Key|The
Second Hourly | Math 1107 | Spring 2009 | CJ Alverson
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. Do not write on both sides 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 |
Clinical Trial Sketch | Venous Thromboembolism
Prevention in Glioblastoma multiforme
(http://clinicaltrials.gov/ct2/show/NCT00790452?cond=glioblastoma&rank=4)
Glioma is the general
name for a tumor that arises from the glial tissue,
which supports and nourishes the brain. Glioblastoma multiforme is the most aggressive of the gliomas, a collection of tumors arising from glia(l
cells) or their precursors within the central nervous system. Clinically, gliomas are divided into four grades; unfortunately, the
most aggressive of these, grade 4 or glioblastoma multiforme (GBM), is also the most
common in humans. GBM is typically fatal, with treatment,
patients have a median survival of approximately 12 months, with fewer than 25%
of patients surviving up to 2 years and fewer than 10% of patients surviving up
to 5 years.
Glial cells support the neurons in place as well as
provide insulations. There are five different types of glia(l
cells): astrocyte
- provides physical and nutritional support for neurons, digests part of dead
neurons as well as regulates the extracelullar fluid
around the neuron; microglia -
digests part of dead neurons; oligodendroglia - provides insulation for neurons (myelin); satellate cell - provides physical support for
neurons in Peripheral Nervous System and Schwann
cell - provides insulation for neurons (myelin).
Deep vein thrombosis (DVT) is the formation of a blood clot in one of the deep
veins within the body. In a pulmonary embolism (PE), the
arteries leading from the heart to the lungs become blocked. The process by
which blood clots occur and travel through the veins is known as venous thromboembolism
(VTE), the collective term for DVT and PE. Aspirin (acetylsalicylic acid)
serves as an anticoagulant and may help to prevent VTE by preventing the
formation of blood clots. Sketch a basic
clinical trial for the prevention of VTE in recently (within 16 weeks)
diagnosed GBM patients. Make your sketch concise and complete, following the
style demonstrated in class, in the second hourly and in case study
summaries.
We
recruit patients who have been diagnosed with Gioblastoma
multiforme(GBM)
within the last 16 weeks. Those who are eligible and who give informed consent
are enrolled in our study.
Enrolled
subjects are randomly assigned to either aspirin or to a placebo version of
aspirin. Double blinding is imposed, so that neither the patients nor the
clinical workers know individual treatment assignments.
Treated
subjects are tracked for the occurrence of venous thromboembolism
(VTE), for aspirin-related side effects and for organ toxicity.
Case Two | Descriptive
Statistics | Duchenne Muscular Dystrophy Survival
Time
Duchenne
muscular dystrophy (DMD) is an inherited disorder characterized
by rapidly progressive muscle weakness which starts in the legs and pelvis and
later affects the whole body. Suppose that we follow individuals diagnosed with
DMD from diagnosis until death, noting age at death in months. Consider a
random sample of individuals who were diagnosed with, and died with DMD. Age
at death in months follows below:
34, 50, 75, 80, 85, 97, 100,
112, 120, 123, 127, 143, 150, 156, 161, 169, 173, 177, 179, 184, 185,
186, 189, 190 190, 193, 194, 196, 196, 197, 199, 200,
203, 204, 207, 210, 213, 215, 227, 228 230, 231, 233, 234, 235, 237, 265
Compute
and interpret the following statistics: sample size, p00, p25, p50, p75, p100, (p75 – p25),
(p100 – p25), (p50-p25). Show
complete detail and work for full credit. Follow case study solutions and
sample hourly keys in presenting your solutions.
Numbers
n p00
p25 p50 p75
p100 range41 range31
range21
47 34
143 190 210
265 122 67 47
range41
= p100 – p25 = 265 – 143 = 122
range31
= p75 – p25 = 210 – 143 = 67
range21
= p50– p25 = 190 – 143 = 47
Interpretation
There are 47 patients with Duchenne muscular dystrophy (DMD) in the sample.
The
shortest-lived DMD patient in the sample was aged 34 months at death.
Approximately
25% of the DMD patients in the sample were aged 143 months or less at death.
Approximately
50% of the DMD patients in the sample were aged 190 months or less at death.
Approximately
75% of the DMD patients in the sample were aged 210 months or less at death.
The
longest-lived DMD patient in the sample were aged 265
months at death.
Approximately
75% of the DMD patients in the sample were agedbetween
143 and 265 months at death. The largest difference in age at death between any
pair of DMD patients in the upper three-quarter sample is 122 months.
Approximately
50% of the DMD patients in the sample were aged between 143 and 210 months at
death. The largest difference in age at death between any pair of DMD patients
in the middle half sample is 67 months.
