Multiple regression of cost data: use of generalised linear models
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.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Cost data and QALYs will be analysed using generalised linear models to account for non-normal distributions.
“Cost data and QALYs will be analysed using generalised linear models to account for non-normal distributions.83”
From Development, evaluation and implementation of a digital behavioural health treatment for chronic pain: study protocol of the multiphase DAHLIA project (2022) · cites this paper as [83]
Cites
Model selection and multimodel inference: a practical information-theoretic approach.
Guthery, F. S., Burnham, K. P., & Anderson, D. R. (2003) · The Journal of Wildlife Management · doi:10.2307/3802723 · Cited by 41,495 · see citing works
(2005) · Springer eBooks · doi:10.1007/0-387-27255-0_9 · Cited by 20,333 · see citing works
Longitudinal data analysis using generalized linear models
LIANG, K.-Y., & ZEGER, S. L. (1986) · Biometrika · doi:10.1093/biomet/73.1.13 · Cited by 18,550 · see citing works
Practical Statistics for Medical Research.
Walter, S., & Altman, D. G. (1992) · Biometrics · doi:10.2307/2532320 · Cited by 11,665 · see citing works
A Comparison of Alternative Models for the Demand for Medical Care
Duan, N.-H., Manning, W., Morris, C., & Newhouse, J. (1983) · Journal of Business and Economic Statistics · doi:10.1080/07350015.1983.10509330 · Cited by 1,410 · see citing works
Estimating log models: to transform or not to transform?
Manning, W. G., & Mullahy, J. (2001) · Journal of Health Economics · doi:10.1016/s0167-6296(01)00086-8 · Cited by 1,145 · see citing works
Representing uncertainty: the role of cost‐effectiveness acceptability curves
Fenwick, E. A. L., Claxton, K., & Sculpher, M. J. (2001) · Health Economics · doi:10.1002/hec.635 · Cited by 1,112 · see citing works
Stinnett, A. A., & Mullahy, J. (1998) · Medical Decision Making · doi:10.1177/0272989x98018002s09 · Cited by 1,103 · see citing works
The logged dependent variable, heteroscedasticity, and the retransformation problem.
Manning, W. (1998) · Journal of Health Economics · doi:10.1016/s0167-6296(98)00025-3 · Cited by 959 · see citing works
Much ado about two: reconsidering retransformation and the two-part model in health econometrics.
Mullahy, J. (1998) · Journal of Health Economics · doi:10.1016/s0167-6296(98)00030-7 · Cited by 791 · see citing works
Hoch, J. S., Briggs, A. H., & Willan, A. R. (2002) · Health Economics · doi:10.1002/hec.678 · Cited by 535 · see citing works
Modeling risk using generalized linear models.
Blough, D., Madden, C., & Hornbrook, M. (1999) · Journal of Health Economics · doi:10.1016/s0167-6296(98)00032-0 · Cited by 473 · see citing works
The Distribution of Health Care Costs and Their Statistical Analysis for Economic Evaluation
Briggs, A., & Gray, A. (1998) · Journal of Health Services Research and Policy · doi:10.1177/135581969800300410 · Cited by 288 · see citing works
Barber, J., & Thompson, S. G. (1998) · BMJ · doi:10.1136/bmj.317.7167.1195 · Cited by 254 · see citing works
Self-citationLinear regression analysis of censored medical costs
Lin, D. Y. (2000) · Biostatistics · doi:10.1093/biostatistics/1.1.35 · Cited by 231 · see citing works
Using Generalized Linear Models to Assess Medical Care Costs
Blough, D., & Ramsey, S. (2000) · Health Services & Outcomes Research Methodology · doi:10.1023/a:1012597123667 · Cited by 225 · see citing works
The Use of the Bootstrap Statistical Method for the Pharmacoeconomic Cost Analysis of Skewed Data
Desgagné, A., Castilloux, A., Angers, J., & LeLorier, J. (1998) · PharmacoEconomics · doi:10.2165/00019053-199813050-00002 · Cited by 180 · see citing works
Methods for Comparison of Cost Data
Zhou, X., Melfi, C. A., & Hui, S. L. (1997) · Annals of Internal Medicine · doi:10.7326/0003-4819-127-8_part_2-199710151-00063 · Cited by 129 · see citing works
Walter (1998) · doi:10.1002/(sici)1097-0258(19980115)17:1
Flagged first, then by citations
1 of the 20 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Truby, H., Baic, S., deLooy, A., Fox, K. R., Livingstone, M. B. E., Logan, C. M., Macdonald, I. A., Morgan, L. M., Taylor, M. A., & Millward, D. J. (2006) · BMJ · doi:10.1136/bmj.38833.411204.80 · Cited by 284 · see citing works
The Burden of Gastrointestinal Anastomotic Leaks: an Evaluation of Clinical and Economic Outcomes
Hammond, J., Lim, S., Wan, Y., Gao, X. Y., & Patkar, A. D. (2014) · Journal of Gastrointestinal Surgery · doi:10.1007/s11605-014-2506-4 · Cited by 270 · see citing works
“(%) 1,528 (14) 1,172 (13) 356 (20) Others, No.”
