Elisa Long, an assistant professor of operations management at the UCLA Anderson School of Management and an expert in probability and statistics, teaches a data and decisions course in Anderson’s full-time M.B.A. program. Her goal, she said, is to distill for students the most relevant information for their business objectives, to “connect the dots” so that they can use statistics and probability directly to solve problems or enhance their work.
Recently, she had a chance to practice the basic principles she imparts to her students when she was invited to write an article for the Washington Post that connects the dots between her victory as a contestant on “The Price Is Right” and her diagnosis and treatment of a rare, aggressive form of breast cancer related to the BRCA1 gene mutation she carries. — Carolyn Gray Anderson from the Anderson school’s blog.
The first roll landed on 5, the number I most dreaded.
I was on “The Price Is Right,” facing elimination in the Dice Game, one of the show’s classics. The rules: Cast four large, red foam dice, one at a time, and guess whether the numbers in the price of a prize — in this case, a 2014 Kia Soul — are higher or lower than the numbers you roll. I knew that guessing “higher” after a 1, 2 or 3 and “lower” after a 4, 5 or 6 correctly identifies each digit with 83 percent probability, resulting in an overall win probability just shy of 50 percent. So when I saw that 5, I should have guessed lower.
But one of the fundamental principles in probability and statistics — a course I teach at UCLA — is Bayes’ Rule, which essentially governs how subjective probabilities are updated as new information becomes available. I modified my default calculations by accounting for all the information I had accumulated from watching past shows and my knowledge (albeit limited) of Korean SUVs. So I put my faith in the number 6, guessing that the car would be worth at least $16,000. For the next three die rolls (a 2, 4 and 5), I returned to the basic strategy.
Finally, host Drew Carey announced the Kia’s actual price: $16,232. Amid audience cheers, he turned to me and smiled. “Congratulations, Elisa! You just won a new car! You are so lucky!”
Indeed, as I had learned two months earlier, I am exceptionally talented at hitting low probabilities. This episode of “The Price Is Right” was a special aimed at raising breast cancer awareness, and I had just been diagnosed, at 33, with a particularly aggressive type of breast cancer known as triple-negative. Would I survive, and how? Numbers, as usual, contained the answer. While they governed countless choices surrounding surgery, chemotherapy and radiation, they had also just won me a new car.
It’s always a bad sign when your cancer is identified by what it is not. My tumor lacked estrogen, progesterone and HER2 receptors, which meant that the modern, targeted therapies that have saved thousands of lives would not help me. Of the 230,000 women who will be diagnosed with breast cancer in the United States this year, 15 percent will face a similar fate.
Although I have no family history of breast cancer, I learned that I carry a BRCA1 mutation, a.k.a. the Angelina Jolie gene. This gene normally helps repair damaged DNA, but its mutated form results in a lifetime 50 to 80 percent chance of breast cancer and a 40 to 50 percent chance of ovarian cancer. Only 1 in 500 women of non-Jewish descent carry a BRCA mutation. To put that in perspective, gaining admission to Harvard is 26 times more likely than carrying my mutation. What’s more, the chance of getting breast cancer by age 33, even with a BRCA mutation, is less than 3 percent. I was on a roll.
As an assistant professor of decisions, operations and technology management, my research focuses on medical decision-making under uncertainty. I previously built mathematical models of the spread of HIV, studied which factors contribute to long stays in the intensive-care unit and evaluated where to optimally locate Ebola treatment centers in West Africa. For years, I have used statistics to help fight diseases that kill millions. Now, I found myself fighting to save a single particular life: my own.
Cancer requires you to quickly make a complex set of decisions, typically with limited, and often conflicting, information. Some oncologists recommend having surgery first; others prefer chemotherapy first, because they learn whether the tumor responds to the poisons before cutting it out. East Coast oncologists often use a chemotherapy agent called Adriamycin, whose colorful nickname, the “red devil,” owes both to its bright appearance and its impact on one’s bowels. West Coasters often prefer a less-toxic platinum-based therapy plus an organic taxane compound. Within two weeks of my diagnosis, I had read more than 100 journal articles on breast cancer, hoping to find some clarity.
