please please help, I tried my best to provide the data needed to answer the questions, for some reason it will not let me an attachment, so I had to copy and past. The mosaic plots did not transfer but the tables provide the same info on the mosaic plot. thank you

STAT 601 - Spring 2023 - Assignment #2(57 points)

Review the following:

Lecture Handouts: Probability, Binomial Distribution, and the Normal Distribution, there are blank notes and annotated ones. You will also need the normal tables which are linked on the website or use the Normal Probability Calculator in JMP.

Narrated Powerpoint Lectures under heading 5 - Parts 1 - 4

Non-narrated Powerpoint Lectures under heading 5 - Parts 1 - 4

1. Low Birth Weight Risk Factors (NC Birth 10000.JMP)

The purpose of this study was to identify potential risk factors for low birth weight. The following categorical variables were measured and coded as follows:

Contingency Analysis of Low By Previous Preterm

Mosaic Plot

Contingency Table

Previous Preterm By Low

Count Row %	No	Yes	Total
No	9018 91.21	869 8.79	9887
Yes	77 75.49	25 24.51	102
Total	9095	894	9989

Relative Risk

Description	Relative Risk	Lower 95%	Upper 95%
P(Yes|No)/P(Yes|Yes)	0.358604	0.253602	0.507081

Odds Ratio

Odds Ratio	Lower 95%	Upper 95%
3.3693	2.134438	5.318583

Previous Preterm = woman has a previous history of premature labor (Yes or No)

Hyper = hypertension during pregnancy (Yes or No)

Contingency Analysis of Low By Hyper

Mosaic Plot

Contingency Table

Hyper By Low

Count Row %	No	Yes	Total
No	8663 91.84	770 8.16	9433
Yes	432 77.70	124 22.30	556
Total	9095	894	9989

Relative Risk

Description	Relative Risk	Lower 95%	Upper 95%
P(Yes|No)/P(Yes|Yes)	0.366011	0.309016	0.433518

Odds Ratio

Odds Ratio	Lower 95%	Upper 95%
3.229353	2.610219	3.995343

Smoke = smoked during pregnancy (Yes or No)

Contingency Analysis of Low By Smoker

Mosaic Plot

Contingency Table

Smoker By Low

Count Row %	No	Yes	Total
No	8124 91.71	734 8.29	8858
Yes	948 86.18	152 13.82	1100
Total	9072	886	9958

Relative Risk

Description	Relative Risk	Lower 95%	Upper 95%
P(Yes|No)/P(Yes|Yes)	0.599666	0.509453	0.705854

Odds Ratio

Odds Ratio	Lower 95%	Upper 95%
1.774635	1.471715	2.139905

Uterine = uterine irritability during pregnancy (Yes or No)

Contingency Analysis of Low By Uterine

Mosaic Plot

Contingency Table

Uterine By Low

Count Row %	No	Yes	Total
No	9065 91.10	886 8.90	9951
Yes	30 78.95	8 21.05	38
Total	9095	894	9989

Relative Risk

Description	Relative Risk	Lower 95%	Upper 95%
P(Yes|No)/P(Yes|Yes)	0.422922	0.227758	0.78532

Odds Ratio

Odds Ratio	Lower 95%	Upper 95%
2.728367	1.247032	5.969364

Minority = minority status of mother (Nonwhite, White)

Contingency Analysis of Low By Minority

Mosaic Plot

Contingency Table

Minority By Low

Count Row %	No	Yes	Total
Nonwhite	2459 87.29	358 12.71	2817
White	6643 92.51	538 7.49	7181
Total	9102	896	9998

Relative Risk

Description	Relative Risk	Lower 95%	Upper 95%
P(Yes|Nonwhite)/P(Yes|White)	1.696285	1.494901	1.924798

Odds Ratio

Odds Ratio	Lower 95%	Upper 95%
0.55628	0.482901	0.64081

Low = low birth weight indicator (Yes or No) Response/Outcome

a) For each risk factor calculate P(Low = Yes|risk factor present) and P(Low = Yes|risk factor absent) for each of the four potential risk factors. In general, what do these probabilities tell you about each of the potential risk factors? (5 pts.)

b) Use your answers in part (a) to calculate the relative risk (RR) associated with each potential risk factor and put them in the table below. Interpret in words the RR associated with smoking during pregnancy. (5 pts.)

c) Calculate the odds ratio (OR) associated with each characteristic and put them in the table below. Interpret in words the OR associated with smoking during pregnancy. (5 pts.) Problem #1 parts (d) and (e) are on the following page.

Problem #1 parts (d) & (e)

d) Use the results from part (b) and (c) above to complete the table below

Risk Factor	Relative Risk (RR)	Odds Ratio (OR)
Previous history of premature labor
Hypertension during pregnancy
Smoked during pregnancy
Uterine irritability during pregnancy
Minority status of mother

e) Which factor do has the greatest associated risk of having a child with low birth weight? the least? Justify your answers. (2 pts.)

2. Esophageal Cancer and Alcohol Consumption

Tuyns et al. (1977) examined the potential relationship between regular alcohol consumption and esophageal cancer using a case-control study. A sample of 200 esophageal cancer patients was taken and 775 community-based controls were selected to form a comparison group. One potential risk factor examined in the study was whether or not the individual drank 80 or more grams of alcohol/day.

Daily Alcohol Use	Case (Esophageal cancer)	Control (Cancer free)	Row Total
> 80 g	106	100	206
< 80 g	94	675	769
Column Total	200	775	n = 975

a) Why is not valid to calculate P(Esophageal Cancer| Daily Alcohol Use > 80g)? (2 pts.) b) Use the results below to quantify the risk associated with consuming 80 or more grams of alcohol/day. Interpret your findings. (4 pts.)

c) Does this prove that regular alcohol drinking causes esophageal cancer? Explain your answer. (2 pts.)

