Key | The 2^nd Hourly | Math 1107 | Spring Semester 2011

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 | Descriptive Statistics | Angry Barrels of Monkeys

A company, BarrelCorpÔ manufactures barrels and wishes to ensure the strength and quality of its barrels. Chimpanzees traumatized the company owner as a youth; so the company uses the following test (Angry_Barrel_of_Monkeys_Test) Ô of its barrels: Ten (10) chimpanzees are loaded into the barrel. The chimpanzees are exposed to Angry!Monkey!Gas!ä, an agent guaranteed to drive the chimpanzees to a psychotic rage. The angry, raging, psychotic chimpanzees then destroy the barrel from the inside in an angry, raging, psychotic fashion. The survival time, in minutes, of the barrel is noted. A random sample of BarrelCorpÔ barrels is evaluated using the Angry_Barrel_of_Monkeys_TestÔ, and the survival time in minutes of each barrel is noted. The survival time of each barrel is listed below:

.25, .50, .75, 1, 1, 2, 3, 4, 5, 7, 7, 7.5, 8, 8.3, 8.5, 9, 9.5, 9.75, 10, 12, 12, 14, 23, 25, 27, 28, 28, 29, 29, 30, 31, 31, 31, 31, 32, 32, 32, 34, 34, 35, 36, 37, 38, 39, 40, 41, 42, 51, 53, 54, 56, 57, 58, 62, 65, 70, 75, 77, 80, 85, 90, 98

Compute and interpret the following statistics: sample size, p00, p25, p50, p75, p100, (p100-p75), (p75-p50), (p50-p25).

Numbers

n p00 p25 p50 p75 p100 R43 R32 R21

62 0.25 9 31 42 98 56 11 22

range₄₃ = p₁₀₀ – p₇₅ = 98 – 42 = 56

range₃₂ = p₇₅ – p₅₀ = 42 – 31 = 11

range₂₁ = p₅₀ – p₂₅ = 31 – 9 = 22

Interpretation

There are 62 BarrelCorpÔ barrels in our sample.

The BarrelCorpÔ barrel in our sample with the shortest survival time survived .25 minutes (15 seconds) of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 25% of the BarrelCorpÔ barrels in our sample survived 9 minutes or less of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 50% of the BarrelCorpÔ barrels in our sample survived 31 minutes or less of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 75% of the BarrelCorpÔ barrels in our sample survived 42 minutes or less of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

The BarrelCorpÔ barrel in our sample with the longest survival time survived 98 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure.

Approximately 25% of the BarrelCorpÔ barrels in our sample survived between 42 and 98 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure. The largest possible difference in survival time between any pair of barrels in our upper- quarter sample is 56 minutes.

Approximately 25% of the BarrelCorpÔ barrels in our sample survived between 31 and 42 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure. The largest possible difference in survival time between any pair of barrels in our upper-middle quarter sample is 11 minutes.

Approximately 25% of the BarrelCorpÔ barrels in our sample survived between 9 and 31 minutes of the Angry_Barrel_of_Monkeys_TestÔ prior to failure. The largest possible difference in survival time between any pair of barrels in our lower-middle quarter sample is 22 minutes.

Case Two | Summary Intervals | Pick’s Disease

Pick's disease (Frontotemporal Dementia) is a relatively rare, degenerative brain illness that causes dementia. The first description of the disease was published in 1892 by Arnold Pick. Pick's disease is marked by "Pick bodies", rounded, microscopic structures found within affected cells. Neurons swell, taking on a "ballooned" appearance. Pick's disease is usually sharply confined to the front parts of the brain, particularly the frontal and anterior temporal lobes. The first symptoms of Pick's disease are often personality change, and a decline in function at work and home. Eventually, they enter a terminal vegetative state. Suppose that we identify a random sample of deceased cases of Pick’s Disease – time from initial diagnosis to death is given in years:

0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 ,6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 11, 12, 12, 14, 13, 19.

Let m denote the sample mean spot count, 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.

