modeling the mean: parametric curves. using the applied longitudinal analysis textbook by garrett fitzmaurice, 2nd edition.

Using the dataset "Rat" study of weight gain from https://content.sph.harvard.edu/fitzmaur/ala/ do the following.

The data are from a study of weight gain, where investigators randomly assigned 30 rats to three treatment groups: treatment 1 was a control (no additive); treatments 2 and 3 consisted of two different additives (thiouracil and thyroxin respectively) to the rats drinking water. Weight was measured at baseline (week 0) and at weeks 1, 2, 3, and 4. Note: Due to an accident at the beginning of the study, data on 3 rats from the thyroxin group are unavailable. Variable List: ID Group Y1 Y2 Y3 Y4 Y5

the variable group is coded 1=control 2=thiouracil and 3= thyroxin

1. Read the data in and put the data in a univariate or long format with five records per subject

2. Using linear trend: Assume that the rate of increase in each group is approximately constant throughout the duration of the study. Assuming an unstructured covariance matrix, construct a test of whether the rate of increase differs in the group

3. based on the result from number 2, what is the estimated rate of increase in mean weight in the control group, in group 2 and in group 3.

4. using spline model for this. The study investigators conjectured that there would be an increase in weight, but that the rate of increase would level-off toward the end of the study. they also conjectured that this pattern of change may differ in the three treatment groups. assuming an unstructured covariance matrix, construct a test of this hypothesis.

5. compare and contrast the result from number 2 and number 4. does a model of only linear trend in time adequately account for the pattern of change in the three treatment groups? provide result that support that conclusion

6. given the results of all the analyses, what conclusions can be drawn about the effect of the additives on the pattern of change in weight?