Case Studies 2004 Session4

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					         Biostatistics Case Studies


                  Session 4:
A Comparison of Repeated Measures Analyses of
                 Serial Data


             Peter D. Christenson
                 Biostatistician

            http://gcrc.humc.edu/Biostat
                    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 5 post-
treatment periods.

Primary analysis ?
“The present study compares … A,B, and C for the
management of … hypertension.” ?
            Data Collected for Sitting dbp

                                      Number of Subjects
               Visit #    Week        A        B         C
Baseline          1         -1              311 total
Acute*            2         0       100       93         95
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.
              Stated Statistical Analysis

The entire statistical analysis section of the paper states:

“The difference from baseline for each parameter was
compared across the three treatment groups and the
baseline level itself at each visit by an analysis of
covariance.
Confidence limits for differences between pairs of treatments
were examined as well as test of significance (at the 0.05
level) between pairs of treatments.”
                   Interpretation of
              Stated Statistical Analysis
Stated:

“The difference from baseline for each parameter was
compared across the three treatment groups and the
baseline level itself at each visit by an analysis of
covariance.”

Interpretation (I think):

For dbp, they examined 5 outcomes: Δ0, Δ2, Δ4, Δ6, and Δ12,
where each Δ is change in dbp from baseline (1 week prior
to week 0) and the subscript denotes the week.

For each Δ, the mean was found for each group, then
adjusted for baseline dbp, and the adjusted means were
then compared among groups.
Sitting dbp from Figure 2

                        A: Carvedilol
                        B: Nifedipine
                        C: Atenolol




                    A

                B
           C
                Results for Sitting dbp

“The results for dbp mirrored those of sbp quite closely [no
significant treatment differences], with the average
hypotensive effect after 2 weeks being 10 mm Hg and
increasing to approximately 13 mm Hg by 12 weeks of
treatment with the three regimens. Overall, there was no
significant difference between the three antihypertensive
therapies (Fig. 2).”

Although not specifically stated, the comparisons were
restricted to the 255 subjects who provided data at all five
post-therapy visits.
        ANOCOV Results for Sitting dbp Δ2
                         Adj’d Mean Δ12     Adj’d Mean Δ2
             A                 -12.3              -8.0
            B                  -12.3              -9.3
            C                  -14.2             -11.4
   Overall p:                   0.24             0.033
   Post Hoc (Tukey) p:
          A vs. B               1.00              0.60
          A vs. C               0.31             0.027
          B vs. C               0.31              0.24

So, A and C do not differ in changes at 12 weeks, Δ12, which
may be what the authors call “overall”, and may the most
relevant outcome here.
Yet, there are other differences in the treatments, such as Δ2 .
         Issues with Multiple Measurements
If comparisons are made at every visit and there are many
    visits, potential false positives may be likely due to multiple
    comparisons.

What are relevant treatment differences? Possibilities:
• Average over post-therapy visits (or other summary).
• Changes from baseline to final visit.
• Comparisons at each visit are indeed the 1º concern.
• Any difference in profile over time.
• Changes from baseline to each other visit, as in the paper,
  but still, any difference in this profile, or each visit, or …?
• Changes from visit to the following visit, but still, any
  difference in this profile, or each visit, or …?
• The rate of change over time, where individual weeks are
  not important.
               Multiple Uses of “Multiple”
Multiple Regression:
   Outcome: say, dbp at 12 weeks
   Predictors: treatment, covariates (age, baseline dbp,
               duration of HTN, weight, other meds, etc.)

Multivariate ANOVA (MANOVA):
   Outcome: say, (dbp, HR) at 12 weeks, as a set of 2
              outcomes
   Predictors: treatment

Repeated Measures: (as in this paper)
   Outcome: say, (dbp2, dpb4, dbp6), as a set of 3 outcomes
   Predictors: treatment
or
   Outcome: dbp
   Predictors: week, treatment
Repeated Measures Analyses: Approach A


Use MANOVA with (dbp0, dpb2, dbp4, dpb6 dbp12), as a set
   of 5 outcomes.

   Can define “contrasts” among the set of 5, such as
     changes Δ2, Δ4, Δ6, and Δ12 from baseline, or
     changes between subsequent visits.

   A contrast could be linear or quadratic trend.

   Can include covariates.

