For the final project, you will use statistical methods to analyze…
Question For the final project, you will use statistical methods to analyze… For the final project, you will use statistical methods to analyze hypothetical clinical trial data using the artofstat web app. Suppose that 200 patients who undergo a surgical procedure were randomly assigned to one of two groups: 1. Group A received an experimental treatment following the procedure. 2. Group B received a conventional treatment following the procedure. The duration of stay in the hospital following the procedure is the outcome (response) variable of interest. The research question is whether the experimental treatment affects the duration of stay in the hospital following the surgical procedure. Data from the clinical trial are stored in the included excel file. As a first step, open the excel file attached to this project. The following provides the layout of the file. Column A is Patient ID Column B is the group variable (A=experimental, B=conventional) Column C is the duration of stay in the hospital in days Column D contain patients’ sex (1 = MALE, 2 = FEMALE) Column E contains patients’ age (in years) Column F has patients’ body mass index (BMI), calculated as weight in kilograms divided by height in meters squared. The data come from a randomized trial, meaning that the differences in hospital stays may be attributable to the experimental versus conventional treatment. The idea is that randomization creates two very similar groups, so that everything for the two groups is the same, except for the treatments they receive. Thus, when differences in outcomes are found, they can be attributed to the treatment received as opposed to other factors such as age, sex, or BMI. PART 1 In practice, when randomization is performed, the groups may or may not be the same at intake on every variable. To verify the success of randomization, that is, to verify that the randomization created two similar groups, we will compare the groups on other variables such as age, sex, and BMI. If the groups are similar, that helps us know that the differences in outcome (hospital stay) are due to the experimental treatment and not attributable to other factors that were not equalized by the randomization. Analyze the differences between group A and B, based on age (Column E). Since age is a quantitative variable, we will compare the mean age in groups A and B. : mean age of Group A – mean age of Group B = 0 : mean age of Group A – mean age of Group B ≠ 0 Use WebApps>Confidence Intervals & Tests Comparing Two Groups>Compare Two Means>Confidence Interval & Significance Test Choose the option for enter data: “Provide own”. Name of response variable: AGE, with group 1 label: Group A and group 2 label: Group B. Copy the data from the excel sheet “Group A” tab from Column E (AGE) and paste into artofstat Group A. Copy the data from the excel sheet “Group B” tab from Column E (AGE) and paste into artofstat Group B. 1. What is the mean age for the group receiving the experimental treatment (Group A)? 2. What is the mean age for the group receiving the conventional treatment (Group B)? 3. What is the test statistic and p-value? Based on the p-value and 0.05 level of significance, what decision is reached? a. There is not enough evidence to conclude that the mean age in Group A differs from the mean age in Group B OR b. There is enough evidence to conclude that the mean age in Group A is different from the mean age in Group B. Following the same procedures as above, analyze the difference between group A and B, based on BMI (column F): : mean BMI of Group A – mean BMI of Group B =0 : mean BMI of Group A – mean BMI of Group B ≠0 4. What is the mean BMI for the group receiving the experimental treatment (Group A)? 5. What is the mean BMI for the group receiving the conventional treatment (Group B)? 6. Based on the p-value and 0.05 level of significance, what decision is reached? a. There is not enough evidence to conclude that the mean BMI in Group A differs from the mean BMI in Group B OR b. There is enough evidence to conclude that the mean BMI in Group A is different from the mean BMI in Group B. Since sex (Column D) is a categorical variable, we need a different statistical test to analyze the difference in gender between the two groups. We will use a chi-square analysis to test the following hypothesis: : the conditional distribution of sex is the same for Groups A and B : the conditional distribution of sex is not the same for Groups A and B Use WebApps> Inference for Comparing Several Groups > Chi-Squared Test. Choose the option for enter data: “Individual Observations”, name of 1st variable: Group, name of 2nd variable: Sex. Using the “ALL” tab in excel, for Var 1, copy and paste data for group (Column B) Using the “ALL” tab in excel, for Var 2, copy and paste data for Sex (Column D), then hit “Submit.” 7. Females make up what percent of group A? (Hint: look at the contingency table at the cell which contains the row variable A and the column variable 2, then divide that number by the total for sample size for group A) 8. Females make up what percent of group B? 9. For the chi-square test comparing the distribution of sex in two groups, what is the value of the chi-square test statistic? 10. What is the p-value? 