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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Turner, D. A., Paul, S. K., Stone, M. A., Juarez-Garcia, A., Squire, I. B., & Khunti, K. (2008) · Heart · doi:10.1136/hrt.2007.125708 · Cited by 54
Health care costs and resource utilization for different asthma severity stages in Colombia: a claims data analysis
Flórez-Tanus, Á., Padilla, D. P., Zakzuk, J., Caraballo, L. R., & Alvis‐Guzmán, N. (2018) · World Allergy Organization Journal · doi:10.1186/s40413-018-0205-4 · Cited by 52
Estimating the Effectiveness of DPYD Genotyping in Italian Individuals Suffering from Cancer Based on the Cost of Chemotherapy-Induced Toxicity
Fragoulakis, V., Roncato, R., Fratte, C. D., Ecca, F., Bartsakoulia, M., Innocenti, F., Toffoli, G., Cecchin, E., Patrinos, G. P., & Mitropoulou, C. (2019) · The American Journal of Human Genetics · doi:10.1016/j.ajhg.2019.04.017 · Cited by 52
STATISTICAL METHODS FOR COST‐EFFECTIVENESS ANALYSES THAT USE OBSERVATIONAL DATA: A CRITICAL APPRAISAL TOOL AND REVIEW OF CURRENT PRACTICE
Kreif, N., Grieve, R., & Sadique, Z. (2012) · Health Economics · doi:10.1002/hec.2806 · Cited by 54
“• The fit of models estimated through a maximum likelihood method can be assessed using loglikelihood based fit statistics, for example, the Akaike Information Criterion or the Bayesian Information Criterion (Barber and Thompson, 2004; Jackson et al., 2011).”
Method
Healthcare Use, Social Burden and Costs of Children With and Without ADHD in Flanders, Belgium
Ridder, A. D., & Graeve, D. D. (2006) · Clinical Drug Investigation · doi:10.2165/00044011-200626020-00003 · Cited by 51
Changes in health care costs before and after smoking cessation
Fishman, P. A., Thompson, E., Merikle, E. P., & Curry, S. J. (2006) · Nicotine & Tobacco Research · doi:10.1080/14622200600670314 · Cited by 51
METHODS FOR COVARIATE ADJUSTMENT IN COST‐EFFECTIVENESS ANALYSIS THAT USE CLUSTER RANDOMISED TRIALS
Gomes, M., Grieve, R., Nixon, R. M., Ng, E. S. W., Carpenter, J. R., & Thompson, S. G. (2012) · Health Economics · doi:10.1002/hec.2812 · Cited by 50
Self-citation
Comparison of statistical and machine learning models for healthcare cost data: a simulation study motivated by Oncology Care Model (OCM) data
Mazumdar, M., Lin, J.-Y., Zhang, W., Li, L., Liu, M., Dharmarajan, K., Sanderson, M., Isola, L., & Hu, L.-Y. (2020) · BMC Health Services Research · doi:10.1186/s12913-020-05148-y · Cited by 40
“Gamma GLM is often used in practice to capture these features [6, 7].”
Method
Conducting Trial-Based Economic Evaluations Using R: A Tutorial
Ben, Â. J., van Dongen, J. M., Alili, M. E., Eßer, J., Broulíková, H. M., & Bosmans, J. E. (2023) · PharmacoEconomics · doi:10.1007/s40273-023-01301-7 · Cited by 48
“gamma, Gaussian) can be specified [61].”
Association of Refill Adherence and Health Care Use Among Adults with Hypertension in an Urban Health Care System
Stroupe, K. T., Teal, E., Tu, W., Weiner, M., & Murray, M. D. (2006) · Pharmacotherapy The Journal of Human Pharmacology and Drug Therapy · doi:10.1592/phco.26.6.779 · Cited by 48
“Deyo-Charlson Comorbidity Index score 0 6145 (60) 1380 (28) 1 3132 (30) 1687 (34) 2 648 (6) 955 (20) 3 209 (2) 440 (9) > 3 175 (2) 435 (9)”
Regression-adjusted matching and double-robust methods for estimating average treatment effects in health economic evaluation
Kreif, N., Grieve, R., Radice, R., & Sekhon, J. S. (2013) · Health Services and Outcomes Research Methodology · doi:10.1007/s10742-013-0109-2 · Cited by 54
“2.1 Regression adjustment Incremental cost, effectiveness and cost-effectiveness can be modelled with simple generalised linear models (GLM) (Barber and Thompson 2004), two-part models (Buntin and Zaslavsky 2004; Basu 2011), semi-parametric methods such as extended estimating equations (Basu and…”
BackgroundMethodInfluential
Intermittent Hemodialysis Versus Continuous Renal Replacement Therapy for Acute Renal Failure in the Intensive Care Unit: An Observational Outcomes Analysis
Rauf, A. A., Long, K. H., Gajic, O., Anderson, S. S., Swaminathan, L., & Albright, R. C. (2008) · Journal of Intensive Care Medicine · doi:10.1177/0885066608315743 · Cited by 48
“Generalized linear modeling techniques were used to assess costs and LOS to account for the nonnegative and typically skewed nature of these economic endpoints.(22) Cost models assumed a logarithmic link function and a γ or Poisson distribution based on the modified Park test recommended by Manning and Mullahy.”