Fortunately, I have a great team. My husband and in-house counsel, Keith Chen, is a behavioral economist and fellow UCLA professor. (Our process for deciding whether to order Thai or Chinese takeout usually involves inquiring about each other’s utility function.) My doctors included a medical oncologist, a radiation oncologist, a surgical oncologist, a plastic surgeon and a reproductive gynecologist.
Because of my cancer’s aggressive nature, my oncologist advised that I begin chemotherapy within three weeks, which left barely enough time to try one round of egg harvesting in the hopes of preserving my fertility. Within 24 hours, I began a nightly ritual of injecting hormones to stimulate my ovaries. Ten days later, my doctor harvested 34 eggs that were then fertilized and genetically tested for my BRCA mutation, resulting in seven healthy embryos that are currently stored in a sub-zero vault in Beverly Hills.
My doctors agreed on one thing: Because my chances of facing another breast cancer were extraordinarily high, given my BRCA mutation, I should have a bilateral mastectomy instead of a breast-conserving lumpectomy. My course was set. Now that I had finished calculating the medical odds and was simply waiting for them to play out, I turned my attention to another game of chance, the one broadcast on national television.
Every August, “The Price Is Right” films a breast cancer awareness special, drawing contestants from an audience of patients and survivors. I thought it might be a fun test of my professional methods — and a great distraction from my disease — so I decided to enter. My preparation was nearly as rigorous as my cancer research.
Each chemo round last summer entailed sitting in a recliner for six hours. I liked to imagine that it was the first-class cabin on a transcontinental flight: Armed with my noise-canceling headphones and comfy slippers, I watched hours of TPIR episodes online to familiarize myself with rules and strategies to maximize the probability of winning, all while getting pumped full of poison. Just as breast cancer is a heterogeneous disease, each game on “The Price Is Right” differs in both the chance of winning and the potential payoff. Some games are entirely based on luck; others rely more on skill.
Getting called down from the audience to Contestant’s Row, where a small set of guests vie to get onstage, is, statistically, the hardest part. In a typical audience of 300, nine people are invited to come on down — a 3 percent probability. Because this was a breast cancer special, only patients and survivors were eligible contestants. That increased my odds to 10 or 20 percent, since many audience members were friends and family. But to even become eligible for that pool, you have to hook the producers.
Starting at 8 on the morning of the taping at CBS Television City in Hollywood, a producer interviews everyone in line for the audience for just 60 seconds. This is your moment to shine. You tell them your story, why you would make the ideal contestant. I mentioned that I was a UCLA professor and that I had just completed my third chemo infusion the day before.
When the producers asked what my favorite TPIR game was, I avoided the common mistake of saying Plinko, a popular game in which contestants drop discs down a giant pegboard, watching them bounce around until they ultimately land in a slot with a cash payoff. Minimal skill is required. Instead, I told the producer that I loved Pay the Rent, a newer game with a top prize of $100,000 but few winners. Most contestants play a naive strategy of ranking items from cheapest to most expensive, but with a little foresight, players can significantly increase their chances of winning. The producer seemed to like this explanation.
If you’re one of the lucky few selected for Contestant’s Row, you still have to win your way onto the stage. Each entrant must bid on the price of an item — in my case, three pairs of Miu Miu heels — and whoever bids closest, without going over, wins that item and the opportunity to play a bigger game onstage. Here, there’s a last-mover advantage. It’s better to listen closely to the other bids and avoid playing a dominated strategy. My competitors bid $1,000, $1,200 and $1,302, so instead of bidding somewhere between them, the only reasonable choices were $1, $1,001, $1,201 and $1,303. If you’re the fourth contestant to bid, the strategy of bidding $1 more than the highest bid wins about 54 percent of the time, so with my bid of $1,303, I won (the actual retail price of the shoes was $2,070).