Methods for Improving Regression Analysis for Skewed Continuous or Counted Responses
Afifi, A. A., Kotlerman, J. B., Ettner, S. L., & Cowan, M. J. (2006) · Annual Review of Public Health · doi:10.1146/annurev.publhealth.28.082206.094100 · Cited by 263 · see citing works
Livingston, G., Kelly, L., Lewis-Holmes, E., Baio, G., Stephen Morris, A., Patel, N. V., Omar, R., Katona, C., & Cooper, C. (2014) · Health Technology Assessment · doi:10.3310/hta18390 · Cited by 244 · see citing works
Stephen Morris, A., Hunter, R. M., Ramsay, A. I. G., Boaden, R., McKevitt, C., Perry, C., Pursani, N., Rudd, A. G., Schwamm, L. H., Turner, S., et al. (2014) · BMJ · doi:10.1136/bmj.g4757 · Cited by 216 · see citing works
Health literacy and the use of healthcare services in Belgium
Vandenbosch, J., den Broucke, S. V., Vancorenland, S., Avalosse, H., Verniest, R., & Callens, M. G. (2016) · Journal of Epidemiology & Community Health · doi:10.1136/jech-2015-206910 · Cited by 182 · see citing works
New models for old questions: generalized linear models for cost prediction
Moran, J. L., Solomon, P. J., Peisach, A. R., & Martin, J. (2007) · Journal of Evaluation in Clinical Practice · doi:10.1111/j.1365-2753.2006.00711.x · Cited by 177 · see citing works
“It has been suggested that health care expenditure and use data frequently have a log-normal or gamma distribution and the studies using GLM for cost analysis have focused on the gamma response distribution [6,10].”
Regression models for analyzing costs and their determinants in health care: an introductory review
Gregori, D., Petrinco, M., Bo, S., Desideri, A., Merletti, F., & Pagano, E. (2011) · International Journal for Quality in Health Care · doi:10.1093/intqhc/mzr010 · Cited by 176 · see citing works
“0, usually via an appropriate model in the linear or GLM class.”
BackgroundInfluentialCarregaro, R. L., Tottoli, C. R., Rodrigues, D. D. S., Bosmans, J. E., da Silva, E. N., & van Tulder, M. W. (2020) · PLoS ONE · doi:10.1371/journal.pone.0230902 · Cited by 147 · see citing works
“Considering individual data on productivity losses, we adopted a generalized linear model [32] with a gamma regression to the response variables absence from work (in days), and lost productivity costs per person (in US$), to determine which factors contribute the most to a greater absence from work and lost productiv…”
BackgroundMethodSimoni, J. M., Wei, Y. J., Qian, J., Zuckerman, I. H., Stuart, B., Shaffer, T., Dalal, A. A., & Bryant‐Comstock, L. (2012) · The American Journal of Geriatric Pharmacotherapy · doi:10.1016/j.amjopharm.2012.04.002 · Cited by 131 · see citing works
Nixon, R. M., & Thompson, S. G. (2005) · Health Economics · doi:10.1002/hec.1008 · Cited by 128 · see citing works
“In our example, we used a gamma distribution for costs and an identity link function, whereby the covariates acted additively on the predicted mean, in line with recent analyses of the same data [37].”
