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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Variance Estimation in Complex Survey Sampling for Generalized Linear Models
Natarajan, S., Lipsitz, S. R., Fitzmaurice, G. M., Moore, C. G., & Gonin, R. (2008) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/j.1467-9876.2007.00601.x · Cited by 23
“The approach that is proposed in the paper is particularly useful for non-standard variance functions; in particular, the variance function for the medical cost data that was proposed by Blough and Ramsey (2000) and Barber and Thompson (2004) is of the form v.”
BackgroundMethodInfluential
Expanding Paramedicine in the Community (EPIC): study protocol for a randomized controlled trial
Drennan, I. R., Dainty, K. N., Hoogeveen, P., Atzema, C. L., Barrette, N., HAWKER, G. A., Hoch, J. S., Isaranuwatchai, W., Philpott, J., Spearen, C., et al. (2014) · Trials · doi:10.1186/1745-6215-15-473 · Cited by 22
“[31] however, additional estimation methods (for example, generalized linear models [32]) and different uncertainty”
Method
The Protease Inhibitor Monotherapy Versus Ongoing Triple Therapy (PIVOT) trial: a randomised controlled trial of a protease inhibitor monotherapy strategy for long-term management of human immunodeficiency virus infection
Paton, N. I., Stöhr, W., Oddershede, L., Arenas‐Pinto, A., Walker, S., Sculpher, M. J., Dunn, D. T., & on behalf of the PIVOT trial team (2016) · Health Technology Assessment · doi:10.3310/hta20210 · Cited by 22
Determinants of major direct medical cost categories among patients with osteoporosis, osteoarthritis, back pain or fibromyalgia undergoing outpatient rehabilitation
Stucki, G., Sabariego, C., & Brach, M. (2011) · Journal of Rehabilitation Medicine · doi:10.2340/16501977-0845 · Cited by 22
Economic Analysis of Apixaban Therapy for Patients With Atrial Fibrillation From a US Perspective
Cowper, P. A., Sheng, S., Lópes, R. D., Anstrom, K. J., Stafford, J. A., Davidson-Ray, L. D., Al‐Khatib, S. M., Ansell, J., Dorian, P., Husted, S., et al. (2017) · JAMA Cardiology · doi:10.1001/jamacardio.2017.0065 · Cited by 22
Effects of a Community-Based Program for Oral Health and Nutrition on Cost-Effectiveness by Preventing Disability in Japanese Frail Elderly: A Quasi-Experimental Study Using Propensity Score Matching
Tomata, Y., Watanabe, T., Sugiyama, K., Zhang, S., Sugawara, Y., & Tsuji, I. (2017) · Journal of the American Medical Directors Association · doi:10.1016/j.jamda.2017.02.014 · Cited by 22
Predicting hospital costs for patients receiving renal replacement therapy to inform an economic evaluation
On behalf of the ATTOM Study Group, Li, B., Cairns, J., Fotheringham, J., & Ravanan, R. (2015) · The European Journal of Health Economics · doi:10.1007/s10198-015-0705-x · Cited by 22
“Part two involved fitting a generalised linear model (GLM) for those patients with positive costs [12, 13].”
Method
Use of the 6-Min Walk Distance to Identify Variations in Treatment Benefits From Implantable Cardioverter-Defibrillator and Amiodarone
Fishbein, D. P., Hellkamp, A. S., Mark, D. B., Walsh, M. N., Poole, J. E., Anderson, J., Johnson, G. W., Lee, K. L., & Bardy, G. H. (2014) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2014.02.602 · Cited by 22
“Peak VO(2): a simple yet enduring standard.”
