Nurs 701 assignment - statistical analysis questions

Question

Assignment - Statistical Analysis Questions

For each of the questions below, carry out an appropriate analysis to answer the research questions.  The JMP files for some of the questions are located on the Datasets page.

1. Weiner et al. (1979) in their paper "Correlations among history of angina, ST-segment response and prevalence of coronary-artery disease in the Coronary Artery Surgery Study (CASS)" published in the New England Journal of Medicine 301: 230-235, the researchers related clinical diagnosis of chest pain to the results of angiographic examination of the coronary arteries. The following data were obtained are presented below and they are also found in the data file:Chest Pain-Vessels.JMP.

Number of Vessels Diseased

Chest Pain	0 - Vessels	1 - Vessel	2 - 3 Vessels	Row Totals
3 - Definite Angina	66	135	419	620
2 - Probable Angina	179	139	276	594
1 - Nonischemic Pain	197	39	15	251
Column Totals	442	313	710	n = 1,465

a) Calculate the following measures of association Phi, Cramer's V, Pearson's Contingency Coefficient for these data.  Summarize the results.

b) Calculate both asymmetric Lambda measures and the symmetric Lambda.  Summarize these results. 

c) Calculate the all appropriate measures of association treating both variables as ordinal. Summarize these results.

d) Which measure do you think best represents the degree of association between these two variables?  Explain.

2. Using the NC Birth data from earlier assignments, examine appropriate measures for the association between the pairs of variables shown below.  Discuss the results for each.  If you are unsure what the Kessner&Kotelchuck indices are use Google to find some excellent references for each.   They are both ordinal variables that deal with the adequacy of pre-natal care.

a) The Kessner Index and the Trimester pre-natal care began.

b) The Kessner Index and the Kotelchuck Index.

k) The Kotelchuck Index and the Trimester pre-natal care began.

3. A case-control study was carried out to look at the potential risk for myocardial infarctions associated with oral contraceptive use.  In addition to case-control status and current OC use, the age of the subject was also recorded.  The variable age group described below is a ordinal variable created from the ages of the subjects. The data-file OC-Age-MI.JMPcontains these data and the variables in this file and their coding are defined below.

Case-Control Status

1 = Case (Myocardial Infarction (MI))

2 = Control

Oral Contraceptive Use?

1 = Yes

2 = No

Age Group

1 = 25 - 29 yrs., 2 = 30 - 34 yrs., 3 = 35 - 39 yrs., 4 = 40 - 44 yrs., 5 = 45 - 49 yrs.

a. Ignoring age group, estimate the risk for MI associated with OC use.  Provide both a point estimate and an associated confidence interval for this measure of risk.  Discuss.   In doing this in JMP it will be best to use the OC coded and Case-Control coded so the risk measure is calculated in the preferred way.   The appropriate 2x2 contingency table is shown below so you can easily check your calculation by hand.

b) Fit the logistic regression model using uncoded MI status as the response (dependent variable) and uncoded OC Use as the predictor (independent variable).  What are the parameter estimates (β_o ^{^}&β₁ ^{^}) for the model below:

c) Use the parameter estimate (β₁ ^{^}) to compute the OR associated with oral contraceptive use (OC Use).   Be sure to consider how OC Use is coded when computing the OR.

d) On the previous assignment we used the Cochran Mantel Haenszel test to examine the relationship between MI status and OC use adjusted for the Age Group.  You should have found the p-value for the CMH test to be p < .0001, thus we concluded the relationship between OC use and MI status was statistically significant when taking Age into account.

Another way to take Age Group into account is to use logistic regression. Fit the logistic model for MI status using OC Use and Age Group as covariates.  How does the p-value for OC Use to compare to that from the CMH test?  Is Age a significant covariate in the model?  Explain.

e) Compute the OR for OC Use from the logistic model fit in part (d), how does this estimate compare to the OR_CMH which you computed using the formula included in the previous assignment (Hint: OR_CMH =3.99).

f) JMP will also give you OR's for comparing Age Groups pair wise. Use JMP to find the OR for MI associated with being in Age Group = 4 vs. Age Group 1.  Give both a point estimate for this OR along with the associated confidence interval. Interpret.

4. Rosenberg et al. (1980) studied the relationship between coffee drinking and myocardial infarction in young women, aged 30-49 years.  This retrospective study including 487 cases hospitalized for the occurrence of a myocardial infarction (MI). Nine hundred eighty controls hospitalized for an acute condition (trauma, acute cholecystitis, acute respiratory diseases and appendicitis) were selected.  The measured variables in this study are defined below. These data are contained in the file Coffee-MI.JMP.