BackgroundMethodSelf-citationWhere Is the Value in Ambulatory Versus Inpatient Surgery?
Friedlander, D. F., Krimphove, M. J., Cole, A. P., Marchese, M., Lipsitz, S. R., Weissman, J. S., Schoenfeld, A. J., Ortega, G., & Trinh, Q. (2019) · Annals of Surgery · doi:10.1097/sla.0000000000003578 · Cited by 121 · see citing works
“Following IPTW, gamma generalized linear and logistic regression models adjusted for facility clustering and multiple endpoint comparisons (via the HOLM’s correction) were employed to compare index surgical/30-day costs and odds of 30-day readmission between the ambulatory and inpatient surgery cohorts, respectively.(…”
MethodMaheswaran, H., Petrou, S., MacPherson, P., Choko, A. T., Kumwenda, F., Lalloo, D. G., Clarke, A., & Corbett, E. L. (2016) · BMC Medicine · doi:10.1186/s12916-016-0577-7 · Cited by 111 · see citing works
“As all participants incurred a cost, and the cost data were skewed, we used generalized linear models (GLM) for multivariate analyses of cost data [30].”
Cox, C. E., Lewis, C. L., Hanson, L. C., Hough, C. L., Kahn, J. M., White, D. B., Song, M., Tulsky, J. A., & Carson, S. S. (2012) · Critical Care Medicine · doi:10.1097/ccm.0b013e3182536a63 · Cited by 112 · see citing works
“08b Hospital length of stay 57 (33) 37 (32) .”
MethodStephen Morris, A., Ramsay, A. I. G., Boaden, R., Hunter, R. M., McKevitt, C., Paley, L., Perry, C., Rudd, A. G., Turner, S., Tyrrell, P. J., et al. (2019) · BMJ · doi:10.1136/bmj.l1 · Cited by 106 · see citing works
Whitney, D. G., Kamdar, N. S., Ng, S., Hurvitz, E. A., & Peterson, M. D. (2019) · Clinical Epidemiology · doi:10.2147/clep.s205839 · Cited by 99 · see citing works
How to Deal with Cost Differences at Baseline
van Asselt, A. D. I., van Mastrigt, G. A. P. G., Dirksen, C. D., Arntz, A. R., Severens, J. L., & Kessels, A. G. H. (2009) · PharmacoEconomics · doi:10.2165/00019053-200927060-00007 · Cited by 97 · see citing works
Energy use and height in office buildings
Godoy-Shimizu, D., Steadman, P., Hamilton, I., Donn, M., Evans, S., Moreno, G., & Shayesteh, H. (2018) · Building Research & Information · doi:10.1080/09613218.2018.1479927 · Cited by 91 · see citing works
“For further information about GLM, including an overview of the different options, see Barber and Thompson (2004).”
MethodFritz, J. M., Brennan, G. P., Hunter, S. J., & Magel, J. S. (2013) · Archives of Physical Medicine and Rehabilitation · doi:10.1016/j.apmr.2013.01.008 · Cited by 90 · see citing works
“The generalized linear model allows for parametric analytic methods while accommodating nonnormal distributions and makes inferences about the mean cost directly, avoiding the potential bias of retransformation.(26) Independent variables in the model were patient characteristics, comorbidities, and initial management…”
MethodLittlewood, E., Duarte, A., Hewitt, C. E., Knowles, S. E., Palmer, S., Walker, S., Andersen, P., Araya, R., Barkham, M., Bower, P., et al. (2015) · Health Technology Assessment · doi:10.3310/hta191010 · Cited by 94 · see citing works
“)) to define the relationship between the mean (μi) and covariates (xji).(69) This allows the selection of a distribution that better fits cost data and enables issues with heteroscedasticity (i.”
BackgroundMethodHealthcare Cost and Impact of Persistent Orofacial Pain
Durham, J., Shen, J., Breckons, M., Steele, J., Araújo‐Soares, V., Exley, C., & Vale, L. D. (2016) · Journal of Dental Research · doi:10.1177/0022034516648088 · Cited by 92 · see citing works
“A bootstrapped one-way analysis of variance was then used to examine differences between costs in the 3 cumulative cost categories in line with recommended practice for cost data (Barber and Thompson 2004).”