Players who graduate from Contestant’s Row compete individually in one of many contests, some with improbably low odds, such as Pathfinder and Triple Play, and some (if they are played optimally) that are sure wins, such as Now or Then and Cliff Hangers. Whether you win or lose your game, each player then spins the Big Wheel, a roulette-style disc with each slice marking a number. Whoever is closest to spinning 100 (using one or two spins) without going over wins. As the highest winner among the first three contestants, I got to spin last. My prior probability of winning was 36 percent, slightly higher than one-third, because as the final spinner, I could watch my opponents and observe what number was needed to win, reducing the chance that I busted.
The first contestant spun 55, chose to spin again and then got a 25, for a total of 80. The second player spun 40, then 30, so she was eliminated. I needed to spin an 80, 85, 90, 95 or 100 to advance. The probability of achieving this in one spin was 25 percent. If I didn’t make it on the first spin (a probability of 75 percent), then there was also a 25 percent chance that the sum of two spins was between 80 and 100. So my overall probability of winning or tying at this point was 0.25 + (0.75 × 0.25), or approximately 44 percent.
My first spin landed on a 5. (And yes, the wheel is surprisingly heavy!) My second spin was a 75, tying the first player at 80. We then entered a spin-off, earning us each one additional spin. At this point, my chances of winning jumped to 50 percent. The first player spun an impressive 70, so my probability of beating or tying her slumped back to 35 percent. Finally, after riding the Bayesian roller coaster, I squeaked by with a 75. I was on my way to the Showcase Showdown.
This is where the show’s two top wheel-spinners duel it out. Each contestant bids on his or her own showcase of prizes, and whoever bids closest to the actual retail price, without going over, wins. If both contestants over-bid, neither wins. The contestant with the highest winnings from Contestant’s Row and the Big Wheel — in this case, my opponent — chooses whether to bid on the first showcase or pass it to the other contestant.
The first showcase presented a lovely collection of prizes: three Michael Kors handbags, a $5,000 Rodeo Drive shopping spree and limo ride, and a 2014 Volkswagen Beetle. My opponent decided to defer her turn, so I had to place my bid first. Since there is a big second-mover advantage in bidding (you can observe how well your opponent bids), I decided to be aggressive and bid $30,000. An audible gasp from the audience suggested that I had bid too much. The second showcase revealed a trip to Hawaii and a Mazda MX-5 convertible, for which the other contestant bid $22,384.
After the commercial break, Drew Carey asked us each to tell our breast cancer story. He then revealed a price of $36,501 for the trip and convertible, a difference of $14,117. He walked to my lectern, slowly unveiled his notecard and announced an actual retail price of $30,487, a difference of only $487!
My goal in going on “The Price Is Right” was to play the best I possibly could given tremendous uncertainty in the outcome. The same was true for my breast cancer. The stakes were just higher.
Shortly after completing four grueling months of chemotherapy, it was time for my bilateral mastectomy in November. Thankfully, I had achieved a “pathologic complete response,” which meant that the chemo effectively had killed all of the cancer cells prior to surgery. The implications on my prognosis were huge. With a PCR, my three-year survival probability is 94 percent, similar to women without cancer, compared with 68 percent for triple-negative breast cancer without a PCR. For the first time in my life, I had never felt so lucky to be, essentially, average.
These past few months have given me a new understanding of the term “decision fatigue.” Should I choose a traditional mastectomy or one that preserved my nipples? Implants or autologous tissue reconstruction using my own body fat? Saline or silicone? I face a raft of fertility decisions, including whether it’s safe to become pregnant or if I should use a surrogate, when to surgically remove my ovaries, and whether to receive hormone replacement therapy. Should I regularly test my cancer biomarkers, despite the high rate of false positives? Should I abstain from alcohol (a known cancer risk factor) or drink a minimal amount of red wine (with its cardiovascular and antioxidant benefits)?
The delicate dance of balancing the costs and benefits of this seemingly endless list is something I am just beginning to grapple with. Life, like statistics, is about weighing difficult options with unknowable results. The best any of us can do is collect as much intelligence as possible and make informed decisions. (After all, it worked on “The Price Is Right.”) For now, though, the final cure awaits: I plan to drive my new Kia Soul or Volkswagen Beetle to Rodeo Drive, wearing my new Miu Miu pumps and Michael Kors handbags, and indulge in some retail therapy.
