Cited by 398Statistical Methods and Bayesian InferenceStatistical Methods in Clinical TrialsAdvanced Causal Inference Techniques

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ACCOUNTING FOR DROPOUT BIAS USING MIXED-EFFECTS MODELS

Mallinckrodt, Craig H., Clark, W. Scott, David, Stacy R.·2001·Journal of Biopharmaceutical Statistics

DOI 10.1081/bip-100104194

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Abstract

Treatment effects are often evaluated by comparing change over time in outcome measures. However, valid analyses of longitudinal data can be problematic when subjects discontinue (dropout) prior to completing the study. This study assessed the merits of likelihood-based repeated measures analyses (MMRM) compared with fixed-effects analysis of variance where missing values were imputed using the last observation carried forward approach (LOCF) in accounting for dropout bias. Comparisons were made in simulated data and in data from a randomized clinical trial. Subject dropout was introduced in the simulated data to generate ignorable and nonignorable missingness. Estimates of treatment group differences in mean change from baseline to endpoint from MMRM were, on average, markedly closer to the true value than estimates from LOCF in every scenario simulated. Standard errors and confidence intervals from MMRM accurately reflected the uncertainty of the estimates, whereas standard errors and confidence intervals from LOCF underestimated uncertainty.

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Background
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Method
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Vergeldt, T., Notten, K., Weemhoff, M., van Kuijk, S., Mulder, F., Beets‐Tan, R., Vliegen, R., Gondrie, E., Bergmans, M., Roovers, J., et al. (2015) · BJOG: An International Journal of Obstetrics & Gynaecology · doi:10.1111/1471-0528.13340 · Cited by 35
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Boessen, R., Groenwold, R. H. H., Knol, M. J., Grobbee, D. E., & Roes, K. C. B. (2012) · Journal of Affective Disorders · doi:10.1016/j.jad.2012.08.026 · Cited by 36
“(Mallinckrodt et al., 2001).”
A Smartphone-Based Intervention as an Adjunct to Standard-of-Care Treatment for Schizophrenia: Randomized Controlled Trial
Ghaemi, S. N., Sverdlov, O., van Dam, J., Campellone, T. R., & Gerwien, R. W. (2021) · JMIR Formative Research · doi:10.2196/29154 · Cited by 36
“…change in the total PANSS score from baseline to day 85 or last visit, was analyzed using the mixed effects model for repeated measures (MMRM) [25], applied on the intention-to-treat (ITT) set, which included all participants to whom study treatment was assigned by randomization and who had a…”
Association analysis between variants of the interleukin-1β and the interleukin-1 receptor antagonist gene and antidepressant treatment response in major depression
Tadić, A. (2008) · Neuropsychiatric Disease and Treatment · doi:10.2147/ndt.s2262 · Cited by 37
“…between genotype groups across the treatment period were analyzed using a mixed-effects model repeated-measures methodology (MMRM), as MMRM has been shown to provide highly accurate modeling of treatment outcome while accounting for nonrandom missing data (Mallinckrodt et al 2001, 2003).”
Influential
Onset of antidepressant effect of olanzapine and olanzapine/fluoxetine combination in bipolar depression
Dubé, S., Tollefson, G. D., Thase, M. E., Briggs, S. D., Campen, L. E. V., Case, M. G., & Tohen, M. F. (2007) · Bipolar Disorders · doi:10.1111/j.1399-5618.2007.00491.x · Cited by 35
The effects of relocation and level of affectedness on mood and anxiety symptom treatments after the 2011 Christchurch earthquake
Hogg, D., Kingham, S., Wilson, T., & Ardagh, M. (2016) · Social Science & Medicine · doi:10.1016/j.socscimed.2016.01.025 · Cited by 35
“Research suggests that such likelihood-based mixed-effects repeated measures analyses are the method of choice to account for dropouts in longitudinal studies (Mallinckrodt et al., 2001).”
Method
The Effect of Traumatic Brain Injury History with Loss of Consciousness on Rate of Cognitive Decline Among Older Adults with Normal Cognition and Alzheimer’s Disease Dementia
Tripodis, Y., Alosco, M. L., Zirogiannis, N., Gavett, B. E., Chaisson, C. E., Martin, B. M., McClean, M. D., Mez, J., Kowall, N. W., & Stern, R. A. (2017) · Journal of Alzheimer s Disease · doi:10.3233/jad-160585 · Cited by 35
“Missing data were handled through the mixed effect model framework, which has been shown superior to other method due to the use of maximum likelihood estimation procedures [38].”
Gabapentin enacarbil in Japanese patients with restless legs syndrome: a 12-week, randomized, double-blind, placebo-controlled, parallel-group study