Method
Employment and Income of People Who Experience Mental Illness and Homelessness in a Large Canadian Sample
Poremski, D., Distasio, J., Hwang, S. W., & Latimer, E. A. (2015) · The Canadian Journal of Psychiatry · doi:10.1177/070674371506000902 · Cited by 47
The economic burden of complications during percutaneous coronary intervention
Jacobson, K. M., Long, K. H., McMurtry, E., Naessens, J. M., & Rihal, C. S. (2007) · BMJ Quality & Safety · doi:10.1136/qshc.2006.019331 · Cited by 47
Glycemic control and diabetes-related health care costs in type 2 diabetes; retrospective analysis based on clinical and administrative databases
Esposti, L. D., Esposti, D., Buda, Saragoni, & Sturani, A. (2013) · ClinicoEconomics and Outcomes Research · doi:10.2147/ceor.s41846 · Cited by 46
“A generalized linear model with an identity link function and a gamma distribution was used to estimate the association between health care costs and level of glycemic control.(21) To control for confounding, we included in the model factors including age, gender, Charlson comorbidity index, coexisting illnesses (such…”
Direct medical cost associated with diabetic retinopathy severity in type 2 diabetes in Singapore
Zhang, X., Low, S. K., Neelam, K., Wang, J., Ang, K., Yeo, D., Yip, C. C., Subramaniam, T., Sum, C. F., & Lim, S. C. (2017) · PLoS ONE · doi:10.1371/journal.pone.0180949 · Cited by 47
Relative weight-related costs of healthcare use by children—Results from the two German birth cohorts, GINI-plus and LISA-plus
Breitfelder, A., Wenig, C. M., Wolfenstetter, S. B., Rzehak, P., Menn, P., John, J., Leidl, R., Bauer, C. P., Koletzko, S., Röder, S. W., et al. (2011) · Economics & Human Biology · doi:10.1016/j.ehb.2011.02.001 · Cited by 45
Trends in Mortality and Medical Spending in Patients Hospitalized for Community-Acquired Pneumonia
Ruhnke, G. W., Perraillon, M. C., Kitch, B. T., & Cutler, D. (2010) · Medical Care · doi:10.1097/mlr.0b013e3181f38006 · Cited by 46
“We also performed 2 generalized linear model (GLM) regressions to analyze cost trends, both of which specified cost as the dependent variable, using a gamma distribution and log-link function.(20) Because of a nonrandom pattern of residuals in the highest-cost 1% of hospitalizations, this 1% was eliminated from the an…”
Method
The second Randomised Evaluation of the Effectiveness, cost-effectiveness and Acceptability of Computerised Therapy (REEACT-2) trial: does the provision of telephone support enhance the effectiveness of computer-delivered cognitive behaviour therapy? A randomised controlled trial.
Brabyn, S., Araya, R., Barkham, M., Bower, P., Cooper, C., Duarte, A., Kessler, D., Knowles, S. E., Lovell, K., Littlewood, E., et al. (2016) · Health Technology Assessment · doi:10.3310/hta20890 · Cited by 36
“The regression model applied for the incremental analysis of costs in the base case was a generalised linear model.(34) This type of model was preferred to an OLS model, as cost data tend to be heavily skewed and follow a non-normal distribution, which leads to violations of the OLS assumptions.”
