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Question 1 [Total 10 marks] Note: This question does not require Stata. Table 1.1 below gives the results for two randomised controlled trials comparing oral ibuprofen versus placebo in children suffe

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Question 1 [Total 10 marks] Note: This question does not require Stata. Table 1.1 below gives the results for two randomised controlled trials comparing oral ibuprofen versus placebo in children suffering from a migraine. The outcome measure was pain relief at two hours following administration of oral ibuprofen or placebo. A change (increase or decrease) in the risk ratio (oral ibuprofen / placebo) of 10% or more is clinically important. Table 1.1 Trial n per group Ratio of sample proportions (oral ibuprofen / placebo) 95% confidence interval for ratio of population proportions ...

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Question 1 [Total 10 marks] Note: This question does not require Stata. Table 1.1 below gives the results for two randomised controlled trials comparing oral ibuprofen versus placebo in children suffering from a migraine. The outcome measure was pain relief at two hours following administration of oral ibuprofen or placebo. A change (increase or decrease) in the risk ratio (oral ibuprofen / placebo) of 10% or more is clinically important. Table 1.1 Trial n per group Ratio of sample proportions (oral ibuprofen / placebo) 95% confidence interval for ratio of population proportions p-value 1 43 1.60 0.95 to 2.25 0.074 2 165 ?? ?? ?? For Trial 2, the authors presented their results in Table 1.2 below but did not present the ratio of sample proportions, the confidence interval for the ratio of population proportions nor a p-value. Table 1.2 Group Number of children in group Number with pain relief at 2 hours Oral ibuprofen 165 75 Placebo 165 49 a) [3 marks] Complete the three missing entries in Table 1.1 using the data from Table 1.2. b) [5 marks] What is your interpretation of the results of Trials 1 and 2 using all the information provided and calculated, that is, the sample size, ratio of sample proportions, 95% confidence interval for the ratio of population proportions, and the p-value? c) [2 marks] If the above two trials were the only studies currently available with data comparing oral ibuprofen and placebo, would you recommend oral ibuprofen for treating migraines of children? Please explain. 3 Question 2 [Total 20 marks] In order to answer Question 2, you will need to use the Stata dataset assignment2.dta which can be downloaded from the folder “Assignment 2” in the Assessment area on the LMS. Cancer is a collective term that describes many diseases in which some of the body’s cells become defective and multiply out of control. These defective cells can spread to other parts of the body, damaging the surrounding tissue, which may ultimately lead to death. In Australia, the risk of an individual being diagnosed with some type of cancer by the age of 85 years is 1 in 3 for females and 1 in 2 for males. It is well known that the incidence of cancer increases with age. Other established cancer risk factors include family history of disease, alcohol, diet and smoking. This question concerns a new hypothetical case-control study investigating the association between high blood pressure, an established risk factor for coronary heart disease, and the risk of developing cancer. The study investigators measured the following variables: Variable Description id Participant ID age Age (years) sex Gender (Female=0 / Male=1) hbp High blood pressure? (No=0 / Yes=1) bmi Body Mass Index (kg/m2) diab Type II diabetes (No=0 / Yes=1) smoke Smoking (Never=0 / Ever=1) chist Family history of cancer (No=0 / Yes=1) cancer Cancer diagnosis? (No=0 / Yes=1) a) [1 mark] Display the data for the family history of cancer (chist) and cancer diagnosis (cancer) in a 2×2 table. b) [2 marks] Use Stata to produce an appropriate graph to display the relationship between body mass index (bmi) and cancer diagnosis (cancer). Using only this graph, briefly comment on the observed relationship between BMI and cancer? c) [3 marks] Use Stata to calculate and interpret the (unadjusted) odds ratio (OR) for the association between family history of cancer (chist) and cancer diagnosis (cancer). Calculate and interpret the 90% confidence interval for the corresponding population odds ratio. The investigators of this case-control study were interested in the following research questions: “Is there an association between high blood pressure and cancer for individuals: (i) with a family history of cancer, and (ii) with no family history of cancer?” d) [4 marks] Use Stata to calculate and interpret the (unadjusted) odds ratio for the association between high blood pressure (hbp) and cancer (cancer) separately for (i) individuals with a family history of cancer; and (ii) individuals with no family history of cancer. Use Stata to calculate and interpret the 95% confidence interval for each corresponding population odds ratio. 