Inoue, Y., Hirata, K., Uchimura, N., Kuroda, K., Hattori, N., & Takeuchi, M. (2012) · Current Medical Research and Opinion · doi:10.1185/03007995.2012.746217 · Cited by 34
Alemtuzumab improves quality-of-life outcomes compared with subcutaneous interferon beta-1a in patients with active relapsing-remitting multiple sclerosis
González, R. V. A., Kita, M., Crayton, H. J., Havrdová, E., Margolin, D. H., Lake, S. L., Giovannoni, G., & on behalf of the CARE-MS I and II Investigators (2016) · Multiple Sclerosis Journal · doi:10.1177/1352458516677589 · Cited by 33
A Double-Blind and Placebo-Controlled Trial of Aripiprazole in Symptomatic Youths at Genetic High Risk for Bipolar Disorder
Findling, R. L., Youngstrom, E. A., Rowles, B. M., Deyling, E. A., Lingler, J., Stansbrey, R. J., McVoy, M. K., Lytle, S., Calabrese, J. R., & McNamara, N. (2017) · Journal of Child and Adolescent Psychopharmacology · doi:10.1089/cap.2016.0160 · Cited by 33
“These provide highly accurate modeling of treatment outcomes while accounting for nonrandom missing data (i.e., patient dropout) (Gibbons et al. 1993; Mallinckrodt et al. 2001).”
Catechol-O-Methyltransferase Valine158Methionine Polymorphism Moderates Methylphenidate Effects on Oppositional Symptoms in Boys with Attention-Deficit/Hyperactivity Disorder
Salatino‐Oliveira, A., Genro, J. P., Zeni, C., Polanczyk, G. V., Chazan, R., Guimarães, A. P., Callegari-Jacques, S. M., Rohde, L. A., & Hutz, M. H. (2011) · Biological Psychiatry · doi:10.1016/j.biopsych.2011.03.025 · Cited by 33
Points to Consider on Missing Data
Watanabe, H., & TASAKI, T. (2006) · Japanese Journal of Biometrics · doi:10.5691/jjb.27.s33 · Cited by 33
Liberal Acceptance Bias, Momentary Aberrant Salience, and Psychosis: An Experimental Experience Sampling Study
Reininghaus, U., Oorschot, M., Moritz, S., Gayer-Anderson, C. E., Kempton, M. J., Valmaggia, L., McGuire, P. K., Murray, R. M., Garety, P. A., Wykes, T., et al. (2018) · Schizophrenia Bulletin · doi:10.1093/schbul/sby116 · Cited by 34
Comparison of bias-corrected covariance estimators for MMRM analysis in longitudinal data with dropouts
Gosho, M., Hirakawa, A., Noma, H., Maruo, K., & Sato, Y. (2015) · Statistical Methods in Medical Research · doi:10.1177/0962280215597938 · Cited by 31
Semi-parametric and non-parametric methods for clinical trials with incomplete data
O’Brien, P. C., Zhang, D., & Bailey, K. R. (2004) · Statistics in Medicine · doi:10.1002/sim.1963 · Cited by 31
The effect of comprehensive lifestyle intervention or metformin on obesity in young women☆
Lim, S. S., Norman, R. J., Clifton, P. M., & Noakes, M. (2010) · Nutrition Metabolism and Cardiovascular Diseases · doi:10.1016/j.numecd.2009.10.006 · Cited by 31
“In the primary analyses, treatment outcomes were assessed using linear mixed models on all participants who commenced the interventions [21].”
Method
Optimal composite scores for longitudinal clinical trials under the linear mixed effects model
Ard, M. C., Raghavan, N., & Edland, S. D. (2015) · Pharmaceutical Statistics · doi:10.1002/pst.1701 · Cited by 30
“Second, because LME weights can be calculated for known, arbitrary clinical trial designs given sufficient pilot data, the approach can not only be used to determine weights for trials with a longer duration than available pilot data but can also be adapted for the case where the trial endpoint is change from baseline…”
Schizophrenia polygenic risk predicts general cognitive deficit but not cognitive decline in healthy older adults
Kępińska, A. P., MacCabe, J. H., Cadar, D., Steptoe, A., Murray, R. M., & Ajnakina, O. (2020) · Translational Psychiatry · doi:10.1038/s41398-020-01114-8 · Cited by 30
Extending the DeLong algorithm for comparing areas under correlated receiver operating characteristic curves with missing data
Zou, L., Choi, Y., Guizzetti, L., Shu, D., Zou, J., & Zou, G. (2024) · Statistics in Medicine · doi:10.1002/sim.10172 · Cited by 30
“This assumption is well-known in the analysis of longitudinal clinical trials with continuous data as missing at random.”
Maternal cardiovascular hemodynamics in normotensive versus preeclamptic pregnancies: a prospective longitudinal study using a noninvasive cardiac system (NICaS™)
Lavie, A., Ram, M., Lev, S., Blecher, Y., Amikam, U., Shulman, Y., Avnon, T., Weiner, E., & Many, A. (2018) · BMC Pregnancy and Childbirth · doi:10.1186/s12884-018-1861-7 · Cited by 28
“Mixed models are the preferable method of analysis of repeatedly measured outcomes when there are missing data, the repeated measures are irregularly spaced over time, and the sample is small [51, 52].”
Method
Promoting occupational health and teaching quality: The impact of a mindfulness intervention in teacher training
