Missing Data

Missing data is common in health research and must be dealt with before and during analysis. Missing data is a topic of active research. Many publications discuss the causes and patterns of missing data, as well as statistical and practical approaches. Some resources are listed below.

Multiple imputation is a common way to deal with missing data.

Imputation means filling in a missing data point with a value. In the past, it was common to fill in “holes” in the data with the mean of a variable’s available values. This approach, called single imputation, leads to underestimation of a variable’s variance, since one presumed value is standing in for many different unknown values. It can lead to erroneous inference because too many statistical tests return significant results.

Multiple imputation (MI) uses regression on other variables in the data set to generate plausible values where data are missing. It also makes sure there’s some variance in the predicted plausible values. The process includes the following steps:

1. An MI program creates, say, 30 completed data sets, each one including a different dose of random noise
2. The analyst then runs her analysis (e.g., linear mixed model for repeated measures) on each one of the 30 data sets separately
3. The results of each of those 30 analyses are averaged. There’s a special formula to make sure the standard errors of estimates take into account the extra uncertainty

Most major statistical programs can assist with the generation of multiply imputed data sets and the combination of repeated analyses. Two common software options are PROC MI in SAS and the mice package in R.

This page includes publications and tools that our consultants have found useful. The resource list can be downloaded in PDF and BibTeX format at the bottom of this page. For more information on this topic, including advice about how to apply it in your research, consider scheduling a consultation with a biostatistician.

While we hope this resource list serves as a helpful starting point for other researchers, we provide no guarantee of its comprehensiveness or of the accuracy or reliability of the works cited. If you have concerns or suggestions to improve this page, please contact us.

Akl, E. A., M. Briel, J. J. You, et al. (2012). “Potential impact on estimated treatment effects of information lost to follow-up in randomised controlled trials (LOST-IT): systematic review”. In: BMJ 344.may18 1, p. e2809–e2809. ISSN: 1756-1833. DOI: 10.1136/bmj.e2809. http://dx.doi.org/10.1136/bmj.e2809.

Allison, Paul (2002). Missing Data. SAGE Publications, Inc. ISBN: 9781412985079. DOI: 10.4135/9781412985079. http://dx.doi.org/10.4135/9781412985079.

Alosh, Mohamed (2009). “The Impact of Missing Data in a Generalized Integer-Valued Autoregression Model for Count Data”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1039–1054. ISSN: 1520-5711. DOI: 10.1080/10543400903242787. http://dx.doi.org/10.1080/10543400903242787.

Angrist, Joshua D. and Jörn-Steffen Pischke (2008). Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton University Press. ISBN: 9780691120348. DOI: 10.2307/j.ctvcm4j72. http://dx.doi.org/10.2307/j.ctvcm4j72.

Bell, Melanie L, Mallorie Fiero, Nicholas J Horton, et al. (2014). “Handling missing data in RCTs; a review of the top medical journals”. In: BMC Medical Research Methodology 14.1. ISSN: 1471-2288. DOI: 10.1186/1471-2288-14-118. http://dx.doi.org/10.1186/1471-2288-14-118.

Beunckens, Caroline, Geert Molenberghs, Herbert Thijs, et al. (2007). “Incomplete hierarchical data”. In: Statistical Methods in Medical Research 16.5, p. 457–492. ISSN: 1477-0334. DOI: 10.1177/0962280206075310. http://dx.doi.org/10.1177/0962280206075310.

Bhaumik, Dulal K., Anindya Roy, Subhash Aryal, et al. (2008). “Sample Size Determination for Studies with Repeated Continuous Outcomes”. In: Psychiatric Annals 38.12. ISSN: 1938-2456. DOI: 10.3928/00485713-20081201-01. http://dx.doi.org/10.3928/00485713-20081201-01.

