Improving Sensitivity in Treatment Analysis with Covariates
Learn how to enhance the sensitivity of your treatment analysis by incorporating covariates, illustrated through a drug treatment study example. See how the addition of a predictor variable in ANCOVA leads to clearer insights and significant differences in group effects, advancing the analysis from an initial ANOVA.
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Presentation Transcript
Placebo and two treatments Suppose I have a drug treatment study: a-brand name drug (eg. Synthroid) d-generic version of first drug a (L-thyroxin) Placebo- inert substance (sham treatment) X- initial value of physiological parameter which may correlate with Response (related to thyroid function) Response- post-treatment value of physiological parameter (T4 which directly measures thyroid function) Either the brand name or generic should increase the physiological parameter (i.e. increase thyroid function) 2
Suppose I analyze the data and only look at post data (graph first) 4
Now ANOVA No apparent significant differences 5
Maybe we can improve the Model by including another predictor variable, so ANCOVA ANCOVA Model: Yij= + i+ *X+ ij so that i indexes the treatment group and X is now included in the model as a regression variable with slope . 6
New analysis with ANCOVA model This plot looks much more convincing 7
ANCOVA table Now it is clear that there is a treatment group effect, so go on to test group means. 8
Could have done contrasts (not really needed in this case because of the results of the Range test) This contrast tests Drug a vs. Drug d 10
Normality 12
Drugs vs. Placebo This confirms that virtually all Treatment group variation is due to the Placebo vs. Drugs. 14
Why did all of this work? Compare Mean Squares for both models: 2 approximately 36.86 for the Model without Covariate 2 approximately 16.046 for the Model with Covariate It worked because including a meaningful explanatory variable, i.e. the covariate, reduced our estimate of experimental error. 15
