# Statistical Reasoning in Public Health

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Question description

Please find the attached problem and answer them based on the multiple choice and fill blank that's given below the questions

Homework 1, Section B Question 1: An article published in JAMA Pediatrics 1 presents the results of a randomized clinical trial designed to assess the impact of a school-based intervention on depression in Chilean students. Some information from the abstract appears below: The primary outcome of interest was student scores on the Beck-Depression Inventory –II, and the primary predictor of interest was the randomization group (intervention or control). Higher scores on this scale indicate a higher level of depression. Here are some results from the study: 1 Araya R, et al. School Intervention to Improve Mental Health of Students in Santiago, Chile: A Randomized Clinical Trial. JAMA Pediatrics (2013). 1. Likely, why are the depression score means so similar (and not statistically significantly different) at baseline? 2. Why are their fewer subjects in the control and intervention arms at 3 months compared to baseline? The authors used linear regression to analyze the data, as the Beck Depression Score (BDIII) is a continuous measure. For the primary analysis of interest, the difference in BDI-II scores at 3 months of follow up, suppose the author’s fit the following regression model: yˆ  ˆo  ˆ1 x1 , where y is BDI-II score, and x1 = 1 for the students randomized to the intervention group, and 0 for students randomized to the control group. 3. Based on the above results table, what is the value of ˆo ? 4. Based on the above table, report a 95% CI for  o . 5. Based on the above results table, what is the value of ˆ ? 1 6. Based on the above table, report a 95% CI for 1 . (you may need to use a result from SR1 regarding the standard error of a sample mean difference to do this) 7. Is the association between BDI-II scores at 3 months of follow-up and randomization group (intervention/control) statistically significant (alpha=0.05)? (The following is a question to ponder for those who completed the optional material on “sample size and power” from term 1: This does not appear in the Quiz Generator version) This study is a randomized, controlled trial designed to have high power (905) to detect a difference of at least four points in BDI-II between the intervention and control groups. Ultimately, the researchers concluded there was no evidence on an effect of the school based intervention. Why could they make this claim instead of “failing to reject the null hypothesis? Question 2: An article appearing in American Journal of Public Health presents the results of a “modified randomized trial” (authors wording: details are available in the manuscript) to quantify the association between Intensive Housing Placement/ Community Transition Services and repeated homelessness. As per the authors: “We used Cox regression to assess the effect of intervention group on time to exit shelter after April 25, 2010 (limited to exits >= 30 days), and time to first (overnight) return to shelter postexit (through November 30, 2012).” The following graphic shows the resulting survival curve estimated from the Cox model for the second outcome stated in the above text (first time return to shelter). The Cox proportional hazard regression is of the form: ln( hazard of returning to shelter at time t )  ˆo [t]  ˆ1 x1 , where x1= 1 for the intervention group (“home to stay”) and 0 for the control group. 8. Which of the two curves displayed above is a function of ˆo [t] only (ie: does not involve ˆ ?) 1 9. 10. 11. 12. What does the assumption of proportional hazard means for this Cox regression analysis? Will the estimated slope, ˆ1 , be greater than or less than (or equal to) 0? Will the resulting hazard ratio comparing the hazard (incidence) of returning to a shelter for the intervention group compared to the control group greater than, less than or equal to 1? The resulting p-value for testing H o : 1  0 is 0.011. What does this mean about the 95% CI for the hazard ratio comparing the hazard (incidence) of returning to a shelter for the intervention group compared to the control group? Homework 1 Part B Note: Your answers are automatically saved in the background while you work. 1. Likely, why are the depression score means so similar (and not statistically significantly different) at baseline? 2. Why are there fewer subjects in the control and intervention arms at 3 months compared to baseline? 3. Based on the above results table, what is the value of the intercept, beta-naught hat (beta-zero hat)? 4. Based on the above table, report a 95% CI for the intercept, betanaught. 5. Based on the above results table, what is the value of beta1-hat ? 6. Based on the above table, report a 95% CI for beta1. (you may need to use a result from Statistical Reasoning 1 regarding the standard error of a sample mean difference to do this) 7. Is the association between BDI-II scores at 3 months of follow-up and randomization group (intervention/control) statistically significant (alpha=0.05)? 8. Which of the two curves displayed above is a function of only lamba-naught-hat(t) (ie: does not involve beta1-hat ?) a. Home to stay b. Standard Services 9. What does the assumption of proportional hazard means for this Cox regression analysis? 10. Will the estimated slope be greater than or less than (or equal to) 0? a. greater than 0 b. equal to 0 c. less than 0 11. Will the resulting hazard ratio comparing the hazard (incidence) of returning to a shelter for the intervention group compared to the control group be greater than, less than or equal to 1? a. greater than 1 b. equal to 1 c. less than 1 12. The resulting p-value for testing is 0.011. What does this mean about the 95% CI for the hazard ratio comparing the hazard (incidence) of returning to a shelter for the intervention group compared to the control group?

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