Longitudinal Data Analysis of Symptom Score Trajectories Using Linear Mixed Models in a Clinical Trial
DOI:
https://doi.org/10.6000/1929-6029.2013.02.04.7Keywords:
longitudinal studies, randomized controlled trial, linear models, sample sizeAbstract
In clinical trials, longitudinal data are often analyzed using T-tests, anovas or ancovas instead of the more powerful linear mixed models. The purpose of this paper is to demonstrate how the more sophisticated linear mixed models according to the approach of Singer and Willett, which allows special insight into the behaviour of the data, can be used in clinical trials. Individual trajectories of PANNS-MNS Scores from a controlled clinical trial were used to demonstrate all the steps needed for an analysis of longitudinal data. The model is built step by step, model assumptions are checked, time-variant and time-invariant factors are included and the results are interpreted. The unique needs of a clinical trial, such as the calculation of effect sizes or of an appropriate sample size, are taken into account. Finally, a flow chart is presented that would serve as an instruction tool for the analysis of longitudinal data in clinical trials.
References
Langer W. Mehrebenenanalyse – Eine Einführung in Forschung und Praxis. 2. Aufl. Wiesbaden: Verlag für Sozialwissenschaften 2009.
Hox J. Multilevel Analysis. Techniques and Applications. Mahwah, New Jersey: Lawrence Erlbaum Associates, Inc. 2002.
Rogosa D, Brandt D, Zimowski M. A growth curve approach to the measurement of change. Psychol Bull 1982; 90: 726-48. http://dx.doi.org/10.1037/0033-2909.92.3.726 DOI: https://doi.org/10.1037/0033-2909.92.3.726
Willett JB. Questions and answers in the measurement of change. In: Rothkopf E, editor. Review of research in education. Washington DC: AERA 1988; pp. 345-422. DOI: https://doi.org/10.2307/1167368
Rogosa DR, Willett JB. Understanding correlates of change by modelling individual differences in growth. Psychometrika 1985; 50(2): 203-28. http://dx.doi.org/10.1007/BF02294247 DOI: https://doi.org/10.1007/BF02294247
SAS/STAT Software: Changes and enhancements through release 6.12. Cary, NC, USA: SAS Institute Inc. 1997.
Bender S, Olbrich HM, Fischer W, Hornstein C, Schoene W, Falkai P, et al. Antipsychotic efficacy of the antidepressant trimipramine: a randomized, double-blind comparison with the phenothiazine perazine. Pharmacopsychiatry 2003; 36: 61-69. http://dx.doi.org/10.1055/s-2003-39043 DOI: https://doi.org/10.1055/s-2003-39043
Schooler N, Rabinowitz J, Davidson M, Emsley R, Harvey PD, Kopala L, et al. Risperidone and haloperidol in first-episode psychosis: a long-term randomized trial. Am J Psychiatry 2005; 162(5): 947-53. http://dx.doi.org/10.1176/appi.ajp.162.5.947 DOI: https://doi.org/10.1176/appi.ajp.162.5.947
Lerner V, Miodownik C, Kaptsan A, Cohen H, Loewenthal U, Kotler M. Vitamin B6 as add-on treatment in chronic schizophrenic and schizoaffective patients: a double-blind, placebo-controlled study. J Clin Psychiatry 2002; 63(1): 54-58. http://dx.doi.org/10.4088/JCP.v63n0111 DOI: https://doi.org/10.4088/JCP.v63n0111
Amiri A, Noorbala AA, Nejatisafa AA, Ghoreishi A, Derakhshan MK, Khodaie-Ardakani MR, et al. Efficacy of selegiline add on therapy to risperidone in the treatment of the negative symptoms of schizophrenia: a double-blind randomized placebo-controlled study. Hum Psychopharmacol Clin Exp 2007; 23: 79-86. http://dx.doi.org/10.1002/hup.902 DOI: https://doi.org/10.1002/hup.902