MethodExamining Trends in Cost and Clinical Benefit of Novel Anticancer Drugs Over Time
Saluja, R., Arciero, V. S., Cheng, S., McDonald, E. J., Wong, W. W. L., Cheung, M. C., & Chan, K. (2018) · Journal of Oncology Practice · doi:10.1200/jop.17.00058 · Cited by 88 · see citing works
Turnbull, L., Brown, S., Olivier, C., Harvey, I., Brown, J., Drew, P. J., Hanby, A., Manca, A., Napp, V., Sculpher, M., et al. (2010) · Health Technology Assessment · doi:10.3310/hta14010 · Cited by 70 · see citing works
Study of the costs and morbidities of late-preterm birth
Bérard, A., Tiec, M. L., & Vera, M. A. D. (2012) · Archives of Disease in Childhood Fetal & Neonatal · doi:10.1136/fetalneonatal-2011-300969 · Cited by 88 · see citing works
The cost of depression – A cost analysis from a large database
Kleine‐Budde, K., Müller, R., Kawohl, W., Bramesfeld, A., Moock, J., & Wulf Rössler, A. (2012) · Journal of Affective Disorders · doi:10.1016/j.jad.2012.10.024 · Cited by 86 · see citing works
Pressure relieving support surfaces (PRESSURE) trial: cost effectiveness analysis
Iglesias, C. P., Nixon, J., Cranny, G., Nelson, E. A., Cocks, K., Phillips, A., Torgerson, D. J., Mason, S. M., & Cullum, N. A. (2006) · BMJ · doi:10.1136/bmj.38850.711435.7c · Cited by 84 · see citing works
Weichle, T. W., Hynes, D. M., Durazo-Arvizú, R., Tarlov, E., & Zhang, Q. (2013) · SpringerPlus · doi:10.1186/2193-1801-2-614 · Cited by 82 · see citing works
“However, these models are based on the assumption that the regression errors have a normal distribution and linear relationships (Paddock et al. 2004; Barber and Thompson 2004).”
BackgroundMcMain, S. F., Chapman, A. L., Kuo, J. R., Guimond, T., Streiner, D. L., Dixon-Gordon, K. L., Isaranuwatchai, W., & Hoch, J. S. (2018) · BMC Psychiatry · doi:10.1186/s12888-018-1802-z · Cited by 82 · see citing works
Chorozoglou, M., Smith, E., Koerting, J., Thompson, M. J., Sayal, K., & Sonuga‐Barke, E. J. S. (2015) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.12437 · Cited by 77 · see citing works
Keating, C., Neovius, M., Sjöholm, K., Peltonen, M., Narbro, K., Eriksson, J. K., Sjöström, L., & Carlsson, L. M. S. (2015) · The Lancet Diabetes & Endocrinology · doi:10.1016/s2213-8587(15)00290-9 · Cited by 78 · see citing works
Ball, S., Vickery, J., Hobart, J. C., Wright, D., Green, C., Shearer, J., Nunn, A., Cano, M. G., MacManus, D. G., Miller, D. H., et al. (2015) · Health Technology Assessment · doi:10.3310/hta19120 · Cited by 78 · see citing works
Harrison, D., Prabhu, G., Grieve, R., Harvey, S., Sadique, M., Gomes, M., Griggs, K., Walmsley, E., Smith, M., Yeoman, P., et al. (2013) · Health Technology Assessment · doi:10.3310/hta17230 · Cited by 76 · see citing works
Costing and Cost Analysis in Randomized Controlled Trials
Polsky, D. E., & Glick, H. A. (2009) · PharmacoEconomics · doi:10.2165/00019053-200927030-00001 · Cited by 77 · see citing works
“Generalized linear models (GLMs)([3,41,42]) are a class of models that can be used to analyze costs on the log scale while maintaining applicability to the sample mean cost.([43,44]) The GLM can predict the log of mean costs directly, which overcomes the problem faced by the OLS of log costs because with the GLM, a si…”
BackgroundWijeysundera, H., Wang, X.-S., Tomlinson, G., Ko, D. T., & Krahn, M. (2012) · ClinicoEconomics and Outcomes Research · doi:10.2147/ceor.s31552 · Cited by 66 · see citing works
Kerr, C. W., Donohue, K. A., Tangeman, J. C., Serehali, A. M., Knodel, S. M., Grant, P. C., Luczkiewicz, D. L., Mylotte, K. M., & Marien, M. J. (2014) · Journal of Palliative Medicine · doi:10.1089/jpm.2014.0184 · Cited by 75 · see citing works
“The cost total within the last three months of life was modeled as a gamma distribution using a log link function 20 using the generalized linear model procedure.”
