|
|
| Home | Textbook | Newsletter | Discussion Forum | Contact |
 Textbook
|
|
[1] INR Class ProjectCameron Cooper
Ft. Lewis College
In the Spring of 2007, a college algebra professor was diagnosed with advanced
brain cancer. Subsequent to a debulking of the tumor (surgical removal),
radiation treatment, and the initiation of chemotherapy, the professor started
to develop blood clots/pulmonary emboli (PEs). Each PE has an approximate risk
of a 5-10% chance of death. Thus, he was prescribed Coumadin, an anticoagulant
drug, and told that his Coumadin blood level should be between 2.0 -- 3.0 INR
(International Normalized Ratio) units. Below 2.0, he runs the risk of forming
a new clot, and above 3.0, he runs the risk of internal cranial bleed.
An INR level can be determined via either a fingerstick and/or a venipuncture.
For a patient, a fingerstick is obviously preferredoverthe venipuncture for
convenience, damage, and pain purposes. The venipuncture, however, is considered to be the more accurate measurement. In the Fall, the professor received a 4.7 INR level via a fingerstick. Via diagnostic policy at the laboratory, this triggered an automatic venipuncture, which came back as 2.9. He was told to use the venipuncture from that point on, but his veins could only take so much before risking the development of a major clot due to venipuncture damage. Baffled, the professor started to collect ordered pairs (both fingerstick and venipuncture) in an effort to understand better his own INR and to help his doctors gauge his target range on the fingerstick. In 14 visits, the professor collected the following data: Fingerstick Venipuncture (input) (output) 0.0 0.0 4.7 2.9 3.4 2.7 3.7 2.7 3.7 3.3 3.4 2.5 3.2 2.5 2.8 2.24 2.6 1.92 2.8 1.69 3.2 1.85 2.5 1.7 2.2 1.7 3.1 2.08 4.4 3.13
By being proactive, the professor decided to create a predictive model to
determine as closely as possible his own INR from the fingerstick and to make
therapeutic decisions from the model. This would allow him to use the
fingerstick frequently without severe damage per the suggestions of his
doctors. Here are some questions to discuss: 1. Why is this situation dangerous and very bothersome to the professor?
Answer: Different dosing decisions were being made based upon the two
measures. For example, for the first ordered pair, a dosing decision of
discontinuing the Coumadin would be made with a 4.7 INR. On the other hand,
the 2.9 INR would indicate the current dosing is working and to stay on it.
This is a life or death situation. 2. Is this situation a function? Why or why not?
Answer: No, for a given input (i.e. 3.7 INR on a fingerstick), two laboratory
values are being offered via the diagnostic services (i.e., 2.7 and 3.3 for
the 3.7 input). 3. What type of function should be used to predict the venipuncture measure from the fingerstick? If the Fingerstick were perfect, what would the ideal function be?
Answer: This should be a linear relationship. A constant rate of change would
be expected between the two measurements. The ideal function would be Y = X if
the fingerstick were accurate enough. 4. Does this relationship have a meaningful zero?
Answer: Yes, when the INR is zero on the fingerstick machine, it should also
be zero on the venipuncture laboratory machine. 5. Create the model. How good is the model and how much variation is explained?
Answer:
Eighty-seven percent of the variability in the venipuncture measures is
explained by the fingerstick. 6. Provide the professor some guidelines for using the model.
Answer: Using the model, a 2.0 on the venipuncture corresponds to a 2.8 on the
fingerstick. A 3.0 on the venipuncture corresponds to a 4.2 on the
fingerstick. Allowing for some margin of error (a confidence level could be
used here) and per the suggestion of a cardiologist, the professor should
approximately aim for a 3.0 to 4.0 on the fingerstick in regards to dosing
decisions of Coumadin. This approach seemed to provide a reasonable solution
for the professor and his doctors, the cardiologist mentioned earlier in
addition to a pulmonologist and a general practitioner. [2] Trail Mix
Mike wants to sell a Trail Mix at his convenience store. He can buy raisins
for $2.30 per pound, nuts for $4.10 per pound, and pieces of dried fruit for
$3.80 per pound. He wants to make a 50 pound mix of raisins, nuts, and dried
fruit to sell at $3.50 per pound. If he includes three times as many pounds of
raisins as nuts and two times as many pounds of raisins as dried fruit, what
quantities of raisins, nuts, and dried fruit should he use? [3] Where to Meet?
Two brothers, Mike and Jonny, plan to meet for a coffee break on Interstate 84
between Hartford, CT and Newburgh, NY. Mike leaves Hartford at 9:00 AM to
drive toward Newburgh on Interstate 84, 115 miles away. At 9:30 AM Jonny
leaves Newburgh on Interstate 84 to drive to Hartford. If Mike drives at 60
mi/hr and Jonny drives at 65 mi/hr, how far from Newbugh should they plan to
meet? [4] Query
Determine the circumference of a ball such as softball or a basketball. Assume
you placed a band, one inch thick, around the circumference. How much larger
is the outer circumference of the band from the inner circumference? Repeat
the question for a different size ball. Are the results surprising?
Explain. [5] Notices
[6] Pre- and Post-Test in a Refocused College AlgebraDr. Kesler, Mrs. Balakrishnan, Mr. Pontoo
Paine
College
When making curriculum changes, such as changing from a traditional to a
contemporary college algebra course, we are often called upon to demonstrate
the effects on student learning. Pre- and post testing is an effective way of
doing this, along with a comparison of grades and student portfolios. A sample
of such a test prepared by Dr. Kesler, Mrs. Balakrishnan, and Mr. Pontoo of
Paine College is shown on the next two pages. They gave the test during the
first class of this semester (Fall, 2007) and plan to give it (or a similar
version) on the last class of the semester. Although they briefly discussed
the results of the test with their students, they did not return the test to
the students.
Assessing Quantitative Literacy: Pre-Assessment
Directions: Read each problem carefully and give your best response based on
your previous experiences in algebra and some of its implications. The
pre-assessment will be graded but will not count against you or your grade in
this course. Have fun with it! Use the scratch paper to show how you reached
your answer where needed.
* Supported by the National Science Foundation and the U.S. Military Academy. |
|
| Home | Textbook | Newsletter | Discussion Forum | Contact |