Wong M, Oakley SP, Young L, Jiang BY, Wierzbicki A, Panayi G, et al. Infliximab improves vascular stiffness in patients with rheumatoid arthritis. Ann Rheum Dis 2009; 68: 1277-84. http://dx.doi.org/10.1136/ard.2007.086157 DOI: https://doi.org/10.1136/ard.2007.086157
Rogers BA, David LA, Briggs TWR. Sequential outcome following autologous chondrocyte implantation of the knee: A six-year follow-up. Int Orthop (SICOT) 2010; 34: 959-64. http://dx.doi.org/10.1007/s00264-009-0842-x DOI: https://doi.org/10.1007/s00264-009-0842-x
Nakonezny PA, Byerly MJ, Rush AJ. The relationship between serum prolactin level and sexual functioning among male outpatients with schizophrenia or schizoaffective disorder: a randomized double-blind trial of risperidone vs. quetiapine. J Sex Marital Therapy 2007; 33: 203-16. http://dx.doi.org/10.1080/00926230701267829 DOI: https://doi.org/10.1080/00926230701267829
Centorrino F, Meyers AL, Ahl J, Cincotta SL, Zun L, Gulliver AH, et al. An observational study of the effectiveness and safety of intramuscular olanzapine in the treatment of acute agitation in patients with bipolar mania or schizophrenia/ schizoaffective disorder. Hum Psychopharmacol Clin Exp 2007; 22: 455-62. http://dx.doi.org/10.1002/hup.870 DOI: https://doi.org/10.1002/hup.870
Kane JM, Osuntokun O, Kryzhanovskaya LA, Wen Xu, Stauffer VL, Watson SB, Breier A. A 28-week, ranodmized, double-blind study of olanzapine versus aripiprazole in the treatment of schizophrenia. JCP 2009; 70(4): 572-81. DOI: https://doi.org/10.4088/JCP.08m04421
Pienkowski D, Resig JA, Talwalkar V, Tylkowski C. Novel three-dimensional MRI technique for study of cartilaginous
hip surfaces in legg-calve-perthes disease. J Orthop Res 2009; 27: 981-88. http://dx.doi.org/10.1002/jor.20909 DOI: https://doi.org/10.1002/jor.20909
Litt MD, Shafer DM, Kreutzer DL. Brief cognitive-behavioral treatment for TMD pain: Long-term outcomes and moderators of treatment. PAIN 2010; 151: 110-16. http://dx.doi.org/10.1016/j.pain.2010.06.030 DOI: https://doi.org/10.1016/j.pain.2010.06.030
DuHamel KN, Mosher CE, Winkel G, Labay LE, Rini C, Meschian YM, et al. Randomized clinical trial of telephone-administered cognitive-behavioral therapy to reduce post-traumatic stress disorder and distress symptoms after hematopoietic stem-cell transplantation. J Clin Oncol 2010; 28: 3754-61. http://dx.doi.org/10.1200/JCO.2009.26.8722 DOI: https://doi.org/10.1200/JCO.2009.26.8722
Csernansky JG, Mahmoud R, Brenner R. A comparison of risperidone and haloperidol for the prevention of relapse in patients with schizophrenia. N Engl J Med 2002; 346(1): 16-22. http://dx.doi.org/10.1056/NEJMoa002028 DOI: https://doi.org/10.1056/NEJMoa002028
Arato M, O’Connor R, Meltzer HY. A 1-year, double-blind, placebo-controlled trial of ziprasidone 40, 80 and 160 mg/day in chronic schizophrenia: the ziprasidone extended use in schizophrenia (ZEUS) study. Int Clin Psychopharm 2002; 17(5): 207-15. http://dx.doi.org/10.1097/00004850-200209000-00001 DOI: https://doi.org/10.1097/00004850-200209000-00001
Lipkovich I, Deberdt W, Csernansky JG, Buckley P, Peuskens J, Kollak-Walker S, et al. Predictors of risk for relapse in patients with schizophrenia or schizoaffecitve disorder during olanzapine drug therapy. J Psychiatr Res 2007; 41: 305-10. http://dx.doi.org/10.1016/j.jpsychires.2006.07.016 DOI: https://doi.org/10.1016/j.jpsychires.2006.07.016
Celebi N, Tsouraki R, Engel C, Lammerding-Köppel M, Baur P, Riessen R, Weyrich P. Does doctors’ workload impact the supervision and ward activities of final-year medical students? A prospective study. BMC Med Educ 2012; 12: 24. http://dx.doi.org/10.1186/1472-6920-12-24 DOI: https://doi.org/10.1186/1472-6920-12-24
