Biostatistics Case Studies 2006

Peter D. Christenson

Biostatistician

http://gcrc.LAbiomed.org/Biostat

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

A B C

Baseline 1 -1 100 93 95

Acute* 2 0

Post 1 3 2 100 93 94

Post 2 4 4 94 91 94

Post 3 5 6 87 88 93

Post 4 6 12 83 84 91

* 1 hour after 1st dose. We do not have data for this visit.

Sitting dbp from Figure 2

t r eat A B C

dBP

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

Week

- 1 0 1 2 3 4 5 6 7 8 9 10 11 12

A: Carvedilol

B: NifedipineC: 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?

TimeStudy End0

P(Survival)

“Well, in the long run, we’re all

dead.”

Milton Freidman

Economist0

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. LOCFFigure 2: Carvedilol

Week

0 2 4 6 8 10

DB

P

88

90

92

94

96

98

100

102

104

106

N=100 N=100 N=94 N=87 N=83

Mean +/- SE

LOCF: N=100

Completers: N=83

12

Presenting All Data can be MisleadingFigure 2: Carvedilol

Week

0 2 4 6 8 10

DB

P

88

90

92

94

96

98

100

102

104

106

N=100 N=100 N=94 N=87 N=83

Mean +/- SEMean= 103 = 10300/100

12

94.7 = 9470/100

93.1 = 8571/94

103 – 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 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.

0.00

0.25

0.50

0.75

1.00

Sur

viva

l Pro

bab

ility

0 5 10 15 20Years

Kaplan-Meier survival estimate

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 TrendFigure 2: Carvedilol

Week

0 2 4 6 8 10

DB

P

88

90

92

94

96

98

100

102

104

106

N=100 N=100 N=94 N=87 N=83

Mean +/- SEN=100

12

N=100

N=94

How to “line up” the valid Δs when the means don’t match?

N=94Valid est of Δ24

Invalid est of Δ24

Valid est of Δ02

Use Successive Δs Like Survival Successive %sFigure 2: Carvedilol

Week

0 2 4 6 8 10

DB

P

88

90

92

94

96

98

100

102

104

106

N=100 N=100 N=94 N=87 N=83

Mean +/- SE

0

12

-10.2

-8.3

Valid est of Δ24 from N=94

Cumulative Change

Valid est of Δ02 from N=100

Δ46 from N=87 -11.8

Δ6-12 from N=83

Thus, replace this graph …

t r eat A B C

dBP

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

Week

- 1 0 1 2 3 4 5 6 7 8 9 10 11 12

A: Carvedilol

B: NifedipineC: Atenolol

A

B

C

t r eat A B C

dBP

- 15

- 14

- 13

- 12

- 11

- 10

- 9

- 8

- 7

- 6

- 5

- 4

- 3

- 2

- 1

0

Week

0 1 2 3 4 5 6 7 8 9 10 11 12

With this “Cumulative Change” Graph:

A

B

C

A: Carvedilol

B: NifedipineC: Atenolol

So, not much effect on this data

Comparison of Methods

Drug

Treatment

Group

% non-completing

subjects

Changes at Week 12

CompleterMethod

Cum Change

LOCF Method

A 17% 12.6 11.8 11.4

B 10% 12.0 12.0 11.9

C 4% 14.3 14.6 14.5

Randomly omit more:

A 50% 12.9 11.0 10.0

B 44% 10.6 10.4 10.0

C 53% 13.7 14.6 13.1

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.

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.