NURS 701 - Statistical Analysis Questions – Assignment 2
(Due by Midnight - September 13th, 2017)
For each of the questions below, carry out an appropriate analysis to answer the research questions.
- For each question identify the parameter(s) of interest.
Example:
You might state, mean month of the pregnancy that prenatal care began for expecting mothers in North Carolina. - Some questions will require to you carry out an appropriate test to answer the question asked. If possible, be sure to quantify any significant findings using an appropriate confidence interval.
Example:
You might carry out a one-sample t-test to determine if the mean month that prenatal care for expecting mothers began is less than 3 months. If you conclude there is evidence that the mean is less than 3 months, then you should provide a confidence interval for the population mean as well.
- Other questions involve estimation of a population parameter only, i.e. you do not need to carry out a statistical test. You should provide a point estimate for the parameter of interest and a 95% confidence interval.
Example:
You might be asked to estimate the mean month that prenatal care began for expecting mothers in North Carolina. Thus you should report the sample mean and find the confidence interval for population mean.
North Carolina Birth Data
Data description:
The North CarolinaStateCenter for Health Statistics and Howard W. Odum Institute for Research in Social Science at the University of North Carolina at Chapel Hill make publicly available birth and infant death data for all children born in the state of North Carolina. These data can be accessed at:
The data for this assignment is contained in the fileNC Birth (n = 10000).JMP represent a random sample of n = 10,000 births in North Carolina in 2006. The data is linked in the Dataset section of the course website. Also be sure download and print the data description file linked next to the data file. We will be using this data set throughout the course.
PART I - Research Questions and Analysis Tasks (more review)
Conduct an appropriate statistical analysis in JMP to answer the following research questions using the guidelines above. When possible, include all relevant JMP output for answering these research questions. (5 pts. each)
- Is there evidence of a difference between the mean ages of mothers and fathers?
- Is there evidence that the proportion of non-white fathers in NC is greater than the proportion of non-white mothers in NC? The relevant variables are:
Mother Minority = mother’s minority status (white vs. non-white)
Father Minority = father’s minority status (white vs. non-white)
- Is there evidence of a difference in the mean weight gain during pregnancy between non-white and white mothers?
- Is there evidence of a difference between the marital status of non-white and white mothers?
PART II - SAMPLE SIZE AND POWER CALCULATIONS
The questions below deal withpower and sample size calculations for different study designs. These questions are based on the material presented in this week’s lecture on power and sample size. For many of these questions you can use the Sample Size and Power calculator in JMP which is under the DOEmain menu in JMP, however there are few questions where you will need to use the formulae presented in the lecture directly and do the calculations with a calculator. For each question I will inform you whether or not you can use JMP to determine the sample size/power. Also, assume level throughout.
- Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean plasma-glucose concentration in 35-44 year olds is 4.86 mg/dl with a standard deviation = .54 mg/dl. A study of sedentary people in this age group is planned.
a)How many sedentary people would need to be sampled in order to have a power of 80% if the expected difference (or clinically meaningful difference) in plasma-glucose levels is .10 mg/dl? (3 pts.)
b)How many sedentary people would need to be sampled in order to have a power of 80% if the expected difference (or clinically meaningful difference) in plasma-glucose levels is .20 mg/dl? (3 pts.)
c)Construct a plot of Power vs. Sample Size for this study when we wish to detect a .10 mg/dl difference. To do this in JMP input the standard deviation and difference to detect leaving both the Power and Sample Size fields empty. Include this plot below and use it to estimate the power achieved if a sample size n = 100 were used in the study. (3 pts.)
- A pilot study of a new antihypertensive agent is performed for the purpose of planning a larger study. Five patients who have a mean diastolic blood pressure (DBP) of at least 95 mm Hg are recruited for the study and kept on the agent for 1 month. After 1 month the observed mean decline in DBP in these five patients is 4.8 mm Hg with a standard deviation of 9 mm Hg.
If true mean difference in DBP between baseline and 1 month, then how many patients would be needed to have a 90% chance of detecting a significant change in DBP of 5 mm Hg over 1 month using a one-tailed test with a significance level of 5%?
Therefore the hypotheses to be tested are:
Assume that the standard deviation of the DBP difference ( is the same as that observed in the pilot study. This can be done “by hand” using the appropriate formula in the lecture or you could use the Sample Size and Power calculator in JMP using the One Sample Mean option, therefore you can use either. (5 pts.)
- In 1990, for men 45-54 years-old who suffer a myocardial infarction (MI) 25% of them died with 24 hours. This proportion is called the 24-hour case –fatality rate. It is believed that this 24-hour case-fatality rate is currently lower due to advances in the treatment of MI patients.
a)How many MI patients in this population would we need to sample in order to have 80% power to detect a 5 percentage point decrease in the 24-hour case-fatality rate? You can use the DOE > Sample Size and Power > One Sample Proportion option in JMP to do this calculation.
b)How many MI patients in this population would be needed for a power 90% to detect a 5 percentage point decrease?
- The effect of using postmenopausal hormones (PMH) on health outcomes is controversial. Most previous data collected have been from observational studies, and users of PMH may selectively differ from nonusers in ways that difficult to quantify (e.g. more health conscious, more physician visits in which disease outcomes can be identified, etc.) A clinical trial was planned to randomize postmenopausal women to either PMH use or no PMH use and follow them for disease outcomes over a 10-year period. One outcome of special interest is breast cancer.
Suppose the incidence rate of breast cancer among postmenopausal 50-year-old who do not use PMH is 200 per 100,000 women per year. Suppose it is hypothesized that PMH increases the incidence rate of breast cancer by 20%.
a)How many women need to be studied in each group (assume equal sample sizes per group) to have an 80% power using a two-tailed test of detecting the hypothesized increase in breast cancer rate amongst PMH users? You can use the DOE > Sample Size and Power > Two Sample Proportions to do this calculation. (4 pts.)
b)Suppose 20,000 women are recruited to be in each group, what is the power of the test under the same given assumptions? Again you can use JMP to do this calculation by putting the 20,000 as the sample size for each group, specifying and , and leaving the power field empty. (3 pts.)
- Suppose we plan a comparative study of two eye drops (A & B) to reduce the intraocular pressure (IOP) among patients with glaucoma. A contralateraldesign is used, in which drop A is assigned to a random eye and drop B is assigned to the other eye. The patients take the eye drops for 1 month, after which their IOP is measured again. The outcome is a decrease in IOP of 5+ mm Hg in an eye. We expect the following:
(i)That both eyes will be failures (i.e. not show a decrease in 5+ mm Hg) in 50% of patients;
(ii)That both eyes will be successes (i.e. will show a decrease of 5+ mm Hg) in 30% of patients;
(iii)That in 15% of patients the drop A eye will result in a decrease of IOP of 5+ mm Hg but the drop B eye will not;
(iv)That in 5% of patients the drop B eye will show a decrease in IOP of 5+ mm Hg but the drop A eye will not.
a)What method of analysis can be used to compare the efficacy of drop A to drop B? Explain. (2 pts.)
b)How many patients do we need to randomize to achieve 80% power if we have a two-sided test with ?