Birmingham, Jolene and Garrett M. Fitzmaurice (2002). “A Pattern-Mixture Model for Longitudinal Binary Responses with Nonignorable Nonresponse”. In: Biometrics 58.4, p. 989–996. ISSN: 0006-341X. DOI: 10.1111/j.0006-341x.2002.00989.x. http://dx.doi.org/10.1111/j.0006-341X.2002.00989.x.

Chen, Qixuan, Andrew Gelman, Melissa Tracy, et al. (2015). “Incorporating the sampling design in weighting adjustments for panel attrition”. In: Statistics in Medicine 34.28, p. 3637–3647. ISSN: 1097-0258. DOI: 10.1002/sim.6618. http://dx.doi.org/10.1002/sim.6618.

Daniels, Michael J. and Joseph W. Hogan (2008). Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis. Chapman and Hall/CRC. ISBN: 9780429145704. DOI: 10.1201/9781420011180. http://dx.doi.org/10.1201/9781420011180.

Demirtas, Hakan and Joseph L. Schafer (2003). “On the performance of random‐coefficient pattern‐mixture models for non‐ignorable drop‐out”. In: Statistics in Medicine 22.16, p. 2553–2575. ISSN: 1097-0258. DOI: 10.1002/sim.1475. http://dx.doi.org/10.1002/sim.1475.

DeSouza, Cynthia M., Anna T. R. Legedza, and Abdul J. Sankoh (2009). “An Overview of Practical Approaches for Handling Missing Data in Clinical Trials”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1055–1073. ISSN: 1520-5711. DOI: 10.1080/10543400903242795. http://dx.doi.org/10.1080/10543400903242795.

Díaz-Ordaz, Karla, Michael G Kenward, Abie Cohen, et al. (2014). “Are missing data adequately handled in cluster randomised trials? A systematic review and guidelines”. In: Clinical Trials 11.5, p. 590–600. ISSN: 1740-7753. DOI: 10.1177/1740774514537136. http://dx.doi.org/10.1177/1740774514537136.

Fiero, Mallorie H., Shuang Huang, Eyal Oren, et al. (2016). “Statistical analysis and handling of missing data in cluster randomized trials: a systematic review”. In: Trials 17.1. ISSN: 1745-6215. DOI: 10.1186/s13063-016-1201-z. http://dx.doi.org/10.1186/s13063-016-1201-z.

Fitzmaurice, Garrett M., Nan M. Laird, and James H. Ware (2011). Applied Longitudinal Analysis. Wiley. ISBN: 9781119513469. DOI: 10.1002/9781119513469. http://dx.doi.org/10.1002/9781119513469.

Flyer, Paul and Joseph Hirman (2009). “Missing Data in Confirmatory Clinical Trials”. In: Journal of Biopharmaceutical Statistics 19.6, p. 969–979. ISSN: 1520-5711. DOI: 10.1080/10543400903242746. http://dx.doi.org/10.1080/10543400903242746.

Gibbons, Robert D. (2008). “Design and Analysis of Longitudinal Studies”. In: Psychiatric Annals 38.12. ISSN: 1938-2456. DOI: 10.3928/00485713-20081201-03. http://dx.doi.org/10.3928/00485713-20081201-03.

Giusta, Caterina and Roderick J. A. Little “An Analysis of nonignorable nonresponse to income in a survey with rotating panel design”. In: Journal of Official Statistics 27.2, pp. 211-229.

Graham, John W. (2009). “Missing Data Analysis: Making It Work in the Real World”. In: Annual Review of Psychology 60.1, p. 549–576. ISSN: 1545-2085. DOI: 10.1146/annurev.psych.58.110405.085530. http://dx.doi.org/10.1146/annurev.psych.58.110405.085530.

Graham, John W., Scott M. Hofer, Stewart I. Donaldson, et al. (1997). “Analysis with missing data in prevention research.” In: The science of prevention: Methodological advances from alcohol and substance abuse research. American Psychological Association, p. 325–366. ISBN: 1557984395. DOI: 10.1037/10222-010. http://dx.doi.org/10.1037/10222-010.