Beuchel, P., Ophoff, J. G., Cramer, C., & Hautzinger, M. (2022) · Teaching and Teacher Education · doi:10.1016/j.tate.2022.103703 · Cited by 46
Seasonal variations of cough reflex sensitivity in elite athletes training in cold air environment
Turmel, J., Bougault, V., & Boulet, L. (2012) · Cough · doi:10.1186/1745-9974-8-2 · Cited by 29
Internet-Delivered Cognitive Behavioral Therapy for Generalized Anxiety Disorder in Nationwide Routine Care: Effectiveness Study
Ritola, V., Lipsanen, J. O., Pihlaja, S., Gummerus, E.-M., Stenberg, J., Saarni, S. E., & Joffe, G. (2021) · Journal of Medical Internet Research · doi:10.2196/29384 · Cited by 31
“This approach generally performs better than a pure last observation carried forward (LOCF) at handling dropout bias, especially in larger samples (n>400 [51]).”
Method
Clinical Evidence for Predominance of Delta-5 Steroid Production in Women with Polycystic Ovary Syndrome
Rosencrantz, M. A., Coffler, M. S., Haggan, A., Duke, K. B., Donohue, M., Shayya, R. F., Su, H.-C. I., & Chang, R. J. (2011) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/jc.2010-2200 · Cited by 28
“The MMRM revealed the individual doses of hCG at which stimulated 17-OHP responses were significantly greater in PCOS compared with those of normal women, 100 and 250 g (P 0.05).”
MethodInfluential
Cross‐validation of optimized composites for preclinical Alzheimer's disease
Donohue, M., Sun, C., Raman, R., Insel, P. S., Aisen, P. S. S., Initiative, N. A. A. D. N., Lifestyle, A. I. B. A., & Initiative, J. A. D. N. (2016) · Alzheimer s & Dementia Translational Research & Clinical Interventions · doi:10.1016/j.trci.2016.12.001 · Cited by 27
“First, the global treatment effect is much more broad than typical MMRMestimand (i.e., ITT contrast at the final visit).”
Method
Stress reactivity as a putative mechanism linking childhood trauma with clinical outcomes in individuals at ultra-high-risk for psychosis: Findings from the EU-GEI High Risk Study
Paetzold, I., Myin‐Germeys, I., Schick, A., Nelson, B., Velthorst, E., Schirmbeck, F. N., Study, E.-G. H. R., van Os, J., Morgan, C., Hartmann, J., et al. (2021) · Epidemiology and Psychiatric Sciences · doi:10.1017/s2045796021000251 · Cited by 27
“…estimation (H3 and H4) were applied, allowing for the use of all available data under the relatively unrestrictive assumption that data are missing at random and if all variables associated with missing values are included in the model (Little and Rubin, 1987; Mallinckrodt et al ., 2001).”
Multigenetic Pharmacogenomics–Guided Treatment vs Treatment As Usual Among Hospitalized Men With Schizophrenia
Kang, Z., Qin, Y., Sun, Y., Lu, Z., Sun, Y., Chen, H., Feng, X., Zhang, Y., Guo, H., Yan, H., et al. (2023) · JAMA Network Open · doi:10.1001/jamanetworkopen.2023.35518 · Cited by 27
“8) Education, median (IQR), y 9 (9-12) 9 (9-12) 9 (9-12) Duration of illness, median (IQR), mo 25 (6-72) 36 (13-79) 36 (12-72) Family history of schizophrenia 7 (6.”
Relationships between psychosocial outcomes in adolescents who are obese and their parents during a multi-disciplinary family-based healthy lifestyle intervention: One-year follow-up of a waitlist controlled trial (Curtin University’s Activity, Food and Attitudes Program)
Fenner, A. A., Howie, E. K., Davis, M. C., & Straker, L. M. (2016) · Health and Quality of Life Outcomes · doi:10.1186/s12955-016-0501-z · Cited by 27
“Within the linear mixed model, non-biased estimates were calculated for the missing values using likelihood-based estimation which uses information from surrounding responses and the covariance structure which is an appropriate method in studies with high levels of drop-out and drop-out bias [41].”
Method
Item Response Theory to Quantify Longitudinal Placebo and Paliperidone Effects on PANSS Scores in Schizophrenia
Krekels, E., Novakovic, A., Vermeulen, A., Friberg, L. E., & Karlsson, M. (2017) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.12207 · Cited by 27
Development of lung diffusion to adulthood following extremely preterm birth
Satrell, E., Clemm, H. H., Røksund, O. D., Hufthammer, K. O., Thorsen, E., Halvorsen, T., & Vollsæter, M. (2021) · European Respiratory Journal · doi:10.1183/13993003.04103-2020 · Cited by 26
“This was done to reduce any bias caused by missing data and to increase the precision of the estimates [25].”
The handling of missing data in clinical trials
Kenward, M. G. (2013) · Clinical Investigation · doi:10.4155/cli.13.7 · Cited by 27
Intensive Short-Term Dynamic Psychotherapy Trial Therapy
Abbass, A. A., Town, J. M., Ogrodniczuk, J. S., Joffres, M., & Lilliengren, P. (2017) · The Journal of Nervous and Mental Disease · doi:10.1097/nmd.0000000000000684 · Cited by 25
