, S., Pourhoseingholi, M. A., Karkhane, M., Moghimi-Dehkordi, B., Safaee, A., Kimiia, Z., & Alavian, S. M. (2012) · Gastroenterology and hepatology from bed to bench. · Cited by 7
Healthcare Costs of Treating Privately Insured Patients with Acute Myeloid Leukemia in the United States from 2004 to 2014: A Generalized Additive Modeling Approach
Mau, L., Preussler, J. M., Burns, L. J., Leppke, S. N., Majhail, N. S., Meyer, C. L., Mupfudze, T. G., Saber, W., Steinert, P., & Vanness, D. J. (2020) · PharmacoEconomics · doi:10.1007/s40273-020-00891-w · Cited by 7
Palliative Care as a Component of High-Value and Cost-Saving Care During Hospitalization for Metastatic Cancer
Lu, S., Rakovitch, E., Hannon, B. L., Zimmermann, C., Dharmarajan, K. V., Yan, M., de Almeida, J. R., Yao, C. M. K. L., Gillespie, E. F., Chino, F. L., et al. (2024) · JCO Oncology Practice · doi:10.1200/op.23.00576 · Cited by 7
“The generalized linear model 44 with gamma distribution and log link is commonly used to model cross-sectional cost data 45 as this model can handle the positively skewed distribution in cost data and make inferences on mean cost directly.”
Does the cost of cancer care for people in prison differ from those in the general population? Analysis of matched English cancer registry and hospital records
Hunter, R. M., Huynh, J., Lüchtenborg, M., Armes, J., Plugge, E., Taylor, R. M., Visser, R., & Davies, E. (2024) · EClinicalMedicine · doi:10.1016/j.eclinm.2024.102575 · Cited by 7
Evaluation of long-term clinical and health service outcomes following coronary artery revascularisation in Western Australia (WACARP): a population-based cohort study protocol
Gardner, C., Rankin, J. M., Geelhoed, E. A., Nguyen, M., Newman, M. A. J., Cutlip, D. E., Knuiman, M. W., Briffa, T. G., Hobbs, M., & Sanfilippo, F. M. (2014) · BMJ Open · doi:10.1136/bmjopen-2014-006337 · Cited by 7
Impact of smoking on health system costs among cancer patients in a retrospective cohort study in Ontario, Canada
Isaranuwatchai, W., de Oliveira, C., Mittmann, N., Evans, W. K., Peter, A., Truscott, R., & Chan, K. (2019) · BMJ Open · doi:10.1136/bmjopen-2018-026022 · Cited by 7
“literature has called for more up-to-date and precise health care cost estimates of smoking.(9, 32)”
Background
Tuberculosis hospitalization expenditures per patient from private health insurance claims data, 2010–2014
Owusu‐Edusei, K., Marks, S. M., Miramontes, R., Stockbridge, E. L., & Winston, C. A. (2017) · The International Journal of Tuberculosis and Lung Disease · doi:10.5588/ijtld.16.0587 · Cited by 7
“16,17 19 To reduce the potential problem of high multi-collinearity, which can affect the magnitude and therefore the interpretation of the estimated coefficients of the control variables, 20 we checked the variance inflation factor (VIF < 10) and condition number (<15) based on Belsley et al.’s…”
Assessment of Canadian provincial expenditures in depressed patients treated with venlafaxine XR versus SSRIs: the APEX Study
Monfared, A. A. T., Han, D., Sheehy, O., Bexton, B., & LeLorier, J. (2005) · Current Medical Research and Opinion · doi:10.1185/030079906x80314 · Cited by 7
Effectiveness and Cost-Effectiveness of Receiving a Hearing Dog on Mental Well-Being and Health in People With Hearing Loss: Protocol for a Randomized Controlled Trial
Stuttard, L., Hewitt, C. E., Fairhurst, C. M., Weatherly, H. L. A., Walker, S., Longo, F., Maddison, J., Boyle, P., & Beresford, B. (2020) · JMIR Research Protocols · doi:10.2196/15452 · Cited by 6
“A regression analysis will be undertaken to account for any baseline differences in study participants between the trial arms using appropriate techniques to account for non-normality of outcomes and costs data [45].”
Method
The Economic Burden of Severe Acute Malnutrition with Complications: A Cost Analysis for Inpatient Children Aged 6 to 59 Months in Northern Senegal
Wassonguema, B., N’Diaye, D. S., Michel, M., Ngabirano, L., Frison, S., Ba, M., Siroma, F., Brizuela, A. V., Audibert, M., & Chevreul, K. (2024) · Nutrients · doi:10.3390/nu16142192 · Cited by 6
The Cost-Effectiveness of the SMART Work & Life Intervention for Reducing Sitting Time
Cox, E., Walker, S., Edwardson, C. L., Biddle, S., Clarke-Cornwell, A. M., Clemes, S. A., Davies, M. J., Dunstan, D. W., Eborall, H., Granat, M. H., et al. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph192214861 · Cited by 6
“Costing and absenteeism regressions used a log-link transformation and gamma family form to account for the bounded right-skewed nature of the dependant variable [37].”
Method
Secondary healthcare costs after mastectomy and immediate breast reconstruction for women with breast cancer in England: population-based cohort study
Mohiuddin, S., Hollingworth, W., Glynn, J., Jones, T., Johnson, L., Potter, S., Brighter Study Group, Holcombe, C., O’Donoghue, J. M., Browne, J. P., et al. (2023) · British journal of surgery · doi:10.1093/bjs/znad149 · Cited by 6
Excess Bed Days and Hospitalization Costs Associated With 30‐Day Complications Following Catheter Ablation of Atrial Fibrillation
Ngo, L., Denman, R. A., Hay, K. E., Kaambwa, B., Ganesan, A. N., & Ranasinghe, I. (2023) · Journal of the American Heart Association · doi:10.1161/jaha.123.030236 · Cited by 6
Publication Patterns of Cancer Cost-Effectiveness Studies Presented at Major Conferences
Chan, K., Siu, E., Mozessohn, L., & Cheung, M. C. (2013) · Current Oncology · doi:10.3747/co.20.1438 · Cited by 6
Healthcare utilization costs of emerging adults with mood and anxiety disorders in an early intervention treatment program compared to a matched cohort
John‐Baptiste, A., Li, L., Isaranuwatchai, W., Osuch, E. A., & Anderson, K. K. (2019) · Early Intervention in Psychiatry · doi:10.1111/eip.12790 · Cited by 6
“We tested the identity and log links, to determine the relationship between the mean cost and the cost distribution (Barber & Thompson, 2004).”
Method
Cross‐sectional study of electrocardiographic pattern in healthy children resident at high altitude
Huicho, L., & Niermeyer, S. (2007) · American Journal of Physical Anthropology · doi:10.1002/ajpa.20563 · Cited by 6
Investigating whether the Johns Hopkins ACG case-mix system explains variation in UK general practice
O'Sullivan, C. (2011) · UCL Discovery (University College London) · Cited by 6
Cost-effectiveness of patient observation on cranial CT use with minor head trauma
Singh, S., Hearps, S. J. C., Nishijima, D. K., Cheek, J. A., Borland, M. L., Dalziel, S. R., Holmes, J. F., Kuppermann, N., Babl, F. E., & Hoch, J. S. (2022) · Archives of Disease in Childhood · doi:10.1136/archdischild-2021-323701 · Cited by 5
Partnering for change (P4C) in Sweden- a study protocol of a collaborative school-based service delivery model to create inclusive learning environments
Baric, V. B., Yngve, M., Holmefur, M., Feldman, I., Wilder, J., Johansen, K., Klang, N., Lidström, H., & Borgestig, M. (2023) · BMC Public Health · doi:10.1186/s12889-023-17053-0 · Cited by 10
“QALYs will be analysed with general regression model (GLM) [48], which allows for the control of confounders and adjustments to baseline.”
Method
Healthcare resource utilization and economic burden of multiple sclerosis in Chinese patients: results from a real-world survey
Sun, C., Jia, Y., Li, H., Qiao, X., Tang, M., Geng, M., Jones, E., Pike, J., Unsworth, M., & Hu, M. (2024) · Scientific Reports · doi:10.1038/s41598-024-64713-1 · Cited by 6
“Generalized linear models (GLMs) with log link and gamma distribution 20 were used to model the association between current EDSS score and costs adjusting for age and sex.”
Cancer in English prisons: a mixed-methods study of diagnosis, treatment, care costs and patient and staff experiences
Davies, E., Lüchtenborg, M., Hunter, R. M., Visser, R., Huynh, J., Pow, R., Plugge, E., Taylor, R. M., & Armes, J. (2025) · Health and Social Care Delivery Research · doi:10.3310/hyrt9622 · Cited by 5
Oncology Patients Are High Cost Outliers in Total Joint Replacement Bundled Payment Systems
Woelber, E., Gundle, K. R., Geddes, J., Schabel, K., Hayden, J. B., Hasan, S. R., Raymond, L. M., & Doung, Y.-C. (2019) · The Journal of Arthroplasty · doi:10.1016/j.arth.2019.08.030 · Cited by 5
Costs of postoperative morbidity following paediatric cardiac surgery: observational study
Hudson, E., Brown, K., Pagel, C., Wray, J., Barron, D. J., Rodrigues, W., Stoica, S. C., Tibby, S. M., Tsang, V. T., Ridout, D. A., et al. (2020) · Archives of Disease in Childhood · doi:10.1136/archdischild-2019-318499 · Cited by 5
Determining the probability of poverty levels of the Indigenous Americans and Black Americans in US using Multiple Regression
Pal, S. S., Paul, S., & Dey, R. (2022) · IJARCCE · doi:10.17148/ijarcce.2022.11340 · Cited by 5