Background
Direct costs of warfarin treatment among patients with atrial fibrillation in a Finnish health care setting
Hallinen, T., Martikainen, J., Soini, E. J., Suominen, L., & Aronkytö, T. (2006) · Current Medical Research and Opinion · doi:10.1185/030079906x100014 · Cited by 22
A Knowledge-Guided Approach for Landslide Susceptibility Mapping Using Convolutional Neural Network and Graph Contrastive Learning
Liu, H., Ding, Q., Yang, X., Liu, Q., Deng, M., & Gui, R. (2024) · Sustainability · doi:10.3390/su16114547 · Cited by 21
Population-Based Trends in Systemic Therapy Use and Cost for Cancer Patients in the Last Year of Life
Pataky, R. E., Cheung, W. Y., de Oliveira, C., Bremner, K. E., Chan, K., Hoch, J. S., Krahn, M. D., & Peacock, S. J. (2016) · Current Oncology · doi:10.3747/co.23.2946 · Cited by 21
The HOME Study: study protocol for a randomised controlled trial comparing the addition of Proactive Psychological Medicine to usual care, with usual care alone, on the time spent in hospital by older acute hospital inpatients
Walker, J., Burke, K., Toynbee, M., van Niekerk, M., Frost, C. D., Magill, N., Walker, S., Sculpher, M. J., White, I. R., & Sharpe, M. (2019) · Trials · doi:10.1186/s13063-019-3502-5 · Cited by 21
Healthcare resource utilization in myeloproliferative neoplasms: a population-based study from Ontario, Canada
Bankar, A., Zhao, H., Iqbal, J., Coxford, R., Cheung, M. C., Mozessohn, L., Earle, C. C., & Gupta, V. K. (2020) · Leukemia & lymphoma/Leukemia and lymphoma · doi:10.1080/10428194.2020.1749607 · Cited by 21
Just a phone call away: is telephone advice enough?
Balmer, N. J., Smith, M., Denvir, C., & Patel, A. (2012) · Journal of Social Welfare and Family Law · doi:10.1080/09649069.2012.675465 · Cited by 21
“The gamma distribution function was chosen since advice time (as with cost data, e.g. Barber and Thompson 2004, Montez-Rath et al. 2006) can only take positive values and is highly skewed.”
Method
Excess direct medical costs of severe obesity by socioeconomic status in German adults
von Lengerke, T., John, J., Mielck, A., & KORA Study Group (2010) · PubMed Central · doi:10.3205/psm000063 · Cited by 20
“Following descriptive analysis, annual per-capita costs were analysed by generalized linear modelling as recommended in cost data analysis methodology [32].”
Method
Incremental Dementia-Related Expenditures in a Medicaid Population
Bharmal, M. F., Dedhiya, S. D., Craig, B. Α., Weiner, M., Rosenman, M. B., Sands, L. P., Modi, A., Doebbeling, C. C., & Thomas, J. M. (2011) · American Journal of Geriatric Psychiatry · doi:10.1097/jgp.0b013e318209dce4 · Cited by 20
Economic Burden of Psoriasis and Potential Cost Offsets with Biologic Treatment: A Swedish Register Analysis
Svedbom, A., Dahlén, J., Mamolo, C. M., Cappelleri, J. C., Mallbris, L., Petersson, I. F., & Ståhle, M. (2015) · Acta Dermato Venereologica · doi:10.2340/00015555-2329 · Cited by 20
“In order to control for the potential confounding effect of comorbidities on the mean cost differences between patients and referents in each therapy strata, bootstrapped generalized linear models (GLMs) assuming gamma-distributed costs (31) were fitted to the data.”
Method
Reporting and Analysis of Trial-Based Cost-Effectiveness Evaluations in Obstetrics and Gynaecology
Alili, M. E., van Dongen, J. M., Huirne, J. A. F., van Tulder, M. W., & Bosmans, J. E. (2017) · PharmacoEconomics · doi:10.1007/s40273-017-0531-3 · Cited by 20
Household costs and time to seek care for pregnancy related complications: The role of results-based financing
Chinkhumba, J., de Allegri, M., Mazalale, J., Brenner, S., Mathanga, D., Muula, A., & Robberstad, B. (2017) · PLoS ONE · doi:10.1371/journal.pone.0182326 · Cited by 13
Does Disordered Sleep Moderate the Relationship Between Pain, Disability and Downstream Healthcare Utilization in Patients with Low Back Pain? A Longitudinal Cohort from the US Military Health System.
Rhon, D., O'Hagan, E. T., Mysliwiec, V., & Lentz, T. A. (2019) · Spine · doi:10.1097/brs.0000000000003114 · Cited by 14
“The generalized linear model provides flexibility for analysis of costs with a non-normal distribution.(35) We used a generalized linear model with Tweedie distribution and log link to evaluate cost outcomes.”