Hedeker, Donald and Robert D. Gibbons (1997). “Application of random-effects pattern-mixture models for missing data in longitudinal studies.” In: Psychological Methods 2.1, p. 64–78. ISSN: 1082-989X. DOI: 10.1037/1082-989x.2.1.64. http://dx.doi.org/10.1037/1082-989X.2.1.64.

Hedeker, Donald and Robert D. Gibbons (2006). Longitudinal Data Analysis. Wiley Series in Probability and Statistics. Wiley. ISBN: 9780470036488. DOI: 10.1002/0470036486. http://dx.doi.org/10.1002/0470036486.

Hedeker, Donald and Jennifer S. Rose (2000). “The Natural History of Smoking: A Pattern–Mixture Random-Effects Regression Model”. In: Multivariate Applications in Substance Use Research: New Methods for New Questions. Ed. by Jennifer S. Rose, Laurie Chassin, Clark C. Presson and Steven J. Sherman. Hillsdale, NJ: Psychology Press, pp. 79-112. ISBN: 9781410604217. DOI: 10.4324/9781410604217. http://dx.doi.org/10.4324/9781410604217.

Herbert, Robert D., Jessica Kasza, and Kari Bø (2018). “Analysis of randomised trials with long-term follow-up”. In: BMC Medical Research Methodology 18.1. ISSN: 1471-2288. DOI: 10.1186/s12874-018-0499-5. http://dx.doi.org/10.1186/s12874-018-0499-5.

Horton, Nicholas J and Ken P Kleinman (2007). “Much Ado About Nothing: A Comparison of Missing Data Methods and Software to Fit Incomplete Data Regression Models”. In: The American Statistician 61.1, p. 79–90. ISSN: 1537-2731. DOI: 10.1198/000313007x172556. http://dx.doi.org/10.1198/000313007X172556.

Ibrahim, Joseph G. and Geert Molenberghs (2009). “Missing data methods in longitudinal studies: a review”. In: TEST 18.1, p. 1–43. ISSN: 1863-8260. DOI: 10.1007/s11749-009-0138-x. http://dx.doi.org/10.1007/s11749-009-0138-x.

Ibrahim, Joseph G, Ming-Hui Chen, Stuart R Lipsitz, et al. (2005). “Missing-Data Methods for Generalized Linear Models: A Comparative Review”. In: Journal of the American Statistical Association 100.469, p. 332–346. ISSN: 1537-274X. DOI: 10.1198/016214504000001844. http://dx.doi.org/10.1198/016214504000001844.

Kolamunnage-Dona, Ruwanthi, Colin Powell, and Paula Ruth Williamson (2016). “Modelling variable dropout in randomised controlled trials with longitudinal outcomes: application to the MAGNETIC study”. In: Trials 17.1. ISSN: 1745-6215. DOI: 10.1186/s13063-016-1342-0. http://dx.doi.org/10.1186/s13063-016-1342-0.

Kong, Fanhui, Yeh-Fong Chen, and Kun Jin (2009). “A Bias Correction in Testing Treatment Efficacy Under Informative Dropout in Clinical Trials”. In: Journal of Biopharmaceutical Statistics 19.6, p. 980–1000. ISSN: 1520-5711. DOI: 10.1080/10543400903242753. http://dx.doi.org/10.1080/10543400903242753.

Lavori, Philip W., C. Hendricks Brown, Naihua Duan, et al. (2008). “Missing Data in Longitudinal Clinical Trials Part A: Design and Conceptual Issues”. In: Psychiatric Annals 38.12. ISSN: 1938-2456. DOI: 10.3928/00485713-20081201-04. http://dx.doi.org/10.3928/00485713-20081201-04.

Little, Roderick J. A. (1988). “A Test of Missing Completely at Random for Multivariate Data with Missing Values”. In: Journal of the American Statistical Association 83.404, p. 1198–1202. ISSN: 1537-274X. DOI: 10.1080/01621459.1988.10478722. http://dx.doi.org/10.1080/01621459.1988.10478722.

