stat assignment
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STA 536 assignment 2 (Due on Sunday, March 13 th ) SCORE ________________/
_Name_____________________________________________ URI ID _____________________
Problem 1 [18]: FLW Chapter 5 (Problem 5.1). Make sure you complete all parts of the problem.
The National Cooperative Gallstone Study (NCGS) was designed to study the safety of chenodiol for the treatment of cholesterol gallstones because this treatment may raise serum cholesterol. Serum cholesterol (mg/dl) was measured at baseline, and at 6, 12, 20, and 24 months of follow-up. Some cholesterol values were missing due to missed visits, inadequate or lost laboratory specimens, or termination of patient follow-up. In this problem, you will analyze a subset of the data on patients who were randomly assigned to the high-dose (750mg/d) or placebo group. The data is provided in an external file (e.g., cholesterol.sas7bdat for SAS, cholesterol.dta for R) and each row has 7 variables: Group (1 = High-dose, 2 = Placebo), ID, Y1, Y2, Y3, Y4, and Y5. 5.1.1 Read from the external file and keep it in a multivariate or wide format. 5.1.2 Compute the sample means, standard deviations, and variances of the serum cholesterol levels at each occasion for each treatment group. 5.1.3 Produce a time plot of the mean of the serum cholesterol levels versus time (in months) for the two treatment groups [for example, using PROC GGPLOT]. Provide a title and label the axis. Use a short paragraph to interpret your observations from the plot. 5.1.4 Reformat the data from a multivariate or wide format to a univariate or long format with 5 records per subjects. 5.1.5 Assuming an unstructured covariance matrix, conducted an analysis of response profiles using the PROC MIXED procedure [it can better handle missing data better than PROC GLM]. Determine whether the patterns of change from baseline in the mean serum cholesterol levels over time differ in the two groups. Formulate the null hypothesis that the patterns of change in the mean response over time are the same across groups and the alternate hypothesis is that the patterns of change in the mean response over time are not the same across groups. Interpret the results of the test. 5.1.6 report the estimated 5×5 covariance and correlation matrices for the 5 repeated measurements of serum cholesterol. 5.1.7 In the NCGS Trial there are two groups (placebo and high-dose) and five measurement occasions (month 0, 6, 12, 20, 24). Specify the primary outcome Yij and the set of covariates (inputs) Xqij in the model [pay attention to dummy variables], where i corresponds to subject index and j to cholesterol measurement occasions. Write the regression model for the mean serum cholesterol. 5.1.8 Let L denote a contrast matrix of known weights and the vector of linear regression parameters from the model assumed in Problem 5.1.7. Specify the matrix L such that H 0 : L =0, would be equivalent to the null hypothesis that the patterns of change over time do not differ in the two treatment groups.
5.1.9 Estimate the time-specific means (using the model form 5.1.7) in the two groups and compare them with sample means obtained in Problem 5.1. 5.1.10. With baseline (month 0) and the placebo group (group 2) as the reference group, provide the interpretation of each of the estimated regression coefficients in terms of the effect of the treatment on the patterns of change in mean serum cholesterol.
Problem 2[12]: FLW Chapter 6 (Problem 6.1). Make sure you complete all parts of the problem.
In the study of weight gain 30 rats were randomly assigned to 3 treatment groups: treatment 1 (control), and treatment 2 (thiouracil) and treatment 3 (thyroxin) with additives added to the rat drinking water. The weight (in grams) of the rats was measured at baseline (week 0) and at weeks 1, 2, 3, and 4. Due to an accident at the beginning of the study, data on 3 rats from the thyroxin group are unavailable. The data was stored in an external file (rat.sas7bdat for SAS, and rat.dta for R). Each row of the data set has 7 variables: ID Group (1=control, 2=thiouracil, 3=thyroxin) Y 1 Y 2 Y 3 Y 4 Y 5.
6.1.1 & 6.1.2. Read the data from the external file and keep it in a long format with 5 records per subject. Compute the mean weights (in grams) at each measurement occasion for each treatment groups and produce a time plot of the observed mean weight (in grams) versus time (in weeks) for the three treatment groups. Provide a title and label the axis. Use a short paragraph to interpret your observations from the plot. 6.1.3 Assuming the rate of increase in each group is approximately constant throughout the duration of the study and that an unstructured covariance matrix, conduct a test of whether the rate of increase differs in the groups. Formulate appropriate null and alternative hypotheses, provide estimated regression summaries based on a model with linear trends for the weight data from the study, and interpret the results. 6.1.4 Using a single graph, construct a time plot to display the estimated mean weight versus time (in weeks) for the three groups. [Hint: in SAS, you can use the OUTP option to the MODEL statement to output a dataset with predicted values and use them to plot estimated mean weights (in grams) against time (in weeks) for the three treatment groups using PROC GGPLOT procedure].
6.1.5 Compute the estimated rates of increase in mean weight for each of the three groups. 6.1.6 The study investigators conjectured that there would be an increase in weight, but that rate of increase would level-off towards the end of the study (suggestive quadratic trends over time). They also conjectured that the pattern of change may differ in the three treatment groups. Assuming an unstructured covariance matrix, test the proposed hypotheses by including quadratic time term (a possibly interaction term) in the model, thereby modeling the non- linearity in the trend over time. Formulate the null and alternative hypothesis, summarize and interpret the results.
6.1.7 & 6.1.8 Compare and contrast results from Problems 6.1.3 & 6.1.6 [use AIC or BIC criteria].