We discuss inference for longitudinal clinical trials subject to possibly informative dropout. A selection of available methods is reviewed for the simple case of trials with two timepoints. Using data from two such clinical trials, each with two treatments, we demonstrate that different analysis methods can at times lead to quite different conclusions from the same data. We investigate properties of complete-case estimators for the type of trials considered, with emphasis on interpretation and meaning of parameters. We contrast longitudinal and crossover designs and argue that for crossover studies there are often good reasons to prefer a complete case analysis. More generally, we suggest that there is merit in an approach in which no untestable assumptions are made. Such an approach would combine a dropout analysis, an analysis of complete-case data only, and a careful statement of justified conclusions.
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References
1.
LairdNM. Missing data in longitudinal studies. Stat Med1988; 7: 305–315.
2.
LittleRJA. Modeling the dropout mechanism in repeated-measures studies. J Am Stat Assoc1995; 90: 1112–1121.
MolenberghsGKenwardMG. Missing data in clinical studies, Chichester: Wiley, 2007.
5.
DanielsMJHoganJW. Missing data in longitudinal studies: strategies for Bayesian modelling and sensitivity analysis, Boca-Raton: Chapman and Hall/CRC Press, 2008.
6.
PhilipsonPMHoW-KHendersonR. Comparative review of methods for handling drop-out in longitudinal studies. Stat Med2008; 27: 6276–6298.
7.
European Medicines Agency. Guideline on missing data in confirmatory clinical trials: EMA/CPMP/EWP/1776/99 Rev 1. London: European Medicines Agency, 2010.
8.
National Research Council. The prevention and treatment of missing data in clinical trials. Washington, DC: The National Academies Press, 2010.
9.
MolenberghsGBeunckensCSottoC. Every missingness not at random model has a missingness at random counterpart with equal fit. J Roy Stat Soc Ser B2008; 70: 371–388.
10.
RobinsJGillR. Non-response models for the analysis of non-monotone ignorable missing data. Stat Med1997; 16: 39–56.
11.
DigglePFarewellDHendersonR. Analysis of longitudinal data with drop-out: objectives, assumptions and a proposal (with discussion). Appl Stat2007; 56: 499–550.
12.
AalenOGunnesN. A dynamic approach for reconstructing missing longitudinal data using the linear increments model. Biostatistics2010; 11: 453–472.
13.
MeinertC. Terminology–a plea for standardization. Control Clin Trial1980; 1(2): 97–97.
14.
DufoilCBrayneDClaytonD. Analysis of longitudinal studies with death and drop-out:a case study. Stat Med2004; 23: 2215–2226.
15.
DidelezV. Discussion of: Analysis of longitudinal data with drop-out: objectives, assumptions and a proposal (by P. Diggle, D. Farewell and R. Henderson). Appl Stat2007; 56: 536–537.
16.
RubinD. Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol1974; 66(5): 688–688.
17.
BuyseM. Generalized pairwise comparisons of prioritized outcomes in the two-sample problem. Stat Med2010; 29: 3245–3257.
18.
CarpenterJRKenwardMGVansteelandtS. A comparison of multiple imputation and doubly robust estimation for analyses with missing data. J Roy Stat Soc Ser A2006; 169: 571–584.
19.
DigglePJKenwardMG. Informative drop-out in longitudinal data analysis (with discussion). Appl Stat1994; 43: 49–93.
20.
LittleRJA. Pattern mixture models for multivariate incomplete data. J Am Stat Assoc1993; 88: 125–134.
21.
FarewellDM. Marginal analyses of longitudinal data with an informative pattern of observations. Biometrika2010; 97: 65–78.
22.
RobinsJMRotnitzkyAZhaoLP. Analysis of semiparametric regression-models for repeated outcomes in the presence of missing data. J Am Stat Assoc1995; 90: 106–121.
23.
RobinsJMRotnitzkyA. Semiparametric efficiency in multivariate regression-models with missing data. J Am Stat Assoc1995; 90: 122–129.
24.
RotnitzkyARobinsJMScharfsteinDO. Semiparametric regression for repeated out-comes with nonignorable nonresponse. J Am Stat Assoc1998; 93: 1321–1339.
25.
RotnitzkyAScharfsteinDOSuTL. Methods for conducting sensitivity analysis of trials with potentially non-ignorable competing causes of censoring. Biometrics2001; 57: 103–112.
26.
ScharfsteinDORotnitzkyARobinsJM. Adjusting for non-ignorable drop-out using semiparametric non-response models (with discussion). J Am Stat Assoc1999; 94: 1096–1146.
27.
ScharfsteinDODanielsMRobinsJM. Incorporating prior beliefs about selection bias into the analysis of randomized trials with missing outcomes. Biostatistics2003; 4: 495–512.
28.
WhiteIRHigginsJPWoodAM. Allowing for uncertainty due to missing data in meta analysis–part 1: two-stage methods. Stat Med2008; 27: 711–727.
29.
HoWKMatthewsJNSHendersonRFarewellDRodgersLR. Dropouts in the AB/BA crossover design. Stat Med2012. (to appear) doi:10.1002/sim.4497.
30.
LittleRSelection and pattern-mixture models. In: FitzmauriceGDavidianMVerbekeGMolenberghsG (eds). Longitudinal data analysis, Boca Raton: Chapman and Hall/CRC Press, 2008, pp. 409–432.
31.
AalenOO. Armitage lecture 2010: Understanding treatment effects: the value of integrating longitudinal data and survival analysis. Stat Med2012. (to appear.
32.
AalenOORø yslandKGranJ. Causality, mediation and time; a dynamic viewpoint. J R Stat Soc Ser A2012. (to appear.
33.
TsiatisADavidianM. Joint modeling of longitudinal and time-to-event data: an overview. Stat Sin2004; 14(3): 809–834.
34.
FrankBSerpellMGHughesJ. Comparison of analgesic effects and patient tolerability of nabilone and dihydrocodeine for chronic neuropathic pain: randomised, crossover, double blind study. Br Med J2008; 336: 199–201.
