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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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