Akacha, Mouna and Hutton, Jane L. (2009) Analysing the rate of change in a longitudinal study with missing data, taking into account the number of contact attempts. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

In longitudinal and multivariate settings incomplete data, due to missed visits, dropouts or non-return of questionnaires are quite common. A longitudinal trial in which potentially informative missingness occurs is the Collaborative Ankle Support Trial (CAST). The aim of this study is to estimate the clinical effectiveness of four different methods of mechanical support after severe ankle sprain. The clinical status of multiple subjects was measured at four points in time via a questionnaire and, based on this, a continuous and bounded outcome score was calculated. Motivated by this study, a model is proposed for continuous longitudinal data with non-ignorable or informative missingness, taking into account the number of attempts made to contact initial non-responders. The model combines a non-linear mixed model for the underlying response model with a logistic regression model for the reminder process. The outcome model enables us to analyze the rate of improvement including the dependence on explanatory variables. The non-linear mixed model is derived under the assumption that the rate of improvement in a given time interval is proportional to the current score and the still achievable score. Based on this assumption a differential equation is solved in order to obtain the model of interest. The response model relates the probability of response at each contact attempt and point in time to covariates and to observed and missing outcomes. Using this model the impact of missingness on the rate of improvement is evaluated for different missingness processes.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Missing observations (Statistics), Medical statistics, Clinical trials -- Mathematical models
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2009
Volume:	Vol.2009
Number:	No.42
Number of Pages:	20
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	1. Horton NJ, Lipsitz SR. Multiple imputation in practice: Comparison of software packages for regression models with missing data. The American Statistician 2001; 55 (3):244–254. 2. Carpenter J, Pocock S, Lamm C. Coping with missing data in clinical trials: A model-based approach applied to asthma trials. Statistics in Medicine 2002; 21:1043–1066. 3. Molenberghs G, Kenward MG. Missing data in clinical studies. Wiley, 2007. 4. Little RJA, Rubin DB. Statistical analysis with missing data. Wiley Interscience, 2002. 5. Rubin DB. Multiple Imputation for Nonresponse in Surveys. Wiley, 1987. 6. Rubin DB. Multiple imputation after 18+ years. Journal of the American Statistical Association 1996; 91:473–489. 7. Schafer JL. Multiple imputation: a primer. Statistical methods in medical research 1999; 8:3–15. 8. Schafer JL. Analysis of incomplete multivariate data. Chapman & Hall, 1997. 9. Diggle PJ, Farewell D, Henderson R. Analysis of longitudinal data with drop-out: objectives, assumptions and a proposal. Journal of the Royal Statistical Society: Series C 2007; 56:1–31. 10. Rubin DB. Inference and missing data. Biometrika 1976; 63:581–592. 11. Molenberghs G, Beunckens C, Sotto C, Kenward MG. Every missing not at random model has got a missing at random counterpart with equal fit. Journal of the Royal Statistical Society: Series B 2008; 70:371–388. 12. Diggle PJ, Kenward MG. Informative drop-out in longitudinal data analysis. Applied Statistics 1994; 43:49–93. 13. Baker SG. Marginal regression for repeated binary data with outcome subject to non-ignorable non-response. Biometrics 1995; 51:1042–1052. 14. Troxel AB, Harrington DP, Lipsitz SR. Analysis of longitudinal data with non-ignorable non-monotone missing values. Applied Statistics 1998; 47:425–438. 15. Wood AM, White IR, Hotopf M. Using number of failed contact attempts to adjust for non-ignorable non-response. Journal of the Royal Statistical Society: Series A 2006; 169:525–542. 16. Jackson D, White IR, Morven L. How much can we learn about missing data? an exploration of a clinical trial in psychiatry. To appear in Journal of the Royal Statistical Society: Series A. 17. Cooke MW, Marsh JL, Clark M, Nakash RA, Jarvis RM, Hutton JL, Szczepura A, Wilson S, Lamb SE. Treatment of severe ankle sprain: a pragmatic randomised controlled trial comparing the clinical effectiveness and costeffectiveness of three types of mechanical ankle support with tubular bandage. The CAST trial. Health Technology Assessment 2009; 13: No.13. 18. Alho JM. Adjusting for nonresponse bias using logistic regression. Biometrika 1990; 77:617–624. 19. Lamb SE, Nakash RA,Withers EJ, Clark M, Marsh JL,Wilson S, Hutton JL, Szczepura A, Dale JR, Cooke C MW. Clinical and cost effectiveness of mechanical support for severe ankle sprains: design of a randomised controlled trial in the emergency department. BMC Musculoskeletal Disorders 2005; 6:1471–2474. 20. Lamb SE, Marsh JL, Hutton JL, Nakash RA, Cooke MW. Mechanical supports for acute, severe ankle sprains: a pragmatic, multi-centre, randomised controlled trial. Lancet 2009; 373:575–581. 21. Roos E, Brandsson S, Karlsson J. Validation of the foot and ankle outcome score for ankle ligament reconstruction. Foot & Ankle International 2001; 22(10):788–794. 22. Sherman M, Le Cessie S. A comparison between bootstrap methods and generalized estimating equations for correlated outcomes in generalized linear models. Communications in Statistics - Simulation and Communication 1997; 26:901–925. 23. Sikorsky K, Stenger F. Optimal quadratures in h p spaces. Association for Computing Machinery, Transactions on Mathematical Software 1984; 3:140–151. 24. SAS/STAT Users Guide, Version 8. Cary, NC: SAS Institute Inc. ,1999. 25. Lunn DJ, Thomas A, Best N, Spiegelhalter D. WinBUGS – a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing 2000; 10:325–337. 26. Neal R. Learning in Graphical Models, chap. Suppressing random walks in Markov chain Monte Carlo using ordered over-relaxation. Kluwer Academic Publishers, Dordrecht, 1998; 205–230. 27. Nakash RA, Hutton JL, Lamb SE, Gates S, Fisher J. Response and non-response to postal questionnaire follow-up in a clinical trial - a qualitative study of the patient’s perspective. Journal of Evaluation in Clinical Practice 2008; 14:226–235.
URI:	http://wrap.warwick.ac.uk/id/eprint/35229

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