Numbers

Numbers

lower2 = m – (2*sd) ≈ 6.11594 – (2*3.19253) ≈ -0.26912 [0/Within first year after Dx]

upper2 = m + (2*sd) ≈ 6.11594 + (2*3.19253) ≈ 12.5010

lower3 = m – (3*sd) ≈ 6.11594 – (3*3.19253) ≈ -3.46165 [0/Within first year after Dx]

upper3 = m + (3*sd) ≈ 6.11594 + (3*3.19253) ≈ 15.6935

Interpretation

At least 75% of the Pick’s disease patients in our sample survived 12.5 years or less after diagnosis.

At least 89% of the Pick’s disease patients in our sample survived 15.6 years or less after diagnosis.

If the survival times for Pick’s disease patients cluster symmetrically around a central value, becoming rare as distance from the center increases, then approximately 95% of the Pick’s disease patients in our sample survived 12.5 years or less after diagnosis and approximately 100% of the Pick’s disease patients in our sample survived 15.6 years or less after diagnosis.

Case Three | 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. A sample of college students is needed for a sample survey. The people running the study decide on the

following: they divide the population of colleges and universities into groups based upon enrollment size and whether the college or university is private or public; next, they used judgment to select one school from each group. Then, a random sample of students was selected from each selected school.

Select the schools randomly in the first stage, then randomly sample students within each selected school.

2. In a comparative 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.

If no standard of care for Z exists, the basis for comparison is placebo. If a standard of care for Z exists, then that standard treatment is the basis for comparison – the “standard” treatment is not presented as standard treatment for Z.

3. 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.

4. Sample survey planning is under way to study voter support levels for a proposed (federal) constitutional amendment. The proposal is to randomly sample US resident adults, aged 18 years or older.

Sample registered voters.

Case Four | Clinical Trial Sketch | Malignant Melanoma

Melanin is a natural substance that gives color to hair, skin, and the iris of the eye. It is produced by cells in the skin called melanocytes. Melanoma is cancer based on malignancy of the melanocytes. Melanoma is the rarest and most serious of the skin cancers. Stage III cancers have spread (metastases) beyond the skin to the lymph nodes. The lymphatic system gives access to other parts of the body. Consider patients with stage three melanoma (whose cancer has spread to lymph nodes at the time of diagnosis) who have had recent, successful surgery. These patients are at high risk of recurrent cancer – cancer that returns after initially successful treatment. Ipilimumab acts by stimulating the immune system, allowing a stringer response to emergent cancer cells. However, the drug can cause complications by over-stimulating the immune system, which can lead to auto-immune attacks on the patients organs.

Primary Outcome Measures: Whether post-operative therapy with ipilimumab improves recurrence-free survival (RFS) as compared to placebo.

Secondary Outcome Measures: Whether post-operative therapy with ipilimumab improves overall survival as compared to placebo. Whether post-operative therapy with ipilimumab improves distant metastases-free survival as compared to placebo. Compare drug safety/adverse event profiles between patients receiving ipilimumab and patients receiving placebo. Compare quality of life and quality-of-life-adjusted survival between the two treatment groups.

Safety/Toxicity: Autoimmune response to drug, kidney/liver toxicity, organ damage, death due to these complications.

Sketch a basic clinical trial for Ipilimumab for the prevention of recurrence of high risk stage III melanoma after complete resection in patients with stage three melanoma (whose cancer has spread to lymph nodes at the time of diagnosis) who have had recent, successful surgery. Make your sketch concise and complete, following the style demonstrated in class, in the second hourly and in case study summaries.

Recruit volunteers who have been recently diagnosed with, and then successfully surgically treated for stage three melanoma with high risk of recurrence (whose cancer had spread to lymph nodes at the time of diagnosis). After briefing the volunteers regarding the details, risks and possible benefits of study participation, those qualified volunteers who give informed consent are enrolled in the trial.

Enrolled subjects are randomly assigned to either Ipilimumab or to Placebo_Ipilimumab. Double blinding is employed, so that neither the treated subjects nor their clinical staff know the individual treatment status of any study subject during the study.

Treated subjects are followed for drug safety issues, including kidney, liver and other major organ-related problems or toxicity, including auto-immune related problems. Treated subjects are followed for the recurrence of melanoma, and for time-to-recurrence for those whose melanoma returns. In full detail, track treated subjects for survival status and time for those whose melanoma returns , track the time-to-distant-spread in those whose melanoma returns. Track treated subjects for quality of life.

Work all four (4) cases.