“This form of estimation provides unbiased estimates under the less restrictive assumption of data missing at random (Mallinckrodt et al., 2001), which allows the probability of data being missing to be dependent on both outcome variables (e.”
Background
Mixed model of repeated measures versus slope models in Alzheimer's disease clinical trials
Donohue, M., & Aisen, P. S. S. (2012) · The journal of nutrition health & aging · doi:10.1007/s12603-012-0047-7 · Cited by 24
The methods for handling missing data in clinical trials influence sample size requirements
Auleley, G.-R., Giraudeau, B., Baron, G., Maillefert, J.-F., Dougados, M., & Ravaud, P. (2004) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2003.09.012 · Cited by 24
A monoamine oxidase B gene variant and short-term antidepressant treatment response
Tadić, A., Rujescu, D., Müller, M. J., Kohnen, R., Stassen, H. H., Dahmen, N., & Szegedi, A. (2007) · Progress in Neuro-Psychopharmacology and Biological Psychiatry · doi:10.1016/j.pnpbp.2007.05.015 · Cited by 24
Internet-delivered cognitive behavioural therapy with and without an initial face-to-face psychoeducation session for social anxiety disorder: A pilot randomized controlled trial
Nordmo, M., Sinding, A. I., Carlbring, P., Andersson, G., Havik, O. E., & Nordgreen, T. (2015) · Internet Interventions · doi:10.1016/j.invent.2015.10.003 · Cited by 23
“Likelihood-based repeatedmeasures analysis generally outperforms traditional methods like last observation carried forward in accounting for dropout bias (Mallinckrodt et al., 2001).”
Method
Early symptom response to antipsychotic medication as a marker of subsequent symptom change: An eighteen-month follow-up study of recent episode schizophrenia
Levine, S. Z., & Leucht, S. (2012) · Schizophrenia Research · doi:10.1016/j.schres.2012.08.030 · Cited by 23
Protocol of a randomized, double-blind, placebo-controlled, parallel-group, multicentre study of the efficacy and safety of nicotinamide in patients with Friedreich ataxia (NICOFA)
the EFACTS or NICOFA study group, Reetz, K., Hilgers, R.-D., Isfort, S., Dohmen, M., Didszun, C., Fedosov, K., Kistermann, J., Mariotti, C., Dürr, A., et al. (2019) · Neurological Research and Practice · doi:10.1186/s42466-019-0038-9 · Cited by 22
Effect of heteroscedasticity between treatment groups on mixed‐effects models for repeated measures
Gosho, M., & Maruo, K. (2018) · Pharmaceutical Statistics · doi:10.1002/pst.1872 · Cited by 22
Multidomain Intervention Trial for Preventing Cognitive Decline among Older Adults with Type 2 Diabetes: J-MIND-Diabetes
Sugimoto, T., Araki, A., Fujita, H., Fujita, K., Honda, K., Inagaki, N., Ishida, T., Kato, J., Kishi, M., Kishino, Y., et al. (2024) · The Journal of Prevention of Alzheimer s Disease · doi:10.14283/jpad.2024.117 · Cited by 23
Double-Blind, Placebo-Controlled Study of the Efficacy of Reboxetine and Citalopram as Adjuncts to Atypical Antipsychotics for Negative Symptoms of Schizophrenia
Usall, J., López‐Carrilero, R., Iniesta, R., Roca, M., Caballero, M. I. I., Rodríguez–Jiménez, R., Oliveira, C., Bernardo, M., Corripio, I., Duran‐Sindreu, S., et al. (2014) · The Journal of Clinical Psychiatry · doi:10.4088/jcp.13m08551 · Cited by 21
Multiple Imputation Approaches for the Analysis of Dichotomized Responses in Longitudinal Studies with Missing Data
Lu, K., Jiang, L., & Tsiatis, A. A. (2010) · Biometrics · doi:10.1111/j.1541-0420.2010.01405.x · Cited by 21
“This is reminiscent of the mixedeffects model repeated measures (MMRM) model proposed by Mallinckrodt, Clark, and David (2001), which is particularly suitable for analyzing clinical trial data because subjects in clinical trials are often evaluated at a fixed and relative small number of time…”
Method
Proportional constrained longitudinal data analysis models for clinical trials in sporadic Alzheimer's disease
Wang, G., Liu, L., Li, Y., Aschenbrenner, A. J., Bateman, R. J., Delmar, P., Schneider, L. S. S., Kennedy, R., Cutter, G., & Xiong, C. (2022) · Alzheimer s & Dementia Translational Research & Clinical Interventions · doi:10.1002/trc2.12286 · Cited by 20
Rationale and design of REWARD (revving-up exercise for sustained weight loss by altering neurological reward and drive): A randomized trial in obese endometrial cancer survivors
Nock, N. L., Dimitropoulos, A., Rao, S. M., Flask, C. A., Schluchter, M., Zanotti, K. M., Rose, P. G., Kirwan, J. P., & Alberts, J. L. (2014) · Contemporary Clinical Trials · doi:10.1016/j.cct.2014.08.008 · Cited by 20
“In terms of handling missing data, we will use the likelihood-based linear mixed modeling approach with baseline values included in the model because it has been shown to be more valid way to deal with dropout in clinical trials as compared to simple imputation procedures such as last observation carried forward [87].”
Method

