# STAT 601 ~ Assignment #2(Due Sunday, February 10 th by 11:59 PM) 75 points Review the following: Lecture Handouts :

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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. (5 pts.)

**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 28 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.)

**6. Diabetes Screening Using Fasting Glucose Levels (12 pts.)**

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 5.31 mole/liter with a standard deviation of 0.58mole/liter. For untreated diabetics the mean is 11.74, and the standard deviation is 3.50. 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 = 6.5.

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

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

Suppose we lower the cutoff value to C = 5.7.

**c)** 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 of C gives a sensitivity of .98 or 98%? How specific is the test when C has this value? (4 pts.)

**7. **Using the article labeled “Parents Diagnosis Dehydration” on the D2L site, answer the following questions using Tables 3 and 4 **(13 pts.)**

For this problem it is important to realize the status of dehydration is known. Some of the children are dehydrated and some are not. The test result is whether the symptom was noted as being present or not by the observer. The observers here are nurses and parents.

a) In Table 4, which two physical signs used by the parents to assess dehydration were the most sensitive? Provide a rationale for your answer.

b) In Table 4, which two physical signs used by the parents to assess dehydration were the most specific? Discuss the meaning of the specificity of these two physical signs.

c) In Table 4, which physical signs of dehydration did the nurses have more true positives than the parents?

d) In Table 4, which physical signs of dehydration did the nurses have more true negatives than the parents?

e) In Table 4, what is the percentage of false negatives for dehydration if the parents reported **Decreased tears**? Please provide the calculations.

f) What does it mean if a screening test is 100% sensitive, as **Decreased tears** was when reported by nurses?

g) What is your interpretation of the specificity of **Ill appearance** as an indicator for clinical dehydration?

h) Were nurses or the parents more sensitive and specific in the reporting of the physical signs of dehydration? Was this an expected finding?

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