Effects of Missing Values on the Analysis of the AB/ BA Crossover Trial

1. Effects of Missing Values on the Analysis of the AB/ BA Crossover Trial Lauren Rodgers Supervisor: Prof JNS Matthews University of Newcastle upon Tyne

2. Outline • Crossover Model • Missing Data • Simulations • Conclusions • Future Work

3. Randomise Trial Subjects SEQUENCE 1 SEQUENCE 2 PERIOD 1: TREATMENT B TREATMENT A PERIOD2: TREATMENT B TREATMENT A

4. AB/ BA Crossover Model • What can we estimate? • treatment effect, t • period effect, p • subject effect, x • Problems • carryover effect • Within subject estimate of treatment effect • between subject variability is eliminated

5. General Mean Period effect Treatment effect Subject effects of subject i in sequence k Random error term ~ AB/ BA Crossover Model Subject i in period j of sequence k Two treatment sequences indexed by k= 1, 2 i= 1,…, mk – patients in sequence k j=1, 2 – treatment period d[j, k]{A, B} – treatment allocated in period j of sequence k

6. Subject Effects • Fixed Effects • general level of each subject has a fixed value • find MLE for xik • produce profile log-likelihood model to remove parameter

7. Subject Effects • xik is a function of subject i’s period 1 and period 2 response • when subject i has no response in any period this MLE cancels out the remaining terms • Model which includes only those with complete data • effectively exclude all data from a subject if any missing data • closed form for treatment estimate even in presence missing data

8. Subject Effects • Random Effects • subject effect has some distribution – • include all available data • can be fitted using a Linear Mixed Effects model • No Missing Data – both models produce same results

9. Missing Data • Generate data • shown for sequence AB only • Introduce MCAR missing data

10. Missing Data • Fixed subject effect • remove all data if subject has any missing • Random subject effect • keep all available data

11. Missing Data • 20%, 40% and 60% of data missing • Pattern in sequences and periods • equal amounts missing in each sequence and period • data missing from period two only • equal amounts missing in each sequence • more missing from second sequence • more data missing in second period • more data missing in second sequence

12. Simulations • Parameters • number of subjects in trial: m= 20, 40, 120 • between and within subject variance • t = tA - tB • amount and pattern of missing data • Output • root mean square error (RMSE) • estimate of t and 95% CI

13. Effect of on RMSE( )

14. Effect of on RMSE( )

15. Pattern of Missing Data

16. 95% CI for Treatment Effect • No missing data: length of CI same • Ratio length fixed: length random – which is smaller? • 20% missing

17. 40% Missing

18. 60% Missing

19. Conclusions • Between subject variance has no effect on fixed effects model but increases RMSE for random effects model • Missing data – some differences for pattern • 95% CI for treatment effect • smaller for fixed effects model with small sample size • as sample size increases random effects model performs better • as amount of missing data increases random effects model performs better

20. Future Work • MCAR missing data – not particularly useful • Data missing in period 2 if a correlate of period 1 response exceeds some threshold l • Misspecified model • fit normal model to non-normal data • Look at current methods to account for missing data

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