Biostatistics Case Studies 2006 Peter D. Christenson Biostatistician Session 3: An Alternative to Last-Observation-Carried-Forward: Cumulative Change

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.

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.

Data Collected for Sitting dbp Visit #Week Number of Subjects ABC Baseline Acute*20 Post Post Post Post * 1 hour after 1 st dose. We do not have data for this visit.

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

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? Time Study End0 P(Survival) “Well, in the long run, we’re all dead.” Milton Freidman Economist 0 1

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.

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.]

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

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

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.

Survival Analysis Concept: Cumulated Probabilities 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 The survival curve below for made-up data for 100 subjects gives the probability of being alive at 5 years as about 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. 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.

Try to Remove Misleading Trend N= N=100 N=94 How to “line up” the valid Δs when the means don’t match? N=94 Valid est of Δ 24 Invalid est of Δ 24 Valid est of Δ 02

Use Successive Δs Like Survival Successive %s Valid est of Δ 24 from N=94 Cumulative Change Valid est of Δ 02 from N=100 Δ 46 from N= Δ 6-12 from N=83

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

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

Comparison of Methods Drug Treatment Group % non- completing subjects Changes at Week 12 Completer Method Cum Change LOCF Method A17% B10% C4% Randomly omit more: A50% B44% C53%

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: 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.

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. 1.If a subject dropped out due to side effects, is he “administratively censored”? Why does it matter? 2.What additional information is necessary in order to use the method we discussed today?

Self Quiz Now, suppose we also have intermediate visits with measurements for some subjects, for the remaining questions. 3.Criticize the use of only completing subjects in the analysis. 4.Criticize the use last-observation-carried-forward. 5.Criticize the use of imputation methods. 6.Criticize the use of mixed models. 7.Criticize the use of today’s method of cumulative change. 8.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.