Intersections and Digressions of Math and Life

 Thanksgiving is easy. With so much to be thankful for, our feelings of gratitude are readily at hand. Adding to that, Colin had scans only two days before the holiday as the hospital emptied out while families in treatment left for visits home and others avoided check-ups during the holiday week. An impending check-up always creates an air of uncertainty, since that one MRI can potentially set into motion an unknown whirlwind of events and decisions. The issue is related less to the relative likelihood of a problem than it is the awareness that change could lurk just over the horizon.

For the person rushing from appointment to appointment, anxiety is quickly sucked into the undertow created by the overwhelming tide of medical discussions, logistics, and social interactions. The next thing I knew, Dr. Gajjar and I were reviewing the results as one of the nurses played with Colin.

The pictures of Colin’s brain and spine have pretty much been looking the same for a while, which is good. Dr. Gajjar believes that the so-called tumor remnant that cups the brain stem is actually scar tissue, based on subtle changes in the picture (and, of course, the fact that it hasn’t done anything suspicious). We had hoped this to be the case but knew that only time would tell. Tumor can recur even in cases where there is nothing visible left on the scan, but it’s most likely to when there is real residual.

We also discussed where Colin is in the prognostic lifecycle of ependymoma. Dr. Gajjar explained that improvements in treatment have changed the course of the disease but done little to alter the overall very long-term survival rate. As a matter of statistical grouping, children tend to relapse either shortly after treatment or in the zone of long-term survival, say five or six years out. The time range for potential relapse is broad and its length demands longer term follow-up than most brain tumors, but the upshot is that there is a lull between the two periods.

Evidently, Colin has passed beyond the period of early relapse. This is no exact science, especially as Colin did not receive the standard treatment for ependymoma and there was a large gap in time (nearly a year) between diagnosis and radiation. Typically, oncologists start the clock at diagnosis, but is that really valid in this case? Nobody really knows, but apparently the combination of time and consistent scans gave Dr. Gajjar confidence in telling us that Colin is likely to be a long-term survivor (with some chance of relapse).

The Goat Behind the Door

In the old TV game show The Price is Right, winning contestants were able to select a prize from behind a door. There were two fabulous prizes, like a trip to Mexico or a washer-dryer set, and then a goat. I often wondered if people actually got to keep the goat if they wanted to, but they never addressed this and it was clear that the concept was that providing an unappealing prize was much funnier than a goose egg (I mean the number “zero,” not an actual goose egg).

Part of the game was that, after a contestant picked a door, the host would open one of the remaining two doors and show what fabulous prize stood behind it (never the goat, as that would defeat the purpose of this exercise). The contestant was then allowed to switch doors and would typically agonize over it but stick with their original door.

From the standpoint of statistics, this is the wrong decision; changing doors increases the chance of winning a prize, although this intuitively makes no sense. Not being a mathematician, my best explanation for this is that the odds of winning are based on the number of available doors. During the first choosing is one in three, or 33%; the odds of winning during the second choosing is one in two, or 50%.

Although we become very dependent on statistics to inform us on medical decisions, statistics are grossly inappropriate for describing an individual. That said, they remain a useful tool to understand what has happened among a certain cohort and to get a general idea of how to interpret a situation. Dr. Gajjar’s news got me to thinking about the Price is Right game, except with more doors and a second goat.                                                              

I apologize in advance for rounding and oversimplifying quite a bit with the numbers, which I do for the sake of a thought exercise. Before neurosurgeons could more consistently achieve complete resections, the basic long-term survival statistic for ependymoma survival was 50-50. Today, this statistic is more like 75-25, but there is still a significant chunk of kids who end up relapsing but surviving beyond five years.

For the sake of this exercise, I’m going to say that the older statistics include no late relapses (this isn’t true) and take Dr. Gajjar’s statement on survival at face value, meaning that overall survival remains 50-50 (I doubt this is completely true, though it is probably true enough to cause him frustration as a physician).

What this means for the game is that we have four doors and two goats, one representing early relapse and another representing late relapse; this works out to the base rate of 50-50. After the period of early relapse passes, the host, in this case Dr. Gajjar, opens a door and reveals a goat that we did not win.

The early relapse goat is now scampering around in the parking lot, leaving the late relapse goat concealed behind his door, munching on tin cans or vulnerable set pieces. What we have left is three doors and that single goat, which represents different, more favorable, odds than we started out with.

Just a Numbers Game

As I say, the math on survival statistics in this exercise isn’t particularly useful, but it illustrates the point that, although the shadow of ependymoma lingers indefinitely, its volume decreases over time. In family support groups, people sometimes bring up the issue of statistics and which ones are accurate.