Kaier, K., Hils, S., Fetzer, S., Hehn, P., Schmid, A., Hauschke, D., Bogatyreva, L., Jänigen, B. M., & Pisarski, P. (2017) · Health Economics Review · doi:10.1186/s13561-016-0141-3 · Cited by 73 · see citing works
The economic impact of chronic pain: a nationwide population-based cost-of-illness study in Portugal
Azevedo, L. F., Costa‐Pereira, A., Mendonça, L., Dias, C. C., & Castro‐Lopes, J. M. (2014) · The European Journal of Health Economics · doi:10.1007/s10198-014-0659-4 · Cited by 73 · see citing works
“After the descriptive analysis, factors associated with total costs were assessed using generalised linear models (GLMs), following current international recommendations [37].”
MethodThe statistical approach in trial-based economic evaluations matters: get your statistics together!
Mutubuki, E. N., Alili, M. E., Bosmans, J. E., Oosterhuis, T., Snoek, F. J., Ostelo, R., van Tulder, M. W., & van Dongen, J. M. (2021) · BMC Health Services Research · doi:10.1186/s12913-021-06513-1 · Cited by 72 · see citing works
Mani, G., Viswanadhapalli, J. K., & Stonier, A. A. (2021) · Journal of Engineering Research · doi:10.36909/jer.10253 · Cited by 71 · see citing works
The Cost of Hyperkalemia in the United States
Betts, K. A., Woolley, J. M., Mu, F., Xiang, C. Q., Tang, W., & Wu, E. Q. (2017) · Kidney International Reports · doi:10.1016/j.ekir.2017.11.003 · Cited by 71 · see citing works
PREDyCES study: The cost of hospital malnutrition in Spain
León-Sanz, M., Brosa, M., Planás, M., García‐de‐Lorenzo, A., Celaya-Pérez, S., & Hernández, J. Á. (2015) · Nutrition · doi:10.1016/j.nut.2015.03.009 · Cited by 72 · see citing works
Wacker, M. E., Holle, R., Heinrich, J., Ladwig, K., Peters, A., Leidl, R., & Menn, P. (2013) · BMC Health Services Research · doi:10.1186/1472-6963-13-278 · Cited by 69 · see citing works
“This approach has been demonstrated to be a suitable method for healthcare costs [41,42].”
MethodFritz, J. M., Brennan, G. P., & Hunter, S. J. (2015) · Health Services Research · doi:10.1111/1475-6773.12301 · Cited by 68 · see citing works
Middleton, J. F., McKinley, R. K., & Gillies, C. L. (2006) · BMJ · doi:10.1136/bmj.38841.444861.7c · Cited by 68 · see citing works
Home‐based pulmonary rehabilitation for COPD using minimal resources: An economic analysis
Burge, A. T., Holland, A. E., McDonald, C. F., Abramson, M. J., Hill, C. J., Lee, A. L., Cox, N. S., Moore, R., Nicolson, C., O’Halloran, P., et al. (2019) · Respirology · doi:10.1111/resp.13667 · Cited by 68 · see citing works
Lewin, G. F., Allan, J., Patterson, C., Knuiman, M. W., Boldy, D. P., & Hendrie, D. V. (2014) · Health & Social Care in the Community · doi:10.1111/hsc.12092 · Cited by 67 · see citing works
“This choice was based on consideration of the distribution of cost and the relationship of variance to mean (Barber & Thompson 2004).”
BackgroundMedical Expenditures Associated With Diabetes Acute Complications in Privately Insured U.S. Youth
Shrestha, S. S., Ping, Z., Barker, L. E., & Imperatore, G. (2010) · Diabetes Care · doi:10.2337/dc10-1406 · Cited by 64 · see citing works
“We used a generalized linear model with log link and gamma distribution to model total, outpatient, and drug expenditures because all youth had positive expenditures and expenditures were highly skewed and right tailed (20).”
