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 | Multi-drug Resistant Human Immunodeficiency Virus (HIV)

HIV and Human Immune response: HIV affects CD-4 and CD-8 cells. CD-4 cells initiate the immune response. CD-8 cells kill infected cells. HIV destroys the human immune system by infecting the CD-4 cells – without CD-4 cells, the human immune system cannot act against infection. First, HIV fuses with a CD-4 cell, and inserts its genetic material into the cell. Then the HIV enzyme reverse transcriptase converts HIV RNA into HIV DNA. Then the HIV enzyme integrase integrates the HIV DNA into the cell’s DNA. The cell then makes copies of the HIV RNA, which is then packaged by the HIV enzyme protease for export outside the cell. HIV medications work by attacking this process. Fusion Inhibitors (FIs) work by inhibiting the fusion of HIV and human cells. If an agent can effectively prevent fusion, replication cannot begin. Reverse Transcriptase Inhibitors (RTIs) work by interfering with the ability of HIV RNA to convert to DNA within human cells. Integrase Inhibitors (IIs) work by inhibiting the integration of HIV DNA into the host cell’s DNA. Protease Inhibitors (PIs) work by inhibiting the breaking of HIV protein long chains into smaller chains. After HIV takes over a cell, that cell manufactures HIV proteins, which are then broken down by protease enzymes into smaller chains, which form the basis for new copies of HIV. Most traditional HIV medications function as either RTIs or PIs, and research continues in the search for effective medications in the FI and II classes. Over time, patients with HIV may develop resistance to one or more HIV medications. Suppose that we have an experimental drug, raltegravir, an integrase inhibitor. We wish to use this medication in patients who are resistant to one or more of the usual drugs. End points for this trial include HIV viral load, Immune function, CD-4 cell count, CD-8 cell count, presence of infections. Sketch a comparative clinical trial for raltegravir + standard HIV therapy versus standard HIV therapy alone for the treatment of patients with HIV who show resistance to one or more of the usual HIV medications. 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 HIV who show resistance to one or more of the usual HIV medications.. Those giving informed consent and who meet appropriate inclusion and exclusion criteria are enrolled in the trial.

Enrolled subjects are randomly assigned to either standard HIV therapy with raltegravir or to standard HIV therapy with placebo_raltegravir. Double-blinding is employed, so that neither the subjects nor the clinical workers know individual treatment status.

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

effectiveness (including HIV viral load, CD4/CD8 cell counts, immune system strength)

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, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 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 – (2*3.7142) ≈ 2.5716[3]

upper2 = m + (2*sd) ≈ 10 + (2*3.7142) ≈ 17.4284[15]

lower3 = m – (3*sd) ≈ 10 – (3*3.7142) ≈ -1.1426[3]

upper3 = m + (3*sd) ≈ 10 + (3*3.7142) ≈ 21.1426[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 3 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 3 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 – p75), (p75 – p50), (p50 – p25) and (p25 – 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 7 or less.

Approximately 50% of the TBI patients in our sample had initial GCS of 12 or less.

Approximately 75% of the TBI patients in our sample had initial GCS of 13 or less.

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

range₄₃ = p₁₀₀ – p₇₅ = 15 – 13 = 2

Approximately 25% 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 quarter sample is 2.

range₃₂ = p₇₅ – p₅₀ = 13 – 12 = 1

Approximately 25% of the TBI patients in our sample had an initial Glasgow Coma Score between 12 and 13. The largest possible difference in initial GCS between any pair of TBI patients in our upper middle quarter sample is 1.

range₂₁ = p₅₀ – p₂₅ = 12 – 7 = 5

Approximately 25% of the TBI patients in our sample had an initial Glasgow Coma Score between 7 and 12. The largest possible difference in initial GCS between any pair of TBI patients in our lower middle quarter sample is 5.

range₁₀ = p₂₅ – p₀ = 7 – 3 = 4

Approximately 25% of the TBI patients in our sample had an initial Glasgow Coma Score between 3 and 7. The largest possible difference in initial GCS between any pair of TBI patients in our lower quarter sample is 4.

Work all four (4) cases.