When statistics are based on scientific studies, they are all accurate, within their own contexts. These figures are useful for understanding relativity but they are poor are describing the absolute because there is no absolute.

Even a seemingly discrete detail can have a significant gray area, such as the question of whether a patient has a “complete resection” or not. Different institutions may interpret one situation in different ways, and it is only through greater experience, education, and professional interaction/publication that these issues get resolved.

The matter of pathology and tumor grading remains extremely controversial for ependymoma because this is not a homogenous disease and the conclusions are based on what samples the pathologist ends up with. Only recently is there a push among pathologists to call an ependymoma with any aggressive features grade III, even if it primarily appears to be a grade II. Furthermore, with a complete resection and treatment, there is little difference in prognosis between the two gradings when the tumor is completely removed, followed by radiation.

Add to this the fact that surgical techniques and technology are changing and treatment protocols have evolved through the year and it is clear how statistics can be confusing. Even today, treatment for a child under three with ependymoma varies considerably depending on the institution and region. Some oncologists are so assiduous at avoiding radiation that they counsel families to go through chemo, sometimes for years, in order to push radiation out to age three. Unfortunately, this also increases the risk of relapse and the need for subsequent surgery before eventual curative treatment.

Of course, the basic problem comes down to the fact that scientists and patient families use statistics for different purposes. Scientists must leverage statistics in order to understand what measures constitute noteworthy improvements or risks, whether that is in the form of a treatment protocol, a surgical technique, or something more subtle. Patient families, however, have no use for the statistics per se but are only concerned with getting a better handle on the outcome of an individual.

Today, faced with Dr. Gajjar’s proclamation that Colin has passed beyond the realm of early relapse, we can use the statistics to validate our sense that Colin is, if not out of the woods, closer to the edge.

Brown Christmas

After all of the drama that came with the pre-Halloween snow storm, we haven’t had any snow since. This meant for some very serious problems for Colin, who came to the belief that Santa would only come if there was snow.

At the same age, Aidan peppered us with questions about how Santa could come down the chimney without getting burned to cinders and how it could be logistically possible for him to traverse the globe and deliver presents in a single evening. Colin is the opposite, with his questions centering around the North Pole and how we can get there to visit.

Colin accepts the presence of multifarious store Santas with a vague understanding that they are representatives of the jolly elf, embracing the present delivering myth with eye gleaming wonder. In anticipation of the big night, he chattered on endlessly, expressing passionate disappointment once Christmas itself had passed. “I want Christmas to come back!”

One of the joys of parenthood is to watch our children become themselves. Over the last few months, Colin’s expressive speech has increased tremendously, and we relish catching glimpses into his interpretation of the world. He is frustrated by the barrier his strangled articulation puts between us, but he continues to make progress and the window into the intricate inner workings of his mind opens wider every day.

Downshifting

Medically, Colin has been pretty stable, but this season has been a grueling one for illness, despite (perhaps because of) the mild winter. After another bout with a respiratory ailment at the beginning of December, we decided to take Colin out of the Head Start program. While it reaped some obvious benefits for him, the long day was very fatiguing and the additional 18 children represented an unacceptable risk of infectious disease exposure.

Colin, whose battery had been running low before the holidays, has perked up with the new schedule. He just doesn’t have the endurance of other kids, and we often find him to be tired. Sometime this spring, we will follow up with a sleep study for him to determine if he has central sleep apnea, which can cause fatigue. We don’t have any particular reason to suspect apnea, but with his history, the chance of having it is higher than usual. With all of his endocrine labs in normal limits, we doubt that this is related to insufficient hormone production.

All in all, we’re all adjusting to the normalcy of our abnormal situation. Colin met one of the milestones we had set out for him: he walked by himself to Santa, several times. We had been coaching him about this goal for months ahead of time, so he knew what was expected of him and happily if tentatively breeched the gap between his parents and a strange man beckoning him to sit on his lap.

On that note, Aidan’s longstanding dread of Santa (when he was young, he would howl in fear when we neared Stew Leonard’s Santa) has reached a petulant crescendo. In those photos where he appears with his brother and the jolly elf, he makes an unpleasant face. This, I soon discovered, was not an autonomic reaction to the situation but a planned response.

After one Santa encounter, which we gravitate to because of Colin, Aidan said, “I’m so glad I didn’t have to sit on his lap!” I have since told him to avoid the whole thing entirely. When a helpful elf beckons a “shy” Aidan forward, I silently mouth, “He knows” to get them off the scent, and the boy gets to remain a spectator. I can’t say I’m exactly unhappy about Aidan’s instincts regarding these Santa impersonators, which he fully knows to be just men in a red suit.