MethodThe costs of social anxiety disorder: the role of symptom severity and comorbidities
Stuhldreher, N., Leibing, E., Leichsenring, F., Beutel, M. E., Herpertz, S., Hoyer, J., Konnopka, A., Salzer, S., Strauss, B., Wiltink, J., et al. (2014) · Journal of Affective Disorders · doi:10.1016/j.jad.2014.04.039 · Cited by 63 · see citing works
Safley, D. M., Amin, A. P., House, J. A., Baklanov, D. V., Mills, R., Giersiefen, H., Bremer, A., & Marso, S. P. (2012) · American Heart Journal · doi:10.1016/j.ahj.2012.10.004 · Cited by 63 · see citing works
Healthcare costs of paternal depression in the postnatal period
Edoka, I. P., Petrou, S., & Ramchandani, P. G. (2011) · Journal of Affective Disorders · doi:10.1016/j.jad.2011.04.005 · Cited by 62 · see citing works
An Educational Review About Using Cost Data for the Purpose of Cost-Effectiveness Analysis
Franklin, M., Lomas, J., Walker, S., & Young, T. (2019) · PharmacoEconomics (Auckland) · doi:10.1007/s40273-019-00771-y · Cited by 48 · see citing works
Cost of Treating Pressure Ulcers for Veterans with Spinal Cord Injury
Stroupe, K. T., Manheim, L. M., Evans, C. T., Guihan, M., Ho, C., Li, K., Cowper-Ripley, D. C., Hogan, T. P., Andre, J. R. S., Huo, Z., et al. (2011) · Topics in Spinal Cord Injury Rehabilitation · doi:10.1310/sci1604-62 · Cited by 58 · see citing works
Postoperative Remote Automated Monitoring: Need for and State of the Science
McGillion, M. H., Duceppe, E., Allan, K. S., Marcucci, M., Yang, S. S., Johnson, A. P., Ross-Howe, S., Peter, E. H., Scott, T., Ouellette, C., et al. (2018) · Canadian Journal of Cardiology · doi:10.1016/j.cjca.2018.04.021 · Cited by 57 · see citing works
Chen, C.-Y., Liu, C.-Y., Su, W.-C., Huang, S.-L., & Lin, K.-M. (2008) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-007-0416-y · Cited by 57 · see citing works
“As to the factors associated with autismrelated services utilization within the year of diagnosis, we turned to Generalized Linear Models in a gamma distribution with a log link function given that an extremely skewed distribution of frequency of outpatient visits failed to satisfy the assumptions for ordinary least s…”
MethodLatimer, E. A., Rabouin, D., Cao, Z., Ly, A., Powell, G. A., Aubry, T., Distasio, J., Hwang, S. W., Somers, J. M., Stergiopoulos, V., et al. (2017) · CMAJ Open · doi:10.9778/cmajo.20170018 · Cited by 58 · see citing works
Association of antipsychotic polypharmacy with health service cost: a register-based cost analysis
Baandrup, L., Sørensen, J. R., Lublin, H., Nordentoft, M., & Glenthoj, B. Y. (2011) · The European Journal of Health Economics · doi:10.1007/s10198-011-0308-0 · Cited by 56 · see citing works
“We report the model that is most appropriate for the data based on graphic inspections of the distribution of residuals and the Akaike information criterion [29].”
MethodThompson, S. G., Nixon, R. M., & Grieve, R. (2006) · Journal of Health Economics · doi:10.1016/j.jhealeco.2006.02.001 · Cited by 55 · see citing works
“Barber & Thompson, 2004 ), so that we model the log of the means θij:”
InfluentialSelf-citationHennessee, I., Chinkhumba, J., Briggs‐Hagen, M., Bauleni, A., Shah, M. P., Chalira, A. E., Moyo, D., Dodoli, W., Luhanga, M., Sande, J., et al. (2017) · Malaria Journal · doi:10.1186/s12936-017-2038-y · Cited by 54 · see citing works
“Generalized linear models (GLMs) were therefore used to analyse cost data while taking into account the non-normal distribution of the data [30].”
