Biostatistics Case Studies 2006

1. Biostatistics Case Studies 2006 Session 3: An Alternative to Last-Observation-Carried-Forward: Cumulative Change Peter D. Christenson Biostatistician http://gcrc.LAbiomed.org/Biostat

2. Case Study Hall S et al: A comparative study of Carvedilol, slow release Nifedipine, and Atenolol in the management of essential hypertension. J of Cardiovascular Pharmacology 1991;18(4)S35-38.

3. Case Study Outline Subjects randomized to one of 3 drugs for controlling hypertension: A: Carvedilol (new) B: Nifedipine (standard) C: Atenolol (standard) Blood pressure and HR measured at baseline and 4 post-treatment periods. Primary analysis is unclear, but changes over time in HR and bp are compared among the 3 groups.

4. Data Collected for Sitting dbp * 1 hour after 1st dose. We do not have data for this visit.

5. Sitting dbp from Figure 2 A: Carvedilol B: Nifedipine C: Atenolol A B C

6. Basic Issues • Reasons for missing data: • Administrative choice: long-term study ends; early termination; interim analyses. • Related to treatment; subject choice. Unknown. • Time-specific or global differences between treatments: • Time course? Specific times? Only end? • Do groups differ in the following Kaplan-Meier curves? 1 “Well, in the long run, we’re all dead.” Milton Freidman Economist P(Survival) 0 0 Study End Time

7. Some Typical Summaries • Use all available data: • only in graphs, not analysis. • in analysis with mixed models • in analysis with imputation from modeling. • Use only completers: • Sometimes only require final visit. • Sometimes require all visits. • Last-observation-carried-forward (LOCF): • Project last value to all subsequent visits • Sometimes interpolate for intermediate missing visits.

8. Today’s Method • Only interested in baseline to final visit change. • Have data at intermediate visits. • Less bias than LOCF. • More power than Completer analysis. • More intuitive than mixed models for repeated measures (MMRM). • Less robust than MMRM if dropout is related to subject choice. [Often unknown if.]

9. All vs. Completers vs. LOCF LOCF: N=100 Completers: N=83 12

10. Presenting All Data can be Misleading Mean= 103 = 10300/100 103 – 94.7 has meaning 94.7 – 93.1 does not 94.7 = 9470/100 93.1 = 8571/94 12

11. Presenting All Data can be Misleading • Difficulty is that adjacent means involve different subjects. • Would prefer an interpretable estimate of change for adjacent visits. • Solution? • Use analogy to how this is handled with survival analysis.

12. Suppose in a mortality study that we want the probability of surviving for 5 years. • If no subjects dropped by 5 years, then this prob is the same as the proportion of subjects alive at that time. • If some subjects are lost to us before 5 years, then we cannot use the proportion because we don’t know the outcome for the dropped subjects, and hence the numerator. • We can divide the 5 years into intervals using the dropped times as interval endpoints. Ns are different in these intervals. • Then, find proportions surviving in each interval and cumulate by multiplying these proportions to get the survival probability. • See next slide for example. Survival Analysis Concept: Cumulated Probabilities

13. The survival curve below for made-up data for 100 subjects gives the probability of being alive at 5 years as about 0.35. • Suppose 9 subjects dropped at 2 years and 7 dropped at 4 yrs and 20, 20, and 17 died in the intervals 0-2, 2-4, 4-5 yrs. • Then, the 0-2 yr interval has 80/100 surviving. • The 2-4 interval has 51/71 surviving; 4-5 has 27/44 surviving. • So, 5-yr survival prob is (80/100)(51/71)(27/44)=0.35. Survival Analysis Concept: Cumulated Probabilities Note decreasing Ns providing info at each time interval, as for our data. We need to similarly cumulate. Kaplan-Meier actually subdivides finer to get earlier surv probs also.

14. Try to Remove Misleading Trend N=100 How to “line up” the valid Δs when the means don’t match? Valid est of Δ02 N=94 Valid est of Δ24 N=100 Invalid est of Δ24 N=94 12

15. Use Successive Δs Like Survival Successive %s 0 Valid est of Δ02 from N=100 Cumulative Change Δ6-12 from N=83 -8.3 -10.2 Valid est of Δ24 from N=94 -11.8 Δ46 from N=87 12

16. Thus, replace this graph … A: Carvedilol B: Nifedipine C: Atenolol A B C

17. With this “Cumulative Change” Graph: A: Carvedilol B: Nifedipine C: Atenolol A So, not much effect on this data B C

18. Comparison of Methods

19. Summary for Cumulative Change Method • Developed by Peter O’Brien at Mayo Clinic. • More powerful than completer method and less biased than LOCF . • Useful for creating a less misleading graphical display. • Can perform statistical comparisons of the cumulative changes. See O’Brien(2005) Stat in Med; 24:341-358. • Those comparisons are the same as t-test if no dropout. • More intuitive than mixed model repeated measures (MMRM – see Case Studies 2004 Session 3). • More potential for bias than MMRM if subjects choose to drop out. • Same lack of bias as MMRM if administratively censored.

20. Self Quiz • For all questions, consider a study with 2 treatment groups that has scheduled visits at baseline and at study end. Primary outcome is change from baseline to study end, but not all subjects are measured at study end. • If a subject dropped out due to side effects, is he “administratively censored”? Why does it matter? • What additional information is necessary in order to use the method we discussed today?

21. Self Quiz • Now, suppose we also have intermediate visits with measurements for some subjects, for the remaining questions. • Criticize the use of only completing subjects in the analysis. • Criticize the use last-observation-carried-forward. • Criticize the use of imputation methods. • Criticize the use of mixed models. • Criticize the use of today’s method of cumulative change. • Explain the advantage of the suggested graph of cumulated change (slide 17) as compared to a more typical graph of means of all data at each time.