Ditching the Diapers?

Colin may believe in Santa until he’s 30, though hopefully he will be potty trained by then. We have made halting progress, starting more than two years ago when he completed high-dose chemo. At that point, he could hold his torso well enough to feasibly put him on the toilet (fully supported, of course), so I tried to get him used to that idea, though that project was a complete failure for a long time.

The whole process has been in fits and starts, probably accelerated by a gift from Santa of a bag of M&Ms destined to be potty rewards. Yes, we’ve moved to a completely candy-based incentive system. First, one candy per unit of production. Now, we give bonus points (two M&Ms!) if he tells us he has to go. In an intermediate phase, he got one if he simply admitted when asked, but he doesn’t get compensated for that any more.

We had a hallmark moment recently when he exclaimed he had to use the potty and successfully made it in time to deliver a package I was pleased not to have smeared inside a pull-up. However, we mostly tend to catch him based on the expression on his face – even Aidan helps us identify critical moments.

Oddly enough, Colin is completely continent to urine overnight, so we allow him to sleep in regular underwear. It’s awfully cute and, since I put him in the underwear after his bath, this also necessitates a pre-bed pee, which he happy obliges with, and he is quite cooperative any time you sit him down. The only hurdle right now is getting him to tell us. In the horserace between independent walking and potty training, I’m going to guess that the potty training is taking the lead, but I’m definitely not disappointed.

At one point, someone from the school informed me that there is a legal accommodation for schoolchildren who are incontinent, so that can never prevent him from participating in a classroom. I found both comfort and distress at this news, hoping that our own issues would be resolved before he enters school. For a while, we were starting to worry that there was some kind of neurological impediment to potty training, but that now seems not to be the case. Phew!

The Lucky Ones

People who hear our story often express great sympathy about our plight. I’ve said it before and I’ll say it again, but we’re the lucky ones. Colin’s story was featured in a video playing in some Thanks and Giving corporate partners over the holidays (Pottery Barn, Brooks Brothers, and probably others we don’t know about).

We knew about it but were still surprised to see our own faces on a little screen near the register, Colin being pathetic and cute, depending on which part of the video you see. This new piece features footage taken last fall where he is using his walker and taking a few independent steps, both big milestones for our miracle child.

People’s response to the video is visceral, especially those who work in the store and have gotten to know us through slices of images. As much as they want to share their bottled up compassion with us, we want to redirect it to those who are still in need, families who are newly diagnosed, in the middle of treatment, or have no options left.

There are no two ways of cutting it: we are very lucky he is still with us today, a joyful and loving child whose prospects are looking up. There are so many families that have not been as fortunate, and we have seen many cases turn the wrong way. Too many of our friends now live with a huge gap in their lives, birthdays and other milestones slipping by populated by ghosts.

Another World

When I go to New York for work, I trundle through the bowels of Grand Central Station like so many other commuters. I marvel at the silent barrage of wall and floor advertising, generally vending luxury goods to the streams of highly paid eyeballs that flow through the echoing marble halls. The glossy pictures instruct me that women swoon in jewelry-induced bliss, transported by glittering treasure in a pale blue bag.

The images don’t move me, or at least it’s fair to say they don’t touch me in the intended manner. Putting aside the fact that I am nowhere near the bull’s eye of the target market represented by the walls of Grand Central Station’s Northeast Corridor, I am only reminded of the infinitely more rare treasure I have at home.

It is difficult to convey the heartbreaking cuteness of Colin’s face compressed into a smile. “I missed you, Mom,” he says affectionately, curling around one of my arms. His solid little body is innately adept at tucking itself into my contours when I hold him and he presses a fat cheek against mine.

How can a diamond possibly compete with that? Yes, diamond is a substance with special properties forged in unimaginable pressure, yet it can also be recreated in a lab. Every day, I marvel at the two utterly unique beings (made largely of the same substance as diamonds, carbon) who have sprung from the invisible alchemy of two other utterly unique beings.

I could not have invented a person as interesting as Aidan. Before Colin came along, he alone was enough to satisfy us, yet it’s impossible to imagine – or, more accurately, possible but horrifying – our unit minus one. It was easy to contemplate life plugging along as it had been with our little triad. In knowing him, Colin has become indispensable, like his brother before him.

In math, three equals one minus four. Not so in life. Every day is a miracle, whether you realize it or not. Crappy things may keep raining down, but the treasures still shine through, as long as the math still works out.