Little, Roderick J. A. (1993). “Pattern-Mixture Models for Multivariate Incomplete Data”. In: Journal of the American Statistical Association 88.421, p. 125. ISSN: 0162-1459. DOI: 10.2307/2290705. http://dx.doi.org/10.2307/2290705.

Little, Roderick J. A. (1995). “Modeling the Drop-Out Mechanism in Repeated-Measures Studies”. In: Journal of the American Statistical Association 90.431, p. 1112–1121. ISSN: 1537-274X. DOI: 10.1080/01621459.1995.10476615. http://dx.doi.org/10.1080/01621459.1995.10476615.

Little, Roderick J. A. and Nathaniel Schenker (1995). “Missing Data”. In: Handbook of Statistical Modeling for the Social and Behavioral Sciences. Springer US, p. 39–75. ISBN: 9781489912923. DOI: 10.1007/978-1-4899-1292-3_2. http://dx.doi.org/10.1007/978-1-4899-1292-3_2.

Little, Roderick and Donald Rubin (2019). Statistical Analysis with Missing Data, Third Edition. Wiley. ISBN: 9781119482260. DOI: 10.1002/9781119482260. http://dx.doi.org/10.1002/9781119482260.

Little, Roderick and Linda Yau (1996). “Intent-to-Treat Analysis for Longitudinal Studies with Drop-Outs”. In: Biometrics 52.4. SAS code available at http://sitemaker.umich.edu/rlittle/files/linda.htm, p. 1324. ISSN: 0006-341X. DOI: 10.2307/2532847. http://dx.doi.org/10.2307/2532847.

Ma, Guoguang, Andrea B. Troxel, and Daniel F. Heitjan (2005). “An index of local sensitivity to nonignorable drop-out in longitudinal modelling”. In: Statistics in Medicine 24.14, pp. 2129-2150. DOI: https://doi.org/10.1002/sim.2107. https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.2107.

Marcus, Sue M., Juned Siddique, Thomas R. Ten Have, et al. (2008). “Balancing Treatment Comparisons in Longitudinal Studies”. In: Psychiatric Annals 38.12. ISSN: 1938-2456. DOI: 10.3928/00485713-20081201-05. http://dx.doi.org/10.3928/00485713-20081201-05.

McIsaac, Michael and RJ Cook (2017). “Statistical methods for incomplete data: Some results on model misspecification”. In: Statistical Methods in Medical Research 26.1, pp. 248-267. DOI: 10.1177/0962280214544251. https://doi.org/10.1177/0962280214544251.

Meng, Xiangyi and Nathaniel Schenker (1999). “Maximum likelihood estimation for linear regression models with right censored outcomes and missing predictors”. In: Computational Statistics & Data Analysis 29.4, p. 471–483. ISSN: 0167-9473. DOI: 10.1016/s0167-9473(98)00074-7. http://dx.doi.org/10.1016/S0167-9473(98)00074-7.

Molenberghs, G. (2004). “Analyzing incomplete longitudinal clinical trial data”. In: Biostatistics 5.3, p. 445–464. ISSN: 1468-4357. DOI: 10.1093/biostatistics/kxh001. http://dx.doi.org/10.1093/biostatistics/kxh001.

Molenberghs, Geert, Caroline Beunckens, Ivy Jansen, et al. (2014). “Missing Data”. In: Handbook of Epidemiology. Springer New York, p. 1283–1335. DOI: 10.1007/978-0-387-09834-0_20. http://dx.doi.org/10.1007/978-0-387-09834-0_20.

Molenberghs, Geert and Michael G. Kenward (2007). Missing Data in Clinical Studies. Wiley. ISBN: 9780470510445. DOI: 10.1002/9780470510445. http://dx.doi.org/10.1002/9780470510445.

