Key|The 2^nd Hourly | Math 1107 | Fall Semester 2010

Protocol

You will use only the following resources: Your individual calculator; individual tool-sheet (one (1) 8.5 by 11 inch sheet), writing utensils, blank paper (provided by me) and this copy of the hourly.

Do not share these resources with anyone else. Show complete detail and work for full credit. Follow case study solutions and sample hourly keys in presenting your solutions.

Work all four cases. Using only one side of the blank sheets provided, present your work. Write on one side only of the sheets provided, and present your work only on these sheets. Do not share information with any other students during this hourly.

When you are finished: Prepare a Cover Sheet: Print your name on an otherwise blank sheet of paper. Then stack your stuff as follows: Cover Sheet (Top), Your Work Sheets, The Test Papers, Your Toolsheet. Then hand all of this in to me.

Sign and Acknowledge: I agree to follow this protocol.

Name (PRINTED) Signature Date

Case One | Design Fault Spot

In each of the following a brief description of a design is presented. Briefly identify faults present in the design. Use the information provided. Be brief and complete.

1.1) The objective of a sample survey is to study the attitudes of urban business owners of the United States regarding federal programs, taxation and spending. A random sample of urban residents is employed in this design. Assume that there are no problems with the wording and delivery of the survey instrument.

The survey must sample the appropriate target population – owners of urban businesses. Not every urban resident owns an urban business, and not urban business owner resides in the city.

1.2) In a comparative clinical trial, treatment methods are compared in the treatment of Condition X, which when left untreated leads to severe complications and possibly death. A new surgical method is compared to a standard surgical method. Study physicians classify subjects by the severity of their disease, and assign only the "moderate" subjects to the new surgical method. Only the "severe" subjects are assigned to the standard surgical method.

Randomly assign subjects to treatment without regard to disease severity.

1.3) A random sample of parents of college/university first-year undergraduate students is surveyed about the study practices of their children. The survey questionnaire was properly written, and the sample of parents randomly and reasonably selected. The parents responded to questions about their children's study habits.

The survey must sample the appropriate target population – first-year undergraduates. The parents need not be a reliable source of information regarding their children’s study habits.

1.4) In a proposed clinical trial, treatment methods are compared in the treatment of Condition Z, which when left untreated leads to severe complications and possibly death. Suppose we have a new candidate treatment, and further suppose that a standard treatment for a similar (but different) disease is available. A comparative clinical trial is proposed that would compare these treatments in patients with condition Z.

Use of the standard treatment(for a different condition) is inappropriate for this trial, unless that treatment also serves as a standard treatment for CZ, or if it is being considered an experimental treatment for CZ. If a standard treatment for CZ is available, use it – otherwise, use a placebo group as a basis for comparison.

Case Two | Clinical Trial Sketch | Medicated Cardiovascular Stents

Coronary Artery Disease: The heart continuously pumps blood enriched with oxygen and vital nutrients through a network of arteries to all parts of the body's tissues. The heart muscle itself needs a plentiful supply of oxygen-rich blood, which is provided through a network of coronary arteries. These arteries carry oxygen-rich blood to the heart's muscular walls (the myocardium). Coronary Artery Disease is the most common cause of heart attacks, which occurs when blood flow to the myocardium is interrupted. Heart attack occurs when blood flow is blocked and tissue death occurs from loss of oxygen, severely damaging the heart. Coronary artery disease is the end result of a complex process commonly called "hardening of the arteries"). This causes blockage of arteries and prevents oxygen-rich blood from reaching the heart.

Angioplasty and Stents: A cardiovascular stent props open clogged heart arteries. During an angioplasty, cardiologists use a balloon to push aside heart disease-causing clogs. The opening created by the action of the inflated balloon frequently re-clogs without further intervention. The use of stents is one form of intervention. Stents, a type of metal scaffolding, may be inserted to help keep the artery from re-clogging. Complications from cardiovascular stents can stem from inflammation, clotting and bleeding due to interactions between the stent (usually metallic), the vascular tissue and blood cells. Medicated stents may reduce some of these complications. One accepted approach is to coat stents with drugs that inhibit blood clotting, for example, heparin coated stents are currently FDA licensed. Another approach involves treating the inflammation near the stent site. If the inflammation can be managed, it is thought that clot formation may be reduced. Consider an anti-inflammatory coated stent. Sirolimus is one such drug. A sirolimus coated stent may help control inflammation, thus fighting a new clog, when the artery slowly absorbs some of the drug.

