Suppose you had no idea what the odds of winning the lottery are or how to calculate them. You decide to ask strangers to estimate how likely it is to win and find that of the 10 people you asked, one was a lottery winner. You may conclude from this that it is not all that uncommon and start buying thousands of tickets. If you were to do this though, before you know it all of your money would be gone. This is because you were basing your conclusions off of the results of only a couple of people.

Now suppose you get a disease and need to start taking some drug to help cure it. Wouldn’t you want to make sure that the drug was tested on a large enough group to be able to conclude that it truly is the best way to treat whatever disease you have? My research is about calculating the minimum number of people needed in a study to be able to make clear conclusions about what the best way to treat a patient is.

Traditionally, different drugs would be tested on a large group of people, and the drug that worked the best on average on all of the people would be concluded to be the best way to treat all patients. Everyone is different though, and what is best for some people may not be the same as what would work best for you. This has led to the field of personalized medicine where the goal is to find the best technique for treating every individual and not just finding the best way to treat an entire population in general.

We may be also interested in estimating the best way to treat an individual patient over a period of time in which multiple treatments are assigned to the patient. We could create a set of rules to select optimal treatments for individual patients at each time period. This is called a dynamic treatment regime. To estimate a dynamic treatment regime, a specific type of clinical study called a sequential multiple assignment randomized trial (SMART) is commonly used.

The main goal of my research is to find the minimum number of patients that need to be included in a SMART to meet two specific criteria. The first thing we want is to have enough patients in our study to be able to ensure that our estimated dynamic treatment regime is close to the true unknown optimal treatment regime. This criterion is similar to our lottery example where we want to ensure that our estimate for the proportion of lottery tickets that are winners is close to the true unknown proportion of all lottery tickets that are winners. We also want to be able to have enough patients to conclude whether or not using a personalized approach is significantly better than the standard way of treating patients. If we know we can find a sample size that ensures we meet these criteria that is of a reasonably small size, then we know that we can effectively find improved ways to treat patients. This has the potential to greatly improve the way in which patients are treated for many different illnesses.