Molenberghs, Geert and Geert Verbeke (2005). Models for discrete longitudinal data. Springer Series in Statistics. Part VI, Chapters 26-32, considers missing data analysis.. New York: Springer Science+Business Media, Inc. DOI: 10.1007/0-387-28980-1. http://dx.doi.org/10.1007/0-387-28980-1.

Molenberghs, Geert, Geert Verbeke, Herbert Thijs, et al. (2001). “Influence analysis to assess sensitivity of the dropout process”. In: Computational Statistics & Data Analysis 37.1, p. 93–113. ISSN: 0167-9473. DOI: 10.1016/s0167-9473(00)00065-7. http://dx.doi.org/10.1016/S0167-9473(00)00065-7.

Moore, K. L. and M. J. van der Laan (2009). “Increasing Power in Randomized Trials with Right Censored Outcomes Through Covariate Adjustment”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1099–1131. ISSN: 1520-5711. DOI: 10.1080/10543400903243017. http://dx.doi.org/10.1080/10543400903243017.

Nie, L., H. Chu, Y. Cheng, et al. (2009). “Marginal and Conditional Approaches to Multivariate Variables Subject to Limit of Detection”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1151–1161. ISSN: 1520-5711. DOI: 10.1080/10543400903243033. http://dx.doi.org/10.1080/10543400903243033.

Powney, Matthew, Paula Williamson, Jamie Kirkham, et al. (2014). “A review of the handling of missing longitudinal outcome data in clinical trials”. In: Trials 15.1. ISSN: 1745-6215. DOI: 10.1186/1745-6215-15-237. http://dx.doi.org/10.1186/1745-6215-15-237.

Rässler, Susanne, Donald B. Rubin, and Schenker, Nathaniel. (2008). “Incomplete Data”. In: International Handbook of Survey Methodology. Ed. by Edith D. de Leeuw, Joop Hox and Don Dillman. New York: Routledge. ISBN: 9780805857528. DOI: 10.4324/9780203843123.ch19. http://dx.doi.org/10.4324/9780203843123.ch19.

Raykov, Tenko and George A. Marcoulides (2013). “Identifying Useful Auxiliary Variables for Incomplete Data Analyses: A Note on a Group Difference Examination Approach”. In: Educational and Psychological Measurement 74.3, p. 537–550. ISSN: 1552-3888. DOI: 10.1177/0013164413511326. http://dx.doi.org/10.1177/0013164413511326.

Resseguier, Noémie, Roch Giorgi, and Xavier Paoletti (2011). “Sensitivity Analysis When Data Are Missing Not-at-random”. In: Epidemiology 22.2. SensMice” package, p. 282. ISSN: 1044-3983. DOI: 10.1097/ede.0b013e318209dec7. http://dx.doi.org/10.1097/EDE.0b013e318209dec7.

Robins, James M., Andrea Rotnitzky, and Lue Ping Zhao (1995). “Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data”. In: Journal of the American Statistical Association 90.429, p. 106–121. ISSN: 1537-274X. DOI: 10.1080/01621459.1995.10476493. http://dx.doi.org/10.1080/01621459.1995.10476493.

Rombach, Ines, Crispin Jenkinson, Alastair Gray, et al. (2018). “Comparison of statistical approaches for analyzing incomplete longitudinal patient-reported outcome data in randomized controlled trials”. In: Patient Related Outcome Measures Volume 9, p. 197–209. ISSN: 1179-271X. DOI: 10.2147/prom.s147790. http://dx.doi.org/10.2147/PROM.S147790.

Rombach, Ines, Oliver Rivero-Arias, Alastair M. Gray, et al. (2016). “The current practice of handling and reporting missing outcome data in eight widely used PROMs in RCT publications: a review of the current literature”. In: Quality of Life Research 25.7, p. 1613–1623. ISSN: 1573-2649. DOI: 10.1007/s11136-015-1206-1. http://dx.doi.org/10.1007/s11136-015-1206-1.