Authors: Barber, J., & Thompson, S.
Affiliations: University College London (GB)
MRC Biostatistics Unit (GB)
ORCID: Barber, Julie
Thompson, Simon
Venue: Journal of Health Services Research & Policy
Publisher: SAGE Publications
Published: 2004-10-02
Volume: 9
Issue: 4
Pages: 197-204
ISSN: 1355-8196 (ISSN-L)
1758-1060
DOI: 10.1258/1355819042250249
OpenAlex: W1996146145
Cited by: 404
References: 20
Citations by year: 2026: 11 · 2025: 11 · 2024: 17 · 2023: 18 · 2022: 27 · 2021: 29 · 2020: 32 · 2019: 29 · 2018: 32 · 2017: 28 · 2016: 28 · 2015: 23 · 2014: 22 · 2013: 17 · 2012: 20
FWCI: 7.09
Type: journal article
Language: en
Open access: closed
Licence: journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
Locations: Journal of Health Services Research & Policy (publishedVersion)
PubMed (publishedVersion)
UCL Discovery (University College London) (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Health Systems, Economic Evaluations, Quality of Life
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Keywords: cost data, generalized linear models, skewed distributions, gamma distribution, inverse Gaussian distribution, log link function, treatment effects, baseline covariate adjustment, model selection criteria
MeSH terms: Costs and Cost Analysis, United Kingdom, Health Services Research, Normal Distribution, Linear Models

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Multiple regression of cost data: use of generalised linear models

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