3. Assessment of Radiological Tests in the Detection of Coronary Artery Disease

Begg et al. (1988) in their paper "Assessment of Radiological Tests: Control of Bias and Other Design Considerations" looked at the performance of radionuclide ventriculography as a diagnostic test for detecting coronary artery disease. The following results were obtained when using the test on 481 individuals known to have coronary artery disease and 452 individuals who do not have the disease.

Test Result	Coronary Artery Disease (D+)	Disease Absent (D-)	Column Total
Positive (T+)	322	70	392
Negative (T-)	159	382	541
Row Total	481	452	n = 933

a) Calculate the sensitivity, specificity, false positive, and false negative probabilities using the results above. (4 pts.)

b) For a population in which the prevalence of coronary artery disease is .10 (or 10%) calculate the probability that an individual has coronary artery disease given that they test positive using radionuclide ventriculography, i.e., what is the positive predictive value of this test? (3 pts.)

c) For the same population, what is the probability that a person that tests negative does not have coronary artery disease, i.e., what is the negative predictive value of this test? (3 pts.)

4. Middle Ear Effusion in Breast-Fed and Bottle-Fed Infants(5 pts.) A common symptom of otitus media in young children in the prolonged presence of fluid in the middle ear, known a middle-ear effusion. The presence of fluid may result in temporary hearing loss and interfere with normal learning skills in the first two years of life. One hypothesis is that babies who are breast-fed for at least 1 month build up some immunity against the effects of the disease and have less prolonged effusion than do bottle-fed babies. A small study of 24 pairs of babies is set up, where the babies are matched on a one-to-one basis according to age, sex, socioeconomic status, and type of medications taken. One member of the matched pair is a breast-fed baby, and other member is a bottle fed baby. The outcome variable is the duration of middle-ear effusion after the first episode of otitus media. The results are shown below.

Pair Number	Duration of effusion in breast-fed baby	Duration of effusion in bottle-fed baby	Difference	Sign of Difference
1	12	18	6	+
2	11	35	24	+
3	3	7	4	+
4	24	182	158	+
5	7	6	-1	-
6	28	33	5	+
7	58	223	165	+
8	9	17	8	+
9	39	57	18	+
10	17	76	59	+
11	17	186	169	+
12	12	29	17	+
13	52	39	-13	-
14	14	15	1	+
15	12	21	9	+
16	30	28	-2	-
17	14	8	-6	-
18	15	27	12	+
19	65	77	12	+
20	10	12	2	+
21	7	8	1	-
22	19	26	7	+
23	34	28	-6	-
24	17	20	3	+

Do these data provide evidence that breast-fed babies have shorter durations of effusion when compared to bottle-fed babies that are the same age, sex, socioeconomic status, and on the same medications? Use the binomial distribution to answer this question and carefully justify your answer. Note: When the paired difference is zero, we drop that observation from the results and adjust n accordingly. (5 pts.)

P value: 0.0113

5. Use of Cyclosporine in Treatment of Aplastic Anemia Patients(5 pts.)

Frickhofen et al. (1991) performed a study on the effect of using cyclosporine in addition to antilymphocyte globulin and methylprednisolone in the treatment of aplastic anemia patients. There was a sample of 43 patients that received the cyclosporine in addition to the other treatment. Historically, the use of antilymphocyte globulin and methylprenisolone without cyclosporine results in complete or partial remission in 40 percent of aplastic anemia patioents at the end of three months of treatment. We wish to determine if the use cyclosporine can increase significantly the percentage of patients experiencing complete or partial remission. In the clinical trial conducted by the researchers 25 of the 43 patients receiving cyclosporine in addition to the traditional treatment achieved complete or partial remission within three months.

Can we conclude on the basis of this result that the addition of cyclosporine to the treatment regimen is associated with an increase in the percent of aplastic anemia patients experiencing complete or partial remission? Again use the binomial distribution and carefully justify your answer. (5 pts.)

P value=0.182

6. Diabetes Screening Using Fasting Glucose Levels

A standard test for diabetes is based on glucose levels in the blood after fasting for prescribed period.For healthy people the mean fasting glucose level is found to be 5.35mole/liter with a standard deviation of 0.65mole/liter. For untreated diabetics the mean is 11.50, and the standard deviation is 3.40. In both groups the levels appear to be approximately Normally distributed.

To operate a simple diagnostic test based on fasting glucose levels we need to set a cutoff point, C, so that if a patient's fasting glucose level is at least C we say they have diabetes.If it is lower, we say they do not have diabetes. Suppose we use C = 6.9.

1. What is the probability that a diabetic is correctly diagnosed as having diabetes, i.e. what is the sensitivity of the test? (2 pts.)

Area to the Right of P 0.912 (correctly diagnosed)

Area to the Left P 0.088

1. What is the probability that a nondiabetic is correctly diagnosed as not having diabetes, i.e. what is the specificity? (2 pts.)

Area to the Right of P 0.350

Area to the Left of P is 0.649 Suppose we lower the cutoff value to C = 5.6

1. What is the sensitivity now? (2 pts.)

d)What is the specificity now? (2 pts.)

In deciding what C to use, we have to trade off sensitivity for specificity. To do so in a reasonable way, some assessment is required of the relative "costs" of misdiagnosing a diabetic and misdiagnosing a nondiabetic. Suppose we required a 98% sensitivity.

e) What value for the cutoff, C, gives a sensitivity of .98 or 98%? Also find the specificity of the test if this value of C was used. (4 pts.)