Rothmann, Mark D., Kallappa Koti, Kyung Yul Lee, et al. (2009). “Missing Data in Biologic Oncology Products”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1074–1084. ISSN: 1520-5711. DOI: 10.1080/10543400903242993. http://dx.doi.org/10.1080/10543400903242993.

Schafer, Joseph L. (1997). Analysis of incomplete multivariate data. Vol. 72. Monographs on Statistics and Applied Probability. London: Chapman & Hall.

Schafer, Joseph L. and John W. Graham (2002). “Missing data: Our view of the state of the art.” In: Psychological Methods 7.2, p. 147–177. ISSN: 1082-989X. DOI: 10.1037/1082-989x.7.2.147. http://dx.doi.org/10.1037/1082-989X.7.2.147.

Seaman, Shaun R. and Stijn Vansteelandt (2018). “Introduction to Double Robust Methods for Incomplete Data”. In: Statistical Science 33.2. ISSN: 0883-4237. DOI: 10.1214/18-sts647. http://dx.doi.org/10.1214/18-STS647.

Seaman, Shaun R and Ian R White (2011). “Review of inverse probability weighting for dealing with missing data”. In: Statistical Methods in Medical Research 22.3, p. 278–295. ISSN: 1477-0334. DOI: 10.1177/0962280210395740. http://dx.doi.org/10.1177/0962280210395740.

Shardell, Michelle and Samer S. El-Kamary (2009). “Sensitivity Analysis of Informatively Coarsened Data Using Pattern Mixture Models”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1018–1038. ISSN: 1520-5711. DOI: 10.1080/10543400903242779. http://dx.doi.org/10.1080/10543400903242779.

Shen, Shuyi, Caroline Beunckens, Craig Mallinckrodt, et al. (2006). “A Local Influence Sensitivity Analysis for Incomplete Longitudinal Depression Data”. In: Journal of Biopharmaceutical Statistics 16.3, p. 365–384. ISSN: 1520-5711. DOI: 10.1080/10543400600609510. http://dx.doi.org/10.1080/10543400600609510.

Siddique, Juned, C. Hendricks Brown, Donald Hedeker, et al. (2008). “Missing Data in Longitudinal Trials – Part B, Analytic Issues”. In: Psychiatric Annals 38.12. ISSN: 1938-2456. DOI: 10.3928/00485713-20081201-09. http://dx.doi.org/10.3928/00485713-20081201-09.

Soon, Guoxing (Greg) (2009). “Editorial: Missing Data—Prevention and Analysis”. In: Journal of Biopharmaceutical Statistics 19.6, p. 941–944. ISSN: 1520-5711. DOI: 10.1080/10543400903331226. http://dx.doi.org/10.1080/10543400903331226.

Sullivan, Thomas R, Lisa N Yelland, Katherine J Lee, et al. (2017). “Treatment of missing data in follow-up studies of randomised controlled trials: A systematic review of the literature”. In: Clinical Trials 14.4, p. 387–395. ISSN: 1740-7753. DOI: 10.1177/1740774517703319. http://dx.doi.org/10.1177/1740774517703319.

Ten Have, Thomas R., Sharon-Lise T. Normand, Sue M. Marcus, et al. (2008). “Intent-to-treat vs. Non-intent-to-treat Analyses under Treatment Non-adherence in Mental Health Randomized Trials”. In: Psychiatric Annals 38.12. ISSN: 1938-2456. DOI: 10.3928/00485713-20081201-10. http://dx.doi.org/10.3928/00485713-20081201-10.

Thijs, Herbert, Geert Molenberghs, and Geert Verbeke (2000). “The Milk Protein Trial: Influence Analysis of the Dropout Process”. In: Biometrical Journal 42.5, p. 617–646. ISSN: 1521-4036. DOI: 10.1002/1521-4036(200009)42:5<617::aid-bimj617>3.0.co;2-n. http://dx.doi.org/10.1002/1521-4036(200009)42:5%3C617::AID-BIMJ617%3E3.0.CO;2-N.

