ANCOVA vs ANOVA: Comparing change from baseline between groups in a clinical trial (using SPSS) Background: Dry Eye disease Intact tear film essential for healthy eye. Normal film function requires •Adequate production of tears •Proper spreading and retention on ocular surface •Balanced elimination Mario D Hair Independent Statistics Consultant Figure 1. Diagrammatic representation of the input and output components of the tear system 1
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ANCOVA vs ANOVA: Comparing change from baseline between groups in a clinical trial (using SPSS) Background: Dry Eye disease Intact tear film essential.
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Mario D Hair Independent Statistics Consultant 1
ANCOVA vs ANOVA: Comparing change from baseline between groups in a clinical trial (using SPSS)
Background: Dry Eye diseaseIntact tear film essential for healthy eye. Normal film function requires
•Adequate production of tears•Proper spreading and retention on ocular surface•Balanced elimination
Figure 1. Diagrammatic representation of the input and output components of the tear system
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THE DATA: Tomlinson A, Hair M, McFadyen A. “Statistical Approaches to Assessing Single and Multiple Outcome Measures in Dry Eye Therapy and Diagnosis” The Ocular Surface 2013
Two studies: Khanal et al (2007) & McCann et al (2012) Both Randomised, Parallel , investigator masked
Patients with Dry Eye disease randomly assigned into one of two treatment groupsKhanal :Oil in water emulsion (25) & Hypromellose (26)McCann :Oil in water emulsion (24) & Sodium Hyaluronate (24)
Patients assessed over three measures
Evaporation rate: Typically 30 ± 15 10-7g/cm2/sTear Turnover rate : Typically 9 ± 4 %/minOsmolarity: Typically 310 ± 10 mOsm/l
At baseline and again at 30 days
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Potential Analysis Comparing change from baseline between groups
Two way mixed ANOVA• One within group factor (baseline/30 days measures)• One between group factor (treatment groups)
One way ANOVA: Simple Analysis of change scores (SACS)• Dependent : Change over 30 days• Independent : Treatment group
One way ANCOVA (van Breukelen 2006; Senn 2006)• Dependent : Measure at 30 days• Independent : Treatment group•Covariate: Measure at baseline
Multiple Regression• Dependent : Measure at 30 days• Independent: Measure at baseline & Treatment group
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Case study 1: Khanal data Tear turnover Rate (TTR)
SACS: One way ANOVA on change
Effect size = 24.79/299.37 = 0.083
Conclusion:• Significant difference between treatments, Emulsion better, Small effect
size.
HYPROMELLOSE (n = 26) EMULSION (n = 25)Tear Turnover rate Mean S.D Mean S.DBaseline 8.62 2.86 9.17 3.6130 days 8.99 2.35 10.93 3.29Change (30days – baseline) 0.37 1.85 1.76 2.81
Change in TTR (TTR2 - TTR1) ANOVASum of Squares df Mean Square F Sig.
Between Groups 24.79 1 24.79 4.42 .041Within Groups 274.58 49 5.60Total 299.37 50
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Case study 1: Khanal data Tear turnover Rate (TTR)
One way ANCOVA
Conclusion:• Significant difference between treatments at 30 days once baseline values
are taken into account. Emulsion better, Effect size larger.
Dependent Variable: Tear turnover rate after 30days: ANCOVA Source Type I I I Sum
HYALURONATE 24.46 1.89 20.65 28.28 EMULSION 22.76 1.89 18.95 25.57 Covariates appearing in the model are evaluated at the following values: EVAP1 = 39.92.
HYALURONATE (n = 24) EMULSION (n = 24)Evaporation Mean Standard Deviation Mean Standard DeviationBaseline 31.99 15.43 47.84 21.4630 days 22.98 9.53 24.25 9.35Change 9.01 15.58 23.60 19.31
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Blue = Hyaluronate Red = Emulsion
Ancova: Assumptions1. Independence of the covariate and treatment effect. 2. Homogeneity of regression slopes
Problem: baseline mean scores different
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Case study 4: Khanal data Tear turnover Rate (TTR) (dealing with outlier)
Blue = Emulsion Red = Hypromellose
Recall possible outlier in Emulsion group.TTR baseline = 7.54, TTR 30 days = 19.04, increase = 11.50. Next highest increase is 6.57Standardised residual = 4.47.
Options
1: Omit outlier
SACS: p = 0.074 Effect size 0.065
ANCOVA p = 0.009 Effect size 0.137
2: Non parametric ANOVA:
Kruskal-Wallis p = 0.057
3. Non parametric ANCOVA?Quade (1967), Puri & Sen (1969), Lawson(1983)
Quade’s Rank analysis of covariance (Quade 1967)
• Not explicitly available in SPSS Simplified Procedure.
1. Rank the dependent variable (TTR2) and covariate (TTR1), using RANK procedure using all the data.
2. Run a linear regression of the ranks of the dependent variable on the ranks of the covariate, saving the unstandardised residuals using all the data.
3. Run a one-way analysis of variance (ANOVA), using the residuals from the regression as the dependent variable, and the grouping variable as the factor. The F test resulting from this ANOVA is the F statistic Quade used.
Unstandardized Res ANOVA Sum of Squares df Mean Square F Sig. Between Groups 786.47 1 786.47 7.76 .008 Within Groups 4967.67 49 101.38 Total 5754.14 50
Summary
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TTR (Khanal): Both ANOVA & ANCOVA significant TTR (Khanal without outlier): Only ANCOVA significantEffect size Anova: 0.083 Ancova:0.140 Effect size Anova: 0.065 Ancova:0.137
References• Khanal S, Tomlinson A, Pearce E I, Simmons P A. (2007). Effect of an oil-in-water emulsion on the tear physiology of
patients with mild to moderate dry eye. Cornea. 26(2): p. 175-81. • Lawson A. (1983) Rank Analysis of Covariance: alternative Approaches. Journal of the Royal Statistical Society Series D
32(3) 331-337
• McCann LC, Tomlinson A, Pearce E I, Papa V. (2012). Effectiveness of Artificial Tears in the Management of Evaporative Dry Eye. Cornea. Sep 30. Cornea. 31(1):1-5.
• Miller G A & Chapman J P.(2001).Misunderstanding analysis of covariance. Journal of Abnormal Psychology, 110(1), 40‐
48.
• Puri M L & Sen P K (1969) Analysis of covariance based on general rank scores Annals of Mathematical Statistics 40, 610-618.
• Quade, D. (1967). Rank analysis of covariance. Journal of the American Statistical Association, 62(320), 1187-1200. • Senn S. (2006), Change from baseline and analysis of covariance revisited. Statistics in Medicine, 25: 4334–4344. • Tomlinson A, Hair M, McFadyen A. Statistical Approaches to Assessing Single and Multiple Outcome Measures in Dry
Eye Therapy and Diagnosis. The Ocular Surface 2013. Online publication 10-SEP-2013 doi: 10.1016/j.jtos.2013.05.002
• Van Breukelen G J P (2006) ANCOVA versus change from baseline had more power in randomized studies and more bias in nonrandomized studies J Clin Epidemiol 59 920–925
• Wilcox (2005) Introduction to robust estimation and hypothesis testing (2nd ed) Burlington MA, Elsevier