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Analyzing Survival Rates and Risk Factors in Organ Transplants with Mathematica


Estimate the possibility of injury to a transplanted organ by determining the time series of parameters that could change over the years.


Create a program that displays an array of a patient's information such as prescription history and so on allowing the physician to select a treatment option tailored to the patient.


  • Ability to draw a line plot of any parameter of the transplanted organ by typing in the ID number of a patient
  • Viewing the records of a patient tracing back many years with graphs or figures
Dr. Kazuhiro Iwadoh, Tokyo Women's Medical University
"Mathematica turned out to be the inevitable tool to deal with thousands and thousands of patients' data in electronic files. These days I cannot do without it to get on with one job after another."

Kazuhiro Iwadoh is a doctor studying biostatistics at Tokyo Women's Medical University. He has been using Mathematica for more than twenty years for medical research. Currently he is using Mathematica for the analyses of survival rates and risk factors in patients with solid organ transplantations.

Q: When did you first encounter Mathematica?

A: My first encounter with Mathematica was a Mathematica book that I saw at a bookstore in 1989. At that time, I was teaching math at one of the Japanese preparatory schools for university entrance exams, and used to teach algebra, geometry, and calculus. The Mathematica book was at first nothing more than a book for reference. But indeed, it was nothing less than a mathematical "never ending story." Then, I started studying Mathematica by myself on a laptop computer. At that time, we regularly held nationwide mock exams for the university entrance exams. I used Mathematica to draw space figures and presented them beside an explanation for a problem to help students understand it virtually."

Q: Did you use Mathematica for teaching math?

A: Yes. I also employed it in making textbooks for math classes. It was quick and easy in providing results of numerical and symbolic calculations necessary for the jobs at hand.

Q: Did you use Mathematica in any other way?

A: Yes. I teamed up with a group to set up a preparatory school for the the medical licensing national examination. This time, the team was looking for a programmer and asked me whether I could do it. And I said "Yes," although I did not see how much I could contribute to it initially.

Q: Were you able to contribute to the setting up of the prep school for the medical licensing national examination?

A: Yes. Yes. We held the national mock exam for medical students. The exam was multiple-choice style, and it was easy to convert these test results into binary data. Then, I planned to use Mathematica not only for working out the scores and rankings, but also for analyzing the weaknesses and strengths of each student. Although it was the first time for me coding a large program in Mathematica, all I needed to do was to mathematically connect the binary data and the desired output, paying little attention to programming itself. Then the sensing cards of about 8,000 examinees were collected and analyzed with the program developed in Mathematica. The test result of each student with the individualized assessment was printed out on a sheet of paper and distributed to the students all over Japan.

Q: This is very interesting. Did you continue to use Mathematica when you started working as a surgeon at Tokyo Women's Medical University?

A: Yes. But to tell the truth, when I first started working as a surgeon, I thought I would not need Mathematica anymore. But actually just the opposite happened. To analyze the clinical outcomes in large numbers of patients, Mathematica turned out to be the inevitable tool to deal with thousands and thousands of patients' data in electronic files. These days, I cannot do without it to get on with one job after another.

Q: So how do you use Mathematica now?

A: In Japan, we do not have many biostatisticians, and all the patients' records are not utilized effectively even by many doctors. I use Mathematica as a sort of data mining tool, and with a bit of data sorting processes, I can extract useful information that helps us make more effective decisions. With the graphics features of Mathematica, it is also easy to draw a key figure to understand each patient's condition at a glance.

Q: Could you please elaborate?

A: Sure. Each organ in the body contributes to maintain a homeostasis of various parameters in it. Since the transplanted graft is not so stable as one's own organ, time series of each parameter that could change over years is very important in detecting any injury to it. It is, however, almost impossible for a naked eye to have such a bird's-eye view in a minute. But with Mathematica, it is only a few strokes away to get it.

Q: How did you perform the analysis?

A: I have more than 50,000 results of the patients' blood tests that I received in an Excel® file from the laboratory in the hospital. The built-in function Import in Mathematica is wise enough to import and convert an Excel® file into an executable Mathematica file in a moment. I coded a simple program that draws a line plot of any parameter only by typing in the ID number of a patient. At the same time, the program displays an array of the patient's information such as information at surgery, prescription history, and so on. So records of any patient tracing back many years are now visible with graphs or figures. If it were not for Mathematica, I would only be able to trace back the patient's record for a few months with one parameter at a time. But thanks to Mathematica, I can even see multiple results of many patients at a time from the longitudinal perspective. This is advantageous in selecting a treatment option tailored to a patient.

Q: What do you think differentiates Mathematica from other software products such as SAS and SPSS?

A: The concept and framework of the software per se is completely different between Mathematica and such ready-made products. The latter should be good at dealing with standard statistical jobs with complete dataset. The dataset I usually encounter in biostatistics is, however, incomplete and scattered raw data. The first task I face is to process it into a well-arranged dataset that is ready for computation. Mathematica allows you to code any functions to do this kind of job in a few lines, and by applying these functions to the raw data in an interactive fashion you can set up the desired dataset. The second task is to select an appropriate conventional statistical method to analyze the data, or even to propose a novel statistical strategy to attain the desired assessment. The latter can be done only with a formula manipulation language like Mathematica.

Q: What do you expect to do in the future with Mathematica?

A: Doctors in some medical schools are getting free iPads. With patients' medical records available online, Mathematica would enable the iPad to present tables and figures of any patient only by a few touches that summarize all his/her laboratory findings and medical history, like Wolfram|Alpha. This will free doctors from struggling with huge scrolls of electronic medical records.

Q: How would you describe Mathematica in one phrase?

A: It is very easy to not see the forest for the trees. But with Mathematica, you can see the forest and will even be able to find out its vital system.

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