Background: Dry Eye disease

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


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 measuresEvaporation 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


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


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


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

of Squares df Mean

Square F Sig. Partial Eta

Squared Corrected Model 246.55 2 123.28 29.62 .000 .552 Intercept 114.61 1 114.61 27.54 .000 .365 TTR1 198.44 1 198.44 47.68 .000 .498 Group 32.52 1 32.52 7.81 .007 .140 Error 199.77 48 4.16 Total 5482.72 51 Corrected Total 446.32 50

Group Mean Std. Error 95% CI Emulsion 10.76 .41 9.93 11.58 Hypromellose 9.15 .40 8.35 9.96 Covariates appearing in the model are evaluated at the following values: Pre-Dose Tear turnover rate = 8.89

ANOVA Tear turnover rate after 30 days

Sum of Squares

df Mean Square

F Sig.

Between Groups 48.12 1 48.12 5.92 .019 Within Groups 398.21 49 8.13 Total 446.32 50

Mario D Hair Independent Statistics Consultant

Blue = Emulsion Red = Hypromellose

ANCOVA: Assumptions1. Independence of the covariate and treatment effect. (Miller & chapman 2001,

Senn 2006) 2. Homogeneity of regression slopes

If Homogeneity of slopes is violated

Multilevel modelling or Robust Ancova using R (Wilcox 2005)

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Dependent Variable: Tear turnover rate after 30 days: ANCOVA Source Type I I I Sum

of Squares df Mean

Square F Sig.

Corrected Model 246.57 3 82.19 19.34 .000 Intercept 110.88 1 110.88 26.09 .000 Group 4.12 1 4.12 .97 .330 TTR1 190.62 1 190.62 44.85 .000 Group * TTR1 .02 1 .02 .004 .948 Error 199.75 47 4.25 Total 5482.72 51 Corrected Total 446.32 50


Case study 2: Khanal data Evaporation rate

SACS: ANOVA on change

HYPROMELLOSE (n = 26) EMULSION (n = 25)Evaporation Mean S.D Mean S.DBaseline 31.13 16.09 33.80 17.8330 days 21.96 7.13 23.21 11.22Change (baseline- 30days) 9.17 14.89 10.59 17.33

Change in Evaporation (EVAP1 - EVAP2) ANOVA Sum of Squares df Mean

Square F Sig.

Between Groups 25.52 1 25.52 0.10 .754 Within Groups 12604.18 49 257.23 Total 12629.70 50

Dependent Variable: Evaporation after 30days: ANCOVA Source Type I I I Sum of

Squares df Mean Square F Sig.

Corrected Model 614.78a 2 307.39 3.99 .025 Intercept 2685.59 1 2685.59 34.86 .000 TTR1 594.63 1 594.63 7.72 .008 Group 6.36 1 6.36 0.08 .775 Error 3697.66 48 77.03 Total 30297.05 51 Corrected Total 4312.44 50

ANCOVA

Anova & Ancova

No significant treatment effect

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RecapCASE STUDY 1 CASE STUDY 2

Tear turnover rate: Both ANOVA & ANCOVA Evaporation: Neither ANOVA & ANCOVAsignificant : Effect sizes 0.083 0.140 significant



Case study 3: McCann data Evaporation rate

SACS: ANOVA on change

Conclusion:• Significant difference between treatments, Emulsion better, Small to

Moderate effect size.

Effect size = 0.153

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

Change in Evaporation (EVAP1 - EVAP2) ANOVASum of Squares df Mean Square F Sig.

Between Groups 2554.27 1 2554.27 8.30 .006Within Groups 14155.92 46 307.74Total 16710.19 47


Case study 3: McCann data Evaporation rate

One way ANCOVA

Conclusion:• No significant difference between treatments at 30 days once

baseline values are taken into account.

Dependent Variable: Evaporation at 30days ANCOVA Source Type I I I Sum of Squares df Mean Square F Sig. Partial Eta

Squared Corrected Model 582.55a 2 291.28 3.71 .032 .141 Intercept 2171.91 1 2171.91 27.64 .000 .381 EVAP1 563.31 1 563.31 7.17 .010 .137 Group 29.27 1 29.27 .37 .545 .008 Error 3536.09 45 78.58 Total 30880.57 48 Corrected Total 4118.64 47

Group Mean Std. Error 95% CI 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

Mario D Hair Independent Statistics Consultant

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)


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 N Mean Std. Deviation Emulsion 25 4.00 9.95 Hypromellose 26 -3.85 10.18 Total 51 0.00 10.73

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


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

Evap (Khanal) Neither ANOVA & ANCOVA significant Evap (McCann): Only ANOVA significant

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


Thank you : Any questions?Mario D Hair Independent Statistics Consultant

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Background: Dry Eye disease

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