Stephen Morris, A., Patel, N. V., Baio, G., Kelly, L., Lewis-Holmes, E., Omar, R., Katona, C., Cooper, C., & Livingston, G. (2015) · BMJ Open · doi:10.1136/bmjopen-2014-007382 · Cited by 54 · see citing works
Alberta FICare Level II NICU Study Team, Benzies, K., Shah, V. S., Aziz, K., Isaranuwatchai, W., Palacios-Derflingher, L. M., Scotland, J., Larocque, J., Mrklas, K., Suter, E., et al. (2017) · Trials · doi:10.1186/s13063-017-2181-3 · Cited by 56 · see citing works
Indirect costs associated with metastatic breast cancer
Wan, Y., Gao, X. Y., Mehta, S., Wang, Z., Faria, C., & Schwartzberg, L. S. (2013) · Journal of Medical Economics · doi:10.3111/13696998.2013.826228 · Cited by 53 · see citing works
Turner, D. A., Paul, S. K., Stone, M. A., Juarez-Garcia, A., Squire, I. B., & Khunti, K. K. (2008) · Heart · doi:10.1136/hrt.2007.125708 · Cited by 53 · see citing works
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 · see citing works
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 · see citing works
Kreif, N., Grieve, R., & Sadique, Z. (2012) · Health Economics · doi:10.1002/hec.2806 · Cited by 51 · see citing works
“• 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).”
MethodHealthcare 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 · see citing works
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 · see citing works
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 · see citing works
Self-citationMazumdar, 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 · see citing works
“Gamma GLM is often used in practice to capture these features [6, 7].”
MethodConducting 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 · see citing works
“gamma, Gaussian) can be specified [61].”
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 · see citing works
“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)”
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 48 · see citing works
“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…”
BackgroundMethodInfluentialRauf, 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 · see citing works
“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.”
MethodPoremski, D., Distasio, J., Hwang, S. W., & Latimer, E. A. (2015) · The Canadian Journal of Psychiatry · doi:10.1177/070674371506000902 · Cited by 47 · see citing works
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 · see citing works
Esposti, L. D., Esposti, D., Buda, Saragoni, & Sturani, A. (2013) · ClinicoEconomics and Outcomes Research · doi:10.2147/ceor.s41846 · Cited by 46 · see citing works
“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 · see citing works
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 · see citing works
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 45 · see citing works
“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…”
MethodBrabyn, 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 · see citing works
“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.”
MethodDEEP 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 · see citing works
“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…”
MethodLeininger, 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 44 · see citing works
“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).”
MethodCost 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 · see citing works
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 · see citing works
Moore, P. V., Bennett, K., & Normand, C. E. M. (2017) · Social Science & Medicine · doi:10.1016/j.socscimed.2017.04.038 · Cited by 43 · see citing works
“…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).”
MethodDakin, H., & Gray, A. M. (2017) · Statistics in Medicine · doi:10.1002/sim.7322 · Cited by 43 · see citing works
“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].”
BackgroundDuval, 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 · see citing works
“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).”
MethodGamma 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 · see citing works
“(2002), Buntin and Zaslavsky (2004), Barber and Thompson (2004), Manning and Mullahy (2005), Powers et al. (2005), Dodd et al.”
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 · see citing works
“Regression-based adjustment (e.g. OLS regression, seemingly unrelated regression, a generalized linear model) Barber and Thompson (2004); Gabrio et al.”
BackgroundMethodInfluentialPetta, 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 · see citing works
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 · see citing works
Wenig, C. M. (2010) · The European Journal of Health Economics · doi:10.1007/s10198-010-0278-7 · Cited by 39 · see citing works
“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].”
MethodÖksüz, 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 · see citing works
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 · see citing works
“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.”
MethodRhinovirus 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 · see citing works
GAMMA SHAPE MIXTURES FOR HEAVY-TAILED DISTRIBUTIONS
Venturini, S., Dominici, F., & Parmigiani, G. (2006) · Collection of Biostatistics Research Archive · Cited by 39 · see citing works
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 · see citing works
“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…”
MethodEustache, 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 · see citing works
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 · see citing works
“A generalized linear model for hospitalization cost was specified with an identity link and a gamma distribution function (11).”
MethodHealthcare 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 36 · see citing works
“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)
- 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
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