Approximately
25% of the DMD patients in the sample were aged between 143 and 190 months at
death. The largest difference in age at death between any pair of DMD patients
in the lower middle quarter sample is 47 months.
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.
The schools should be selected randomly.
2. A sample survey design employs a
random sample of the United Kingdom (England, Wales, Scotland, and Northern
Ireland) adult subjects (18 years or older, non-institutionalized). The
research objective of the survey is to determine attitudes of Irish* subjects
regarding Birth Control. Assume that the Survey Instrument is written properly
and delivered in an unbiased way. * Ireland is split into two
countries: Northern Ireland and Ireland
The
survey excludes respondents from Northern Ireland, and includes respondents
from non-Irish components of the United Kingdom.
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. A placebo group is also employed for the “mild” cases.
Assignment
to treatment must be random.
4. A clinical
trial of a new Hepatitis C treatment is designed as follows: subjects are
screened for Hepatitis C infection. Those who test positive for Hepatitis
C infection are then told of their status, and are offered treatment for
Hepatitis C at no cost, and are given no further information. Those who accept
the free treatment offer are then randomly assigned to either a Placebo, or to
the New Treatment Plan.
Abuse
of informed consent, denial of treatment and inappropriate use of placebo
Case
Four | Summary Intervals | The Framingham
Heart Study
The
objective of the Framingham Heart Study was to identify the common factors or
characteristics that contribute to Cardiovascular disease (CVD) by following
its development over a long period of time (since 1948) in a large group of participants who had not
yet developed overt symptoms of CVD or suffered a heart attack or stroke. Blood
pressure is a measurement of the force applied to the walls of the arteries as
the heart pumps blood through the body. Blood pressure readings are measured
in millimeters of mercury (mm Hg) and usually given as 2 numbers. The top
number is the systolic blood pressure reading. It represents the maximum
pressure exerted when the heart contracts. The bottom
number is the diastolic blood pressure reading. It represents the pressure in
the arteries when the heart is at rest. A
sample of FHS adult subjects yields the following readings: (top/bottom)
130/70, 175/75, 136/84, 124/84, 144/88,
128/74, 154/90, 160/92, 210/120, 110/75, 166/108, 100/70, 172/110, 160/90,
145/75, 122/84, 162/80, 156/84, 120/65, 128/84, 130/90, 210/110, 110/68,
160/106, 140/90, 132/72, 120/80, 200/100, 165/105, 132/88, 134/84, 152/74,
138/70, 124/74, 122/80, 155/90, 160/100, 120/80, 200/130, 126/86, 150/100,
135/75, 140/78, 142/85, 146/94, 185/90, 166/78, 190/100, 160/80, 140/80,
150/110, 140/84, 130/82, 130/80, 230/124, 128/72, 220/118, 130/80, 165/95,
208/114, 126/80, 140/90, 166/104, 130/70, 130/80, 120/90
Let m denote the
sample mean, and sd the
sample standard deviation. Compute and interpret the intervals
m ± 2sd and m ±
3sd for systolic blood pressure (SBP),
using Tchebysheff’s Inequalities and the Empirical
Rule. Be specific and complete. Show complete detail
and work for full credit. Follow case study solutions and sample hourly keys in
presenting your solutions.
Numbers
Systolic Blood Pressure (SBP)
n m sd lower2
upper2 lower3 upper3
66 148.9
28.39 92.1 205.7 63.7
234.1
Lower2 = m – 2*sd » 148.9 – 2*28.39 » 92.1
Upper2 = m + 2*sd
» 148.9 + 2*28.39 » 205.7
Lower3 = m – 3*sd » 148.9 – 3*28.39 » 63.7
Upper3 = m + 3*sd
» 148.9 + 3*28.39 » 234.1
Interpretation
There
are 66 Framingham Heart Study (FHS) subjects in the sample.
At
least 75% of the FHS subjects in the sample present systolic blood pressure(SBP) between 92.1 and 205.5 mmHg.
At
least 89% of the FHS subjects in the sample present systolic blood pressure(SBP) between 63.7 and 234.1 mmHg.
If the FHS
subjects’ systolic blood pressures cluster symmetrically around a central
value, becoming rare as the distance from the center increases, then:
approximately 95% of the FHS subjects in
the sample present systolic blood pressure(SBP) between 92.1 and 205.5 mmHg and
approximately100%
of the FHS subjects in the sample present systolic blood pressure(SBP)
between 63.7 and 234.1 mmHg.
Numbers
for diastolic blood pressure (DBP)
n m sd lower2
upper2 lower3 upper3
66 88.1
14.72 58.6 117.5 43.9
132.2
Work
all four (4) cases.