Corresponds to Figure 2.
 Repeated Measures Analyses: Approach B

Use week# as a predictor in ANOVA or mixed model:

             dbp = function (treatment, week).

Fits a separate curve over time for each subject.

Default settings in ANOVA software may not be correct.

Advantage over approach A:
Exact time can be used; categories of week are not
   necessary. For example, subjects may vary, say, over
   days 37 to 50 for nominal week 6 at 42 days.

Corresponds to smooth curves in Figure 2.
        Approaches for our Possible Outcomes
Recall our possibilities for treatment differences :

•   Average over post-therapy visits (or other summary).
•   Changes from baseline to final visit.
•   Comparisons at each visit are indeed the 1º concern.
•   Any difference in profile over time.
•   Changes from baseline to each other visit, as in the paper, but
    still, any difference in this profile, or each visit, or …?
•    Changes from visit to the following visit, but still, any
    difference in this profile, or each visit, or …?
•   The rate of change over time, where individual weeks are not
    important.

Use ordinary (univariate) ANOVA for 1-3.
Use MANOVA approach A for 4-6, with suitable contrast.
Use approach B for 7, if visit times were not exactly on the week.
                      Missing Visits
Only the 255 subjects without any missing visits are used in
this paper.

The MANOVA approach A requires data at each visit.
Software will drop subjects who are missing any visits.

The ANOVA approach B can be tweaked to handle missing
visits with a weighted analysis, but it is difficult.


Mixed models can handle missing visits for both approaches.
Approach A can be more sensitive using mixed models if
there are patterns in correlations over time.
Approach B is called a “random coefficient model”.
          Data Structure for Software
MANOVA Approach A:

patient    dbp1   dbp3   dbp4   dbp5   dbp6

    1        97    101     88     89    86
    2       109     72      .      .     .

Approach B:
     patient     week    dbp
        1        -1       97
        1         2      101
        1         4       88
        1         6       89
        1        12       86
        2        -1      109
            etc ...
         Software for Repeated Measures

SPSS: Analyze > GLM > Repeated >
     [ specify variables , contrasts, options ]

SAS: proc glm;
        class treat;
        model dbp1 dbp3 dbp4 dbp5 dbp6 =
                   treat / solution clparm;
        repeated weeks (-1 2 4 6 12) polynomial /summary;
     run;


With missing visits, use Analyze > Mixed in SPSS, and proc
mixed in SAS. Caution: defaults are likely not correct; needs
experience.
    Successive Visit Comparisons: Approach A
          Use dbp at each of 5 visits      p-value
          Weeks                            <0.0001
          Treatment                          0.08
          Weeks*Treatment                    0.04
          Treatment differences for
            successive weeks:
                 -1 vs. 2 weeks              0.03
                  2 vs. 4 weeks              0.23
                  4 vs. 6 weeks              0.03
                 6 vs. 12 weeks              0.08
Treatments do not differ in dbp averaged over all weeks (p=0.08),
but there is some difference in their profiles over time (p=0.04).
Significant changes occur between baseline and 2 weeks, and
between weeks 4 and 6.
     Rate of Change Comparisons: Approach B*
            Use dbp at each of 5 visits           p-value
            Weeks                                 <0.0001
            Treatment                               0.08
            Weeks*Treatment                         0.04
            Treatment differences for
              polynomial contrasts:
                   Linear                           0.34
                   Quadratic                        0.07
                   Cubic                            0.57
                   Fourth Order                     0.02
Same conclusion that profiles over time vary (p=0.04), but now
due to “waviness” of fourth order term.
* Can use approach A here also, since we’re using week categories, not exact
time.
               Conclusions for this Data

Treatments do not differ in lowering of dbp By 12 weeks.

But treatment effects do differ over time.

Treatment A gives faster effect, since changes from baseline to
week 2 are significantly greater than other treatments.

For this data, modeling rates over time with polynomial
contrasts agrees with successive visit contrasts, but adds no
new information.
Conclusions for Repeated Measures Analyses

If all subjects are measured at all visits:

       Use approach A if categories of time are used. Choose
             most relevant contrasts.

       Use approach B if subjects:
             1. vary in timings of visits (exact time), or
             2. to model relationships over time other than
                    polynomial.


If subjects have missing visits:

       Use a mixed model.

				
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