Sketch a comparative clinical trial for Heparin Coated Stents versus Sirolimus Coated Stents in the treatment of patients with Coronary Artery Disease. Make your sketch concise and complete, following the style demonstrated in class, in the second hourly and in case study summaries.

We recruit subjects with Coronary Artery Disease. Those giving informed consent and who meet appropriate inclusion and exclusion criteria are enrolled in the trial.

Enrolled subjects are randomly assigned to either Heparin Coated Stents or to Sirolimus Coated Stents. Double-blinding is employed, so that neither the subjects nor the clinical workers know individual treatment status.

Treated subjects are followed for toxicity(organ damage, especially kidney/liver),

side effects (including stent-related Complications from cardiovascular stents can stem from inflammation, clotting and bleeding) and

effectiveness (including prevention of recurrence of clogged arteries and subsequent heart attacks)

Case Three | Summary Intervals | Traumatic Brain Injury (TBI) and Glasgow Coma Scale (GCS)

The Glasgow Coma Scale (GCS) is the most widely used system for scoring the level of consciousness of a patient who has had a traumatic brain injury. GCS is based on the patient's best eye-opening, verbal, and motor responses. Each response is scored and then the sum of the three scores is computed. Glasgow Coma Scale Categories: Mild (13-15); Moderate (9-12) and Severe/Coma (3-8). Traumatic brain injury (TBI) is an insult to the brain from an external mechanical force, possibly leading to permanent or temporary impairments of cognitive, physical, and psychosocial functions with an associated diminished or altered state of consciousness. Consider a random sample of patients surviving with TBI, with GCS at initial treatment and diagnosis listed below:

3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15

Let m denote the sample mean, and sd the sample standard deviation. Compute and interpret the intervals

m ± 2sd and m ± 3sd, using Tchebysheff’s Inequalities and the Empirical Rule. Be specific and complete. Show your work, and discuss completely for full credit.

lower2 = m – (2*sd) ≈ 10.84 – (2*3.6497) ≈ 3.5406 [4]

upper2 = m + (2*sd) ≈ 10.84 + (2*3.6497) ≈ 18.1394 [15]

lower3 = m – (3*sd) ≈ 10.84 – (3*3.6497) ≈ -0.1091[3]

upper3 = m + (3*sd) ≈ 10.84 + (3*3.6497) ≈ 21.7891[15]

There are 50 Traumatic Brain Injury(TBI) survivors, each with an initial severity computed as a Glasgow Coma Score (GCS).

At least 75% of the TBI patients in the sample have initial GCS between 4 and 15.

At least 89% of the TBI patients in the sample have initial GCS between 3 and 15.

If the initial GCS severity scores for TBI survivors cluster symmetrically around a central value, becoming rare as distance from the center increases, then:

approximately 95% of the TBI patients in the sample have initial GCS between 4 and 15 and approximately 100% of the TBI patients in the sample have initial GCS between 3 and 15.

Case Four | Descriptive Statistics | Traumatic Brain Injury (TBI) and Glasgow Coma Scale (GCS)

Using the data and context from Case Three, compute and interpret the following statistics: sample size, p00, p25, p50, p75, p100, (p100 – p50), (p75 – p25), (p50 – p00). Be specific and complete. Show your work, and discuss completely for full credit.

There are 50 traumatic brain injury survivors in our sample.

The TBI patient in our sample with most severe initial severity had a Glasgow Coma Score of 3.

Approximately 25% of the TBI patients in our sample had initial GCS of 9 or less.

Approximately 50% of the TBI patients in our sample had initial GCS of 13 or less.

Approximately 75% of the TBI patients in our sample had initial GCS of 14 or less.

The TBI patient in our sample with least severe initial severity had a Glasgow Coma Score of 15.

range₄₂ = p₁₀₀ – p₅₀ = 15 – 13 = 2

Approximately 50% of the TBI patients in our sample had an initial Glasgow Coma Score between 13 and 15. The largest possible difference in initial GCS between any pair of TBI patients in our upper half sample is 2.

range₃₁ = p₇₅ – p₂₅ = 14 – 9 = 5

Approximately 50% of the TBI patients in our sample had an initial Glasgow Coma Score between 9 and 14. The largest possible difference in initial GCS between any pair of TBI patients in our middle half sample is 5.

range₂₀ = p₅₀ – p₀ = 13 – 3 = 10

Approximately 50% of the TBI patients in our sample had an initial Glasgow Coma Score between 3 and 13. The largest possible difference in initial GCS between any pair of TBI patients in our lower half sample is 10.

Work all four (4) cases.