Singer JD, Willet JB. Applied longitudinal data analysis. Modelling change and event occurrence. New York: Oxford University Press 2003. http://dx.doi.org/10.1093/acprof:oso/9780195152968.001.0001 DOI: https://doi.org/10.1093/acprof:oso/9780195152968.001.0001
Klingberg S, Wittorf A, Herrlich J, Wiedemann G, Meisner C, Buchkremer G, et al. Cognitive behavioural treatment of negative symptoms in schizophrenia patients: study design of the TONES study, feasibility and safety of treatment. Eur Arch Psych Clin N 2009; 259(Suppl 2): 149-54. http://dx.doi.org/10.1007/s00406-009-0047-8 DOI: https://doi.org/10.1007/s00406-009-0047-8
Klingberg S, Wölwer W, Engel C, Wittorf A, Herrlich J, Wölwer W, et al. Negative symptoms of schizophrenia as primary target of cognitive behavioral therapy: results of the randomized clinical TONES study. Schizophrenia Bull 2011; 37(Suppl 2): S98-10. http://dx.doi.org/10.1093/schbul/sbr073 DOI: https://doi.org/10.1093/schbul/sbr073
Kay SR, Fiszbein A, Opler LA. The positive and negative syndrome scale (PANSS) for schizophrenia. Schizophrenia Bull 1987; 13(2): 262-76. http://dx.doi.org/10.1093/schbul/13.2.261 DOI: https://doi.org/10.1093/schbul/13.2.261
Klingberg S, Wittorf A, Wiedemann G. Disorganization and cognitive impairment in schizophrenia: independent symptom dimensions? Eur Arch Psych Clin N 2006; 256: 532-40. http://dx.doi.org/10.1007/s00406-006-0704-0 DOI: https://doi.org/10.1007/s00406-006-0704-0
Martin DJ, Garske JP, Davis MK. Relation of the therapeutic alliance with outcome and other variables: A meta-analytic review. JCCP 2000; 68: 438-50. DOI: https://doi.org/10.1037/0022-006X.68.3.438
Flückinger C, Regli D, Zwahlen D, Hostettler S, Caspar F. Der Berner Patienten- und Therapeutenstundenbogen 2000. Ein Instrument zur Erfassung von Therapieprozessen. Z Klin Psychol Psychother 2010; 39 (2): 71-79. http://dx.doi.org/10.1026/1616-3443/a000015 DOI: https://doi.org/10.1026/1616-3443/a000015
Gruber J. Econometrics part 1, Introduction in multiple regression and econometrics. Hagen: University 1982.
Verbeke G, Lesaffre E. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Comput Stat Data An 1997; 23: 541-56. http://dx.doi.org/10.1016/S0167-9473(96)00047-3 DOI: https://doi.org/10.1016/S0167-9473(96)00047-3
Maas CJM, Hox JJ. Robustness issues in multilevel regression analysis. Stat Neerl 2004; 58(2): 127-37. http://dx.doi.org/10.1046/j.0039-0402.2003.00252.x DOI: https://doi.org/10.1046/j.0039-0402.2003.00252.x
Hedges LV, Olkin I. Statistical methods for meta-analysis. London: Academic Press 1985.
Feingold A. Effect sizes for growth-modeling analysis for controlled clinical trials in the same metric as for classical analysis. Psychol Methods 2009; 14(1): 43-53. http://dx.doi.org/10.1037/a0014699 DOI: https://doi.org/10.1037/a0014699
Gunnes N, Seierstad TG, Aamdal S, Brunsvig PF, Jacobsen AB, Sundstrøm S, Aalen OO. Assessing quality of life in a randomized clinical trial: Correcting for missing data. BMC Med Res Methodol 2009; 9: 28. http://dx.doi.org/10.1186/1471-2288-9-28 DOI: https://doi.org/10.1186/1471-2288-9-28
Aalen OO, Gunnes N. A dynamic approach for reconstructing missing longitudinal data using the linear increments model. Biostatistics 2010; 11(3): 53-72. http://dx.doi.org/10.1093/biostatistics/kxq014 DOI: https://doi.org/10.1093/biostatistics/kxq014
Twisk JWR. Applied longitudinal data analysis for epidemiology. Cambridge: University Press 2003.