Troxel, Andrea, Guoguang Ma, and Daniel F. Heitjan (2004). “An index of local sensitivity to nonignorability”. In: Statistica Sinica 14.4. ISNI index, pp. 1221-1237. http://www.jstor.org/stable/24307229.

Verbeke, Geert and Geert Molenberghs (2000). Linear mixed models for longitudinal data. Springer Series in Statistics. Chapters 16-21 consider missing data analysis.. New York: Springer-Verlag. DOI: 10.1007/b98969. http://dx.doi.org/10.1007/b98969.

Verbeke, Geert, Geert Molenberghs, and Caroline Beunckens (2008). “Formal and informal model selection with incomplete data”. In: Statistical Science 23.2, pp. 201-218. DOI: 10.48550/ARXIV.0808.3587. https://arxiv.org/abs/0808.3587.

Verbeke, Geert, Geert Molenberghs, Herbert Thijs, et al. (2001). “Sensitivity Analysis for Nonrandom Dropout: A Local Influence Approach”. In: Biometrics 57.1, p. 7–14. ISSN: 1541-0420. DOI: 10.1111/j.0006-341x.2001.00007.x. http://dx.doi.org/10.1111/j.0006-341X.2001.00007.x.

Walton, Marc K. (2009). “Addressing and Advancing the Problem of Missing Data”. In: Journal of Biopharmaceutical Statistics 19.6, p. 945–956. ISSN: 1520-5711. DOI: 10.1080/10543400903238959. http://dx.doi.org/10.1080/10543400903238959.

Wang, Ming‐Dauh, Jiajun Liu, Geert Molenberghs, et al. (2018). “An evaluation of the trimmed mean approach in clinical trials with dropout”. In: Pharmaceutical Statistics 17.3, p. 278–289. ISSN: 1539-1612. DOI: 10.1002/pst.1858. http://dx.doi.org/10.1002/pst.1858.

Wang, Xiaofei, Yougui Wu, and Haibo Zhou (2009). “Outcome- and Auxiliary-Dependent Subsampling and Its Statistical Inference”. In: Journal of Biopharmaceutical Statistics 19.6, p. 1132–1150. ISSN: 1520-5711. DOI: 10.1080/10543400903243025. http://dx.doi.org/10.1080/10543400903243025.

Wittes, Janet (2009). “Missing Inaction: Preventing Missing Outcome Data in Randomized Clinical Trials”. In: Journal of Biopharmaceutical Statistics 19.6, p. 957–968. ISSN: 1520-5711. DOI: 10.1080/10543400903239825. http://dx.doi.org/10.1080/10543400903239825.

Wood, Angela M, Ian R White, and Simon G Thompson (2004). “Are missing outcome data adequately handled? A review of published randomized controlled trials in major medical journals”. In: Clinical Trials 1.4, p. 368–376. ISSN: 1740-7753. DOI: 10.1191/1740774504cn032oa. http://dx.doi.org/10.1191/1740774504cn032oa.

Xie, Hui (2007). “A local sensitivity analysis approach to longitudinal non‐Gaussian data with non‐ignorable dropout”. In: Statistics in Medicine 27.16, p. 3155–3177. ISSN: 1097-0258. DOI: 10.1002/sim.3117. http://dx.doi.org/10.1002/sim.3117.

Xie, Hui (2009). “Bayesian inference from incomplete longitudinal data: A simple method to quantify sensitivity to nonignorable dropout”. In: Statistics in Medicine 28.22, p. 2725–2747. ISSN: 1097-0258. DOI: 10.1002/sim.3655. http://dx.doi.org/10.1002/sim.3655.

Xie, Hui (2010). “Adjusting for Nonignorable Missingness When Estimating Generalized Additive Models”. In: Biometrical Journal 52.2, p. 186–200. ISSN: 1521-4036. DOI: 10.1002/bimj.200900202. http://dx.doi.org/10.1002/bimj.200900202.

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• missing.bib
• missing_data.pdf
• multiple_imputation.bib