4 The investigators were concerned that smoking may confound the association between high blood pressure and cancer. The investigators amended the research question to the following: “Is the association between high blood pressure and cancer confounded by smoking for individuals: (i) with a family history of cancer, and (ii) with no family history of cancer?” If so, what is the magnitude of the association(s) adjusted for smoking?” e) [6 marks] Use Stata to calculate the odds ratio and the 95% confidence interval for the population odds ratio between high blood pressure (hbp) and cancer (cancer) separately for smokers and non-smokers for: (i) individuals with a family history of cancer; and (ii) individuals with no family history of cancer. Describe the association between high blood pressure (hbp) and cancer (cancer) in the two smoking categories (smoke), separately for: (i) individuals with a family history of cancer; and (ii) individuals with no family history of cancer. f) [2 marks] Use Stata to obtain the Mantel-Haenszel estimate of the odds ratio for the association between high blood pressure (hbp) and cancer (cancer) pooled over the smoking categories (smoke), separately for: (i) individuals with a family history of cancer; and (ii) individuals with no family history of cancer. g) [2 marks] Is there evidence that smoking (smoke) is a confounder of the association between high blood pressure (hbp) and cancer (cancer) for: (i) individuals with a family history of cancer; and (ii) individuals with no family history of cancer. Please explain. Question 3 [Total 6 marks] Note: This question does not require Stata. A pilot study was conducted at a maternal and child health centre in Melbourne, Australia. Out of a random sample of 175 mothers visiting the centre for their child’s 6 months of age assessment, 19 mothers were defined as clinically depressed. a) [1 mark] Calculate the observed proportion of clinically depressed mothers visiting the centre for their child’s 6 months of age assessment. b) [2 marks] Calculate and interpret a 98% confidence interval for the population proportion. c) [2 marks] Calculate the sample size required to obtain an estimate of the population proportion of mothers defined as clinically depressed at their child’s 6 months of age assessment with a precision of ± 3% (i.e. half the width of the 95% confidence interval is 3%). For an initial estimate of the population proportion use the value calculated in the above pilot study. d) [1 mark] What would happen to the required sample size if the investigators changed the precision from ± 3% to ± 2%? 5 Question 4 [Total 4 marks] Note: This question does not require Stata. The cumulative frequency distribution plot below shows data on urinary (Beta-TG) (ng/day/100mL creatinine) excretion in 214 diabetic patients. a) [2 marks] Based on the above cumulative frequency distribution plot, is the distribution of Beta-TG in diabetic patients positively skewed, negatively skewed or symmetric? Give reasons for your answer. Using this data collected from 214 diabetic patients, the study investigators find that the 95% reference range for Beta-TG in diabetic patients is from 16.28 ng/day/100mL creatinine to 43.72 ng/day/100mL creatinine. b) [2 marks] Assume the distribution of Beta-TG in diabetic patients is approximately normally distributed in both the sample and the population. Is it possible to compute the 90% reference range for Beta-TG in diabetic patients from the information provided? If not, explain what required information is missing in order to compute the 90% reference range for Beta-TG in diabetic patients. If yes, compute the 90% reference range for Beta-TG in diabetic patients. 6 Question 5 [Total 5 marks] Note: This question does not require Stata. A randomised controlled trial was conducted to compare nicotine replacement gum versus placebo for stopping smoking. All participants were smokers at the beginning of the study. The primary outcome measure was stopping smoking for six months or more. The researchers reported the following:- “A significantly higher proportion of smokers who received nicotine gum stopped smoking during the 6 months of follow-up compared with the placebo group (p-value <0.05)”. a) [3 marks] What other information should be provided by the researchers in the above statement? b) [2 marks] Is stating p<0.05 sufficient? Please explain.

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Answer 1:
a) For Trial 2: Ratio of sample proportions = 1.53
95% CI for population proportion = (p1-p0) +/- 1.96*Se(p1-p0)
= 0.4545-0.29697 +/- 1.96*se*p1-p0)

Se(p1) = sqrt[(0.4545*(1-0.4545)/165] = 0.038764
Se(p0) = sqrt[(0.2969*(1-0.2969)/165]= 0.035571

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