# The Mathematics of Hope

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## “The mean is mean, but the variance is meaner.”

#### I like to use this phrase when I am introducing hypothesis testing to my marketing research students. In marketing research, we often measure the mean or expected value of a variable based on a random sample of respondents, such as “what proportion of the population will buy our new product?” This may or may not bring good news. But the variance is a measure of uncertainty, and if there is a large variance associated with that mean, then we can’t be very certain at all about the final outcome. In my case, the variance wasn’t meaner; it was my only HOPE.

Over a three week period in August to September 2011, I went from thinking that I probably needed more fiber in my diet, to being diagnosed with stage IV colorectal cancer. Stage IV means that the cancer has spread from the initial tumor to a distant organ. I had a tumor in my colon and the cancer had spread to my liver. My wife, Teresa, was with me as the oncologist detailed my condition and the treatment plan: “We’ll have an initial round of chemotherapy and if that goes well, we’ll operate on the liver. If that goes well, then radiation and chemotherapy. And if that goes well, a couple of operations to get at the original tumor, and then some more chemotherapy.”

I asked, “What if the initial chemotherapy doesn’t go ‘well’?” He replied, “Then it doesn’t make much sense to put you through the rest of the plan.”

I was getting a sense that I wasn’t going to like the answers to my questions. “What are my odds?” The probability that I would live five years was not encouraging; my estimated life expectancy was downright discouraging.

Looking at my wife and me, the doctor said, “Tim, I know you teach statistics and you realize that there are variances around those estimates that I just gave you.” My hope was in the variance.

Difficult conversations followed. Decisions had to be made; everyone didn’t need to know every detail about my condition, but some folks needed to know. One of the most difficult moments in my life was telling my parents that I was probably going to die.

I had to inform my colleagues and the administration here at Mendoza of my condition. If everything went well, then I would be having surgeries and chemotherapy treatment and I would be unable to teach my classes during the spring 2012 semester. As a business school professor, I thought it was funny to think about the cost of my treatment and my life expectancy and conclude that I was a negative NPV project! Nonetheless, my department and the Mendoza school were willing to keep investing in me: teaching schedules were rearranged, colleagues offered to cover courses, plans were made for what I would teach once my treatment was done.

I am very blessed. My treatments and surgeries all went well (I only lost about half of my hair!). There were setbacks, infections, allergic reactions, emergency room visits and many nights in the hospital, but I am relatively young and in otherwise good health. There is always someone on the cancer ward who is in worse shape than you. My colleagues in Mendoza supported me every step of the way. Before my last surgery, one of my daughters said wishfully, “Do you think someone will send us another one of those honey-baked hams?” I thought she was getting a little too comfortable with this routine.

In the fall of 2012, I was finishing up my last rounds of chemotherapy and was back in the classroom teaching undergraduate and graduate sections of a new course, Marketing Analytics. I was able to do the research and write the lectures during my treatment. The last round of chemo was more difficult than I thought it would be; I was tired. Nonetheless, I had lived through my first year of treatment and it felt good to be doing something productive again.

It is now a year later, two years after my diagnosis, and I’m still here, beyond the life expectancy I was given initially by my oncologist. As my wife points out, there have been many blessings from my cancer—for instance, friends and family who scheduled long-postponed physicals and colonoscopies (at least one other case of early stage cancer has been detected and treated). I have been overwhelmed by the love and support from my family, friends and colleagues. I have come to appreciate the Mass and celebrating the Eucharist, the communion of believers, in a way that I could not understand before my cancer.

We probably all know someone who has been diagnosed with cancer; we have colleagues here in Mendoza who are living with cancer (and who were especially helpful and supportive of me). More people now survive cancer than perish. However, if you or someone you love receives a rather dire prognosis, know that in the variance of the estimated probabilities and life expectancies, there is hope.

There is always HOPE.