11. Is there enough evidence to conclude that the distribution of sex is different in the two populations represented by the samples that received experimental versus conventional treatment? PART II While randomization is usually successful, often the researchers choose to statistically control for important factors when analyzing randomized studies, so that not everything is left to chance. To choose these important factors, the researchers need to know whether these factors affect the outcome (hospital stay, in this case). See if age, BMI and sex are related to the duration of hospital stay. Test if duration of hospital stay differs between female and male study participants: : mean duration of hospital stay for males – mean duration of hospital stay for females =0 : mean duration of hospital stay for males – mean duration of hospital stay for females ≠0 Since sex (Column D) is a categorical variable, we need a different statistical test to analyze the difference in gender between the two groups. We will use a chi-square analysis to test the following hypothesis: : the conditional distribution of sex is the same for Groups A and B : the conditional distribution of sex is not the same for Groups A and B Use WebApps> Inference for Comparing Several Groups > Chi-Squared Test. Choose the option for enter data: “Individual Observations”, name of 1st variable: Group, name of 2nd variable: Sex. Using the “ALL” tab in excel, for Var 1, copy and paste data for group (Column B) Using the “ALL” tab in excel, for Var 2, copy and paste data for Sex (Column D), then hit “Submit.” 7. Females make up what percent of group A? (Hint: look at the contingency table at the cell which contains the row variable A and the column variable 2, then divide that number by the total for sample size for group A) 8. Females make up what percent of group B? 9. For the chi-square test comparing the distribution of sex in two groups, what is the value of the chi-square test statistic? 10. What is the p-value? 11. Is there enough evidence to conclude that the distribution of sex is different in the two populations represented by the samples that received experimental versus conventional treatment? PART II While randomization is usually successful, often the researchers choose to statistically control for important factors when analyzing randomized studies, so that not everything is left to chance. To choose these important factors, the researchers need to know whether these factors affect the outcome (hospital stay, in this case). See if age, BMI and sex are related to the duration of hospital stay. Test if duration of hospital stay differs between female and male study participants: : mean duration of hospital stay for males – mean duration of hospital stay for females =0 : mean duration of hospital stay for males – mean duration of hospital stay for females ≠0 Use WebApps>Confidence Intervals & Tests Comparing Two Groups>Compare Two Means>Confidence Interval & Significance Test, Choose the option for enter data “Provide own”, name of response variable: STAY, group 1 label: Males and group 2 label: Females. Copy the data from the excel sheet “MALES” tab from Column C (STAY) and paste into artofstat for Group 1 data. Do the same for group 2 data (females). Be sure to use the “FEMALES” tab data. 12. Which sex has a longer mean length of stay? 13. Based on the p-value for the test of : − =0 versus : − ≠0, what decision do we make at .05 level of significance, retain the null hypothesis or reject it? To investigate the relationship between age and duration of stay, construct a scatterplot of duration of stay versus age. Use Association, Correlation & Regression> Linear Regression. Enter data: your own. Name of X (predictor) variable: AGE, and Name of Y (response) variable: STAY. Copy and paste data from the “ALL” tab for the x var and y var. Under regression options, choose show standard errors & P-values. Use Cohen’s (1962, 1988) benchmarks for classifying correlations of |r| >.1, >.3, >.5 as small, medium, and large. If the |r| is < .1, classify as no association. 14. Classify the strength of the association between duration of stay and age. 15. What percent of variation in response is explained using the predictor age? R-sq= 16. Based on the p-value (for the slope), what can we conclude about the significance of age as an explanatory variable for the duration of stay, is it significant or not significant? 17. Is it important to control for age in trial design (e.g., during randomization)? Repeat these procedures, using BMI as the predictor variable. 18. Classify the strength of the association between duration of stay and BMI. 19. Based on the p-value, what can we conclude about the significance of BMI as an explanatory variable for the duration of stay in the hospital? Is it significant or not significant? 20. Is it important to control for BMI in trial design (e.g., during randomization)? PART III Now you will compare the two groups to see if there is a difference between the groups with respect to the outcome variable, number of days spent in the hospital following the surgical procedure. This is the variable named STAY in the worksheet. We will test: : − =0 : − ≠0 Subscript A refers to the population represented by a sample of patients who received the experimental treatment. Subscript B refers to the population represented by a sample of patients who received the conventional treatment. Use WebApps>Confidence Intervals & Tests Comparing Two Groups>Compare Two Means>Confidence Interval & Significance Test Choose the option for enter data “Provide own”, name of response variable: STAY, group 1 label: Group A and group 2 label: Group B. Copy the data from the excel sheet “GROUP A” tab from Column C (STAY) and paste into artofstat. Do the same for group B [use the “GROUP B” tab, Column C (STAY)]. 21. How many patients were randomized to the experimental group (group A)? 22. How many patients were randomized to the conventional group (group B)? 23. For the test of : − =0 = versus : − ≠0, what is the value of the test statistic? t= 24. Interpret the 95% confidence interval. 25. Based on the p-value and 0.05 level of significance, what decision is reached? a. There is not enough evidence to conclude that the mean number of days in the hospital is different for the experimental and conventional treatments. b. There is enough evidence to conclude that mean number of days in the hospital is different for the experimental and conventional treatment Math Statistics and Probability PH 3200 Share QuestionEmailCopy link Comments (0)