Method
DEEP Study: Indirect and Out-of-pocket Costs of Persistent Orofacial Pain
Breckons, M., Shen, J., Bunga, J. J., Vale, L. D., & Durham, J. (2018) · Journal of Dental Research · doi:10.1177/0022034518773310 · Cited by 45
“As appropriate for cost data with a skewed distribution (Barber and Thompson 2004), generalized linear models (GLMs) with a log-link function were used to examine the relationship between dichotomized GCPS status and out-of-pocket costs and indirect costs, controlling for demographic and socioeconomic factors, includi…”
Method
Cost-effectiveness of spinal manipulative therapy, supervised exercise, and home exercise for older adults with chronic neck pain
Leininger, B. D., McDonough, C. M., Evans, R., Tosteson, T. D., Tosteson, A. N. A., & Brønfort, G. (2016) · The Spine Journal · doi:10.1016/j.spinee.2016.06.014 · Cited by 48
“Generalized estimating equations specifying a poisson distribution and identity link were used to estimate mean costs over the year.[40, 41] Separate models were performed to estimate cost rates for medication use (one week) and lost productivity (one month).”
Method
Cost and cost-effectiveness of cardiac surgery in elderly patients
Gelsomino, S., Lorusso, R., Livi, U., Masullo, G., Lucà, F., Maessen, J. G., & Gensini, G. F. (2011) · Journal of Thoracic and Cardiovascular Surgery · doi:10.1016/j.jtcvs.2011.02.013 · Cited by 43
Comparative effectiveness of pleural drainage procedures for the treatment of complicated pneumonia in childhood
Shah, S. S., Hall, M., Newland, J. G., Brogan, T. V., Farris, R. W. D., Williams, D. J., Larsen, G. Y., Fine, B. R., Levin, J. E., Wagener, J. S., et al. (2011) · Journal of Hospital Medicine · doi:10.1002/jhm.872 · Cited by 43
Counting the time lived, the time left or illness? Age, proximity to death, morbidity and prescribing expenditures
Moore, P. V., Bennett, K., & Normand, C. E. M. (2017) · Social Science & Medicine · doi:10.1016/j.socscimed.2017.04.038 · Cited by 43
“…þ X35 t¼1 gtMtD The use of a log link function in the GLM means the coefficients act multiplicatively on the mean, by taking the exponential they can be expressed as the percentage increase in the mean monthly medication expenditure per unit increase in the covariate (Barber and Thompson, 2004).”
Method
Economic evaluation of factorial randomised controlled trials: challenges, methods and recommendations
Dakin, H., & Gray, A. M. (2017) · Statistics in Medicine · doi:10.1002/sim.7322 · Cited by 43
“6 Transforming costs and QALYs prior to analysis means that coefficients, statistical inference and predictions are on the transformed scale and are not applicable to the natural scale [3,31,34].”
Background
The Contribution of Tobacco Use to High Health Care Utilization and Medical Costs in Peripheral Artery Disease
Duval, S., Long, K. H., Roy, S. S., Oldenburg, N. C., Harr, K., Fee, R. M., Sharma, R. R., Alesci, N. L., & Hirsch, A. T. (2015) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2015.06.1349 · Cited by 42
“Generalized linear modeling assessed the impact of smoking status on total costs (27), and used a logarithmic link function with a gamma distribution on the basis of the modified Park test (28).”
Method
Gamma shape mixtures for heavy-tailed distributions
Venturini, S., Dominici, F., & Parmigiani, G. (2008) · The Annals of Applied Statistics · doi:10.1214/07-aoas156 · Cited by 42
“(2002), Buntin and Zaslavsky (2004), Barber and Thompson (2004), Manning and Mullahy (2005), Powers et al. (2005), Dodd et al.”
A scoping review of statistical methods for trial‐based economic evaluations: The current state of play
Alili, M. E., van Dongen, J. M., Eßer, J., Heymans, M. W., van Tulder, M. W., & Bosmans, J. E. (2022) · Health Economics · doi:10.1002/hec.4603 · Cited by 41
“Regression-based adjustment (e.g. OLS regression, seemingly unrelated regression, a generalized linear model) Barber and Thompson (2004); Gabrio et al.”