Method
What are the important morbidities associated with paediatric cardiac surgery? A mixed methods study
Brown, K., Pagel, C., Ridout, D. A., Wray, J., Anderson, D. R., Barron, D. J., Cassidy, J. V., Davis, P. J., Hudson, E., Jones, A. S., et al. (2019) · BMJ Open · doi:10.1136/bmjopen-2018-028533 · Cited by 20
Cost-minimization study of the percutaneous approach to endovascular aortic aneurysm repair
Hong, J. C., Yang, G. K., Delarmente, B. A., Khera, R., Price, J., Faulds, J., & Chen, J. (2019) · Journal of Vascular Surgery · doi:10.1016/j.jvs.2019.03.040 · Cited by 19
Mental health–related hospitalizations among adolescents and emerging adults with autism in the United States: A retrospective, cross-sectional analysis of national hospital discharge data
McMaughan, D. J., Imanpour, S., Mulcahy, A. C., Jones, J. L., & Criss, M. M. (2023) · Autism · doi:10.1177/13623613221143592 · Cited by 20
“The gamma model accounts for this skewness by down-weighting “outlier” hospital discharges with unusually high costs (Barber & Thompson, 2004).”
Economic evaluation comparing From Home To Operation same day admission and preoperative admission one day prior to the surgery process : a randomized, controlled trial of laparoscopic cholecystectomy
Keränen, J., Soini, E. J., Ryynänen, O., Hietaniemi, K., & Keränen, U. (2007) · Current Medical Research and Opinion · doi:10.1185/030079907x233223 · Cited by 19
Long-term cost-effectiveness of cognitive behavioral therapy versus psychodynamic therapy in social anxiety disorder
Egger, N., Konnopka, A., Beutel, M. E., Herpertz, S., Hiller, W., Hoyer, J., Salzer, S., Stangier, U., Strauss, B. M., Willutzki, U., et al. (2016) · Depression and Anxiety · doi:10.1002/da.22540 · Cited by 19
“…of healthcare services and the patients’ working capacity differently, development of costs between baseline and the end of follow-up after 30 months were explored with generalized linear mixed models with gamma distribution and log link (Barber & Thompson, 2004; Manning, Basu, & Mullahy, 2005).”
Method
Intramural Healthcare Consumption and Costs After Traumatic Brain Injury: A Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) Study
Kaplan, Z. L. R., van der Vlegel, M., van Dijck, J. T. J. M., Pisică, D., van Leeuwen, N., Lingsma, H. F., Steyerberg, E. W., Haagsma, J. A., Majdán, M., & Polinder, S. (2023) · Journal of Neurotrauma · doi:10.1089/neu.2022.0429 · Cited by 18
“001 Median [IQR], years 53 [33-68] 55 [35-70] 47 [29-64] 51 [32-67] 16-25 years 449 15.”
Value-driven cardiac surgery: Achieving “perfect care” after coronary artery bypass grafting
Glotzbach, J. P., Sharma, V., Tonna, J. E., Pettit, J. C., McKellar, S. H., Eckhauser, A. W., Varghese, T. K., & Selzman, C. H. (2018) · Journal of Thoracic and Cardiovascular Surgery · doi:10.1016/j.jtcvs.2018.03.177 · Cited by 18
Development of BMI values of German children and their healthcare costs
Batscheider, A., Rzehak, P., Teuner, C. M., Wolfenstetter, S. B., Leidl, R., Berg, A. V., Berdel, D., Hoffmann, B. H., & Heinrich, J. (2013) · Economics & Human Biology · doi:10.1016/j.ehb.2013.05.007 · Cited by 18
A population‐based estimate of the economic burden of influenza in Peru, 2009–2010
Tinoco, Y. O., Azziz‐Baumgartner, E., Razuri, H. R., Kasper, M. R., Romero, C., Ortiz, E. J., Gómez, J., Widdowson, M., Uyeki, T. M., Gilman, R. H., et al. (2015) · Influenza and Other Respiratory Viruses · doi:10.1111/irv.12357 · Cited by 18
Fractional flow reserve (FFR) versus angiography in guiding management to optimise outcomes in non-ST segment elevation myocardial infarction (FAMOUS-NSTEMI) developmental trial: cost-effectiveness using a mixed trial- and model-based methods
Nam, J., Briggs, A. H., Layland, J. J., Oldroyd, K. G., Curzen, N. P., Sood, A., Balachandran, K. P., Das, R., Junejo, S., Eteiba, H., et al. (2015) · Cost Effectiveness and Resource Allocation · doi:10.1186/s12962-015-0045-9 · Cited by 18
“GLM is the appropriate method when the objective is to obtain efficient estimation of skewed variables [20, 25–27].”