Authors: Mallinckrodt, C. H., Clark, W. S., & David, S. R.
Affiliations: Eli Lilly (United States) (US)
ORCID: Mallinckrodt, Craig H.
Venue: Journal of Biopharmaceutical Statistics
Publisher: Informa UK Limited
Published: 2001-01-01
Volume: 11
Issue: 1-2
Pages: 9-21
ISSN: 1054-3406 (ISSN-L)
1520-5711
DOI: 10.1081/bip-100104194
OpenAlex: W2073155558
Cited by: 398
References: 14
Citations by year: 2026: 12 · 2025: 13 · 2024: 21 · 2023: 12 · 2022: 27 · 2021: 19 · 2020: 20 · 2019: 13 · 2018: 14 · 2017: 14 · 2016: 18 · 2015: 21 · 2014: 16 · 2013: 23 · 2012: 19
FWCI: 11.96
Type: journal article
Language: en
Open access: closed
Locations: Journal of Biopharmaceutical Statistics (publishedVersion)
PubMed (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
Keywords: mixed models, last observation carried forward, missing data, non-ignorable missingness, treatment effect estimation, longitudinal data, randomized controlled trials, standard error estimation
MeSH terms: Analysis of Variance, Humans, Longitudinal Studies, Patient Dropouts, Models, Statistical, Bias, Confidence Intervals, Randomized Controlled Trials as Topic

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ACCOUNTING FOR DROPOUT BIAS USING MIXED-EFFECTS MODELS

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