Elobeid MA, Padilla MA, McVie Th, Thomas O, Brock DW, Musser B, et al. Missing data in randomized clinical trials for weight loss: Scope of the problem, state of the field, and performance of statistical methods. PLoS ONE 2009; 4(8): e6624. http://dx.doi.org/10.1371/journal.pone.0006624 DOI: https://doi.org/10.1371/journal.pone.0006624
Kish L. Statistical design for research. New York: Wiley 1987. http://dx.doi.org/10.1002/0471725196 DOI: https://doi.org/10.1002/0471725196
Willett JB, Singer JD. The design and analysis of longitudinal studies of development and psychopathology in context: Statistical models and methodological recommendations. Dev Psychopathol 1998; 10: 395-26. http://dx.doi.org/10.1017/S0954579498001667 DOI: https://doi.org/10.1017/S0954579498001667
Ridenour TA, Hall DL, Bost JE. A small sample randomized clinical trial methodology using N-of-1 designs and mixed model analysis. Am J Drug Alcohol Abuse 2009; 35: 260-66. http://dx.doi.org/10.1080/00952990903005916 DOI: https://doi.org/10.1080/00952990903005916
Laenen A, Alonso A, Molenberghs G, Vangeneugden T. Reliability of a longitudinal sequence of scale ratings, Psychometrika 2009; 74: 49-64. http://dx.doi.org/10.1007/s11336-008-9079-7 DOI: https://doi.org/10.1007/s11336-008-9079-7
Laenen A, Alonso A, Molenberghs G. A measure for the reliability of a rating scale based on longitudinal clinical trial data. Psychometrika 2007; 72: 443-48. http://dx.doi.org/10.1007/s11336-007-9002-7 DOI: https://doi.org/10.1007/s11336-007-9002-7
Laenen A, Alonso A. The functional living index-cancer: estimating its reliability based on clinical trial data. Qual Life Res 2010; 19: 103-109. http://dx.doi.org/10.1007/s11136-009-9568-x DOI: https://doi.org/10.1007/s11136-009-9568-x
Komárek A, Hansen BE, Kuiper EMM, van Buuren HR, Lesaffre E. Discriminant analysis using a multivariate linear mixed model with a normal mixture in the random effects distribution. Stat Med 2010; 29: 3267-83. http://dx.doi.org/10.1002/sim.3849 DOI: https://doi.org/10.1002/sim.3849
Zhang Z, Buckler ES, Casstevens TM, Bradbury PJ. Software engineering the mixed model for genome-wide association studies on large samples. Brief Bioinform 2009; 10(6): 664-75. http://dx.doi.org/10.1093/bib/bbp050 DOI: https://doi.org/10.1093/bib/bbp050
Yu JM, Pressoir G, Briggs WH, Bi IV, Yamasaki M, Doebley JF, et al. A unified mixed model method for association mapping that accounts for multiple levels of relatedness. Nat Genet 2006; 38: 203-208. http://dx.doi.org/10.1038/ng1702 DOI: https://doi.org/10.1038/ng1702
Subtil F, Rabilloud M. Robust non-linear mixed modelling of longitudinal PSA levels after prostate cancer treatment. Stat Med 2010; 29: 573-87. DOI: https://doi.org/10.1002/sim.3816
Long J, Ryoo J. Using fractional polynomials to model non-linear trends in longitudinal data. Br J Math Stat Psychol 2010; 63: 177-203. http://dx.doi.org/10.1348/000711009X431509 DOI: https://doi.org/10.1348/000711009X431509
ICH Harmonised tripartied guideline: Statistical principles for clinical trials, E9. Washington: Federal Register, 16 September 1998; 63(179) 49583-49598.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2013 C. Engel, C. Meisner, A. Wittorf, W. Wölwer, G. Wiedemann, C. Ring, R. Muche, S. Klingberg
This work is licensed under a Creative Commons Attribution 4.0 International License.
Policy for Journals/Articles with Open Access
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work
Policy for Journals / Manuscript with Paid Access
Authors who publish with this journal agree to the following terms:
- Publisher retain copyright .
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work .