BackgroundMethodInfluential
Healthcare resource utilization and costs of nonalcoholic steatohepatitis patients with advanced liver disease in Italy
Petta, S., Ting, J., Saragoni, S., Esposti, L. D., Shreay, S., Petroni, M. L., & Marchesini, G. (2020) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2020.02.016 · Cited by 41
Cost-effectiveness of internet-delivered vs in-person cognitive behavioral therapy for children and adolescents with obsessive-compulsive disorder
Aspvall, K., Sampaio, F., Lenhard, F., Melin, K., Norlin, L., Serlachius, E., Mataix-Cols, D., & Andersson, E. (2021) · JAMA Network Open · doi:10.1001/jamanetworkopen.2021.18516 · Cited by 39
The impact of BMI on direct costs in Children and Adolescents: empirical findings for the German Healthcare System based on the KiGGS-study
Wenig, C. M. (2010) · The European Journal of Health Economics · doi:10.1007/s10198-010-0278-7 · Cited by 39
“The effect of independent variables on total costs was analysed using a generalised linear mixed regression model (GLIMMIX procedure, SAS), assuming a log-link function and a gamma distribution of the response variable [ 38 , 39].”
Method
COVID-19 healthcare cost and length of hospital stay in Turkey: retrospective analysis from the first peak of the pandemic
Öksüz, E., Malhan, S., Gönen, M. S., Kutlubay, Z., Keskindemirci, Y., & Tabak, F. (2021) · Health Economics Review · doi:10.1186/s13561-021-00338-8 · Cited by 39
Costs and Health-Related Quality of Life in Patients With NMO Spectrum Disorders and MOG-Antibody–Associated Disease
Hümmert, M. W., Schöppe, L. M., Bellmann-Strobl, J., Siebert, N., Paul, F., Duchow, A., Pellkofer, H., Kümpfel, T., Havla, J., Jarius, S., et al. (2022) · Neurology · doi:10.1212/wnl.0000000000200052 · Cited by 39
“Due to this point and the right-skewness of our cost data, we calculated our 95% CIs of the means with SPSS bootstrap function.(27,28) Because of the explorative character of the study, we did not correct for multiple testing.”
Method
Rhinovirus infection and healthcare utilisation in prematurely born infants
Drysdale, S. B., Alcazar‐Paris, M., Wilson, T. M., Smith, M. H., Zuckerman, M. A., Broughton, S. J., Rafferty, G. F., Peacock, J. L., Johnston, S. L., & Greenough, A. (2013) · European Respiratory Journal · doi:10.1183/09031936.00109012 · Cited by 39
GAMMA SHAPE MIXTURES FOR HEAVY-TAILED DISTRIBUTIONS
Venturini, S., Dominici, F., & Parmigiani, G. (2006) · Collection of Biostatistics Research Archive · Cited by 39
End-of-life cost and its determinants for cancer patients in urban China: a population-based retrospective study
Li, Z., Pan, Z., Zhang, L., He, R., Jiang, S., Xu, C., Lu, F., Zhang, P., & Li, B. (2019) · BMJ Open · doi:10.1136/bmjopen-2018-026309 · Cited by 37
“Generalised linear models were used to evaluate the mechanism of the effect of independent variables on the EOL cost because the EOL data were severely positively skewed.(40) 41 Four regression models were conducted for patients with different lengths of survival, the EOL costs were the outcome variables, and the inde…”
Method
A Mobile Phone App Improves Patient-Physician Communication and Reduces Emergency Department Visits After Colorectal Surgery
Eustache, J., Latimer, E. A., Liberman, A. S., Charlebois, P., Stein, B., Fiore, J. F., Feldman, L. S., & Lee, L. (2021) · Diseases of the Colon & Rectum · doi:10.1097/dcr.0000000000002187 · Cited by 37
Economic Analysis of Ticagrelor Therapy From a U.S. Perspective
Cowper, P. A., Pan, W., Anstrom, K. J., Kaul, P., Wallentin, L. C., Davidson-Ray, L. D., Nikolic, E., Janzon, M., Levin, L., Cannon, C. P., et al. (2015) · Journal of the American College of Cardiology · doi:10.1016/j.jacc.2014.11.034 · Cited by 36
“A generalized linear model for hospitalization cost was specified with an identity link and a gamma distribution function (11).”
Method
Healthcare utilization and costs of Veterans screened and assessed for traumatic brain injury
Stroupe, K. T., Smith, B., Hogan, T. P., Andre, J. R. S., Pape, T., Steiner, M. L., Proescher, E., Huo, Z., & Evans, C. T. (2013) · The Journal of Rehabilitation Research and Development · doi:10.1682/jrrd.2012.06.0107 · Cited by 39
“To examine the association of the three TBI screening groups and two TBI evaluation results groups with total direct healthcare costs after controlling for other factors, we used generalized linear models (GLMs) [18].”
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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