Question

4) We now ask you to explore the relationship between regression and ANOVA parametrisations for the 3-group comparison. Write down in algebraic notation the regression model with the grouping variable represented as binary indicator variables (as fitted in 1)) labelling the 3 regression coefficients Bo, B, and 2. Now consider the reparametrised model using "sum-to-zero" coding, i.e. express the model as wtchange E with i = 1, 2, = ia 0. Derive algebraic expressions for the a parameters in terms of the 3, and aa, a B's by equating the two alternative expressions for the mean of each of the four groups [Hint: first eliminate a, from the 3 equations since a3 -a-a] [3 marks]

I only need Question 4 (Image above) answered. I am providing you with the rest of the questions and other information for background information since it is necessary to answer Question 4. I do not need answers to Q1, 2 and 3 - only for Q4

Background information for the question:

The dataset weightloss.dta contains information on 77 patients randomised to undertake one of three diets (referred to as diet A, B and C). Some background information is also available, so weightloss.dta includes the following variables:
Variable name
Description
id: Patient identifier
weight6: Weight at 6 weeks (in kg)
weight0: Baseline weight (in kg)
diet: Diet (1 for diet A, 2 for diet B, 3 for diet C)
age: Age (in years)
sex: Gender (0=female, 1=male)
The aim of the study is to find which diet is best for losing weight. The endpoint is weight change at 6 weeks denoted wtchange that can be easily created using the Stata command: gen wtchange=weight6-weight0. Please keep wtchange as endpoint throughout the assignment.

Part A) – unadjusted analysis
1)Start with and exploratory analysis of the endpoint by type of diet; then carry out an ANOVA on wtchange(using the Stata command anova). The endpoint is assumed normally distributed so no model validation will be required in this exercise. Does dieting appear to be effective? [2 marks]
2) Using a regression model for wtchange, give an unadjusted estimate and 95% confidence interval (CI) for the effect of diet B compared with diet A. Same thing for the effect of diet C with diet A. What is your conclusion so far? [3 marks].
3) The investigator says he/she is interested in the following comparisons:
(i) diet C versus diet B
(ii) diet C versus diets A and B combined
Estimate contrast (i) and give its 95% CI. Does any diet appear to be better than the others? Estimate contrast (ii), provide its 95% CI and summarise the findings [3 marks].

Part B) – adjusted analysis – 7 marks
5) Explain why ANCOVA is in principle a better approach than ANOVA carried out in Part
A) and what covariate we should absolutely adjust for – without any additional model fitting
[2 marks]
6) Carry out the adjusted analysis suggested in 5) using anova. Carry out the same analysis
using regress and give the adjusted diet effect estimates and their 95% CIs. Explain how
they were computed – a small calculation is required for both diet B and diet C. Explain your
conclusions to the investigator. No need further adjustment will be attempted [5 marks].

Answer 1

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