Case-Control Status

1 = Case (Myocardial Infarction (MI))

2 = Control

Drink Coffee?

1 = Yes (5 cups of coffee or more)

2 = No (< 5 cups of coffee)

Smoker Group

1 = Never., 2 = Former, 3 = 1 - 14 cigarettes, 4 = 15 - 24 cigarettes, 5 = 25 - 34 cigarettes, 6 = 35 - 44 cigarettes, 7 = 45+ cigarettes

a) Ignoring smoking group, estimate the OR for MI associated with drinking coffee as defined above.  Provide both a point estimate and an associated confidence interval for this measure of risk. Discuss. In doing this in JMP it will be best to use Cups Coded? And Case-Control as coded above so the risk measure is calculated in the preferred way. The appropriate 2x2 contingency table is shown below so you can easily check your calculation by hand.

b) Now fit the logistic model with Cups and Smoking status as predictors. Is coffee drinking statistically significant?  How does the p-value for Cups compare to the p-value from the CMH test for the relationship between Cups and MI status adjusting for Smoking status? Discuss.

c) Estimate the OR associated with Cups after adjusting for Smoking status by using the OR.  How does this OR compare to the OR_CMH found on your last assignment?

5. ICU Mortality Study

The ICU data set consists of a sample of 200 subjects who were part of a much larger study on survival of patients following admission to an adult intensive care unit (ICU).  The major goal of this study was to develop a logistic regression model to predict the probability of survival to hospital discharge of these patients and to study the factors associated with ICU mortality.

Source: Data were collected at Baystate Medical Center in Springfield, Massachusetts.

a) Build a simple logistic model for outcome status (STA) using only age (Age) as predictor.  Give two interpretations of the effect of age in terms of odd's ratios using one year and an increment of your choosing.  Construct a plot of P(STA=1|Age) in JMP by selecting Fit Y by X and putting Vital Status in the Y box and Age in the X box.  Discuss your results in a well written paragraph.

b) Build a simple logistic model for outcome status (STA) using only type of admission (TYP) as the covariate.  Compare the estimated OR and associated CI obtained from the logistic model to that obtained via the usual method for 2 X 2 tables (i.e. using Fit Y by X with

Y = Vital Status (STA) and X = Type of Admission (TYP)).  Do they agree?  Should they?  Interpret the OR associated with type of admission.

c) The variable Race is coded at three levels. Prepare a table showing the coding of the two dummy variables necessary for including this variable in a logistic regression model.

d) Write down the equation for the logistic regression model of STA on age (Age), cancer status (CAN), CPR status (CPR), infection status (INF), and race (Race). How many parameters does this model contain?

e) Fit the model from part (d). Using the estimates obtained write down the equation for the fitted values, i.e. the estimated probabilities of P(STA=1|X).  The procedure for finding these probabilities is as follows:

(1) Find the predicted value for the logit (L), which is what you get when you plug the covariate values directly into the logistic regression equation.

(2) Find P(STA=1|X) by using the estimated logit (L) from part (1) using P(STA = 1|X) = e^L/1+e^L

Estimate the probability of death for the following patient types:

i) black patients 70 years old without cancer, who did not have CPR performed, and were infection free.

ii) white patients 60 years old with cancer, who did not have CPR performed, and had an infection at the time of admission.

iii) white patients 80 years old with cancer, who did have CPR performed, and were infection free at the time of admission.

iv) asian patients 85 years old without cancer, who did not have CPR performed, and had an infection at the time of admission.

f) Starting will all covariates with the exception of level of consciousness (LOC), use Stepwise model selection methods with P-value threshold as the model selection criterion.  For Prob to Enter select .20 and forProb to Leave select .10, then run both Forward and Backward Selection methods. Do the models selected using Forward and Backward Selection agree?

What predictors are in the final model chosen using these methods?

g) Interpret the odds ratios (OR) for each predictor in this "final" model from part (f).  For any continuous predictors choose an appropriate increment and interpret the odds ratio associated with that increment, e.g. see Heart Rate below.  Put these estimated OR's in a table with the format shown below.  The examples in the table are hypothetical only, i.e. they are not actually ones you should find from your model.

Variable/Factor	OR	95% CI for OR
Heart Rate (c = 5 bpm)	1.35	(1.08, 2.54)
PCO	2.28	(1.35, 3.98)
Etc....	...	...

Attachment:- Assignment Files.rar