Method
The Association Between HbA1c and 1-Year Diabetes-Related Medical Costs: A Retrospective Claims Database Analysis
Boye, K. S., Lage, M. J., & Thieu, V. T. (2022) · Diabetes Therapy · doi:10.1007/s13300-022-01212-4 · Cited by 17
“Specifically, given the skewed nature of cost data, generalized linear models (GLM) with gamma distribution and log link [12] were used to examine diabetes-related total costs, outpatient costs, and drug costs, while diabetes-related acute care costs were examined using a two-part model.”
Method
Viral lower respiratory tract infections and preterm infants’ healthcare utilisation
Drysdale, S. B., Alcazar‐Paris, M., Wilson, T. M., Smith, M. H., Zuckerman, M. A., Peacock, J. L., Johnston, S. L., & Greenough, A. (2014) · European Journal of Pediatrics · doi:10.1007/s00431-014-2380-9 · Cited by 17
“29 Respiratory 323 [1,165] 244 [1,119] 0 [0] 0.”
MethodInfluential
Is an enhanced behaviour change intervention cost-effective compared with physiotherapy for patients with chronic low back pain? Results from a multicentre trial in Israel
Canaway, A., Pincus, T., Underwood, M. R., Shapiro, Y., Chodick, G., & Ami, N. B. (2018) · BMJ Open · doi:10.1136/bmjopen-2017-019928 · Cited by 17
Costs and Their Predictors in Transsphenoidal Pituitary Surgery
Asemota, A. O., Ishii, M., Brem, H., & Gallia, G. L. (2018) · Neurosurgery · doi:10.1093/neuros/nyy441 · Cited by 17
Health outcomes, utility and costs of returning incidental results from genomic sequencing in a Canadian cancer population: protocol for a mixed-methods randomised controlled trial
Shickh, S., Clausen, M., Mighton, C. E., Salazar, M. G., Zakoor, K.-R., Kodida, R., Reble, E., Elser, C., Eisen, A. F., Panchal, S., et al. (2019) · BMJ Open · doi:10.1136/bmjopen-2019-031092 · Cited by 18
Hyperuricemia is associated with increased hospitalization risk and healthcare costs: Evidence from an administrative database in Italy
Esposti, L. D., Desideri, G., Saragoni, S., Buda, S., Pontremoli, R., & Borghi, C. (2016) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2016.06.008 · Cited by 16
“A generalized linear model with an identity link function and a gamma distribution was used to estimate the association between healthcare costs and SUA levels [34].”
Method
Decision Making for Healthcare Resource Allocation: Joint v. Separate Decisions on Interacting Interventions
Dakin, H., & Gray, A. M. (2018) · Medical Decision Making · doi:10.1177/0272989x18758018 · Cited by 16
Health care costs of endovascular compared with open thoracoabdominal aortic aneurysm repair
Rocha, R. V., de Mestral, C., Tam, D. Y., Lee, D. S., Al-Omran, M. A., Austin, P. C., Forbes, T. L., Ouzounian, M., & Lindsay, T. F. (2020) · Journal of Vascular Surgery · doi:10.1016/j.jvs.2020.09.034 · Cited by 16
Incremental medical cost of delirium in elderly patients with cognitive impairment: analysis of a nationwide administrative database in Japan
Igarashi, M., Okuyama, K., Ueda, N., Sano, H., Takahashi, K., Qureshi, Z. P., Tokita, S., Ogawa, A., Okumura, Y., & Okuda, S. (2022) · BMJ Open · doi:10.1136/bmjopen-2022-062141 · Cited by 16
Periodontal treatment associated with decreased diabetes mellitus–related treatment costs
Thakkar‐Samtani, M., Heaton, L. J., Kelly, A. L., Taylor, S. D., Vidone, L., & Tranby, E. P. (2023) · The Journal of the American Dental Association · doi:10.1016/j.adaj.2022.12.011 · Cited by 16
Protocol for a 1-year prospective, longitudinal cohort study of patients undergoing Roux-en-Y gastric bypass and sleeve gastrectomy: the BARI-LIFESTYLE observational study
Jassil, F. C., Carnemolla, A., Kingett, H., Paton, B. M., O’Keeffe, A. G., Doyle, J., Stephen Morris, A., Lewis, N., Kirk, A., Pucci, A. B. F., et al. (2018) · BMJ Open · doi:10.1136/bmjopen-2017-020659 · Cited by 20
“To account for skewness of the cost data, we will use a generalised linear model with gamma family and log link.(58)”
Method

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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