Michael Wallace breaks down assumptions

Monday, June 3, 2019

In his second year of undergraduate studies at the University of Cambridge, Michael Wallace realized that statistics are everywhere when he discovered SIGNIFICANCE magazine. He’s since written a number of articles for the magazine as he believes in helping everyone understand statistics and the importance of the subject in our lives.

Michael WallaceHe began his post-secondary education thinking that he wanted to study pure mathematics, but his attention turned to statistics because he saw the practical applications. While much of his work is theoretical in the field of biostatistics, working with a lot of equations, Wallace is motivated by real-world questions that we are looking to answer.

While completing his PhD at the London School of Hygiene and Tropical Medicine, Wallace put his theoretical education to work with eye doctors at the University of London. Researchers there were completing a study with patients living with amblyopia, a condition where one eye experiences worse vision than the other. Common treatment includes the use of an eye patch over the good eye to retrain the bad eye through use. In this particular study, the eye patch gathered data.

This practical work taught Wallace about the importance of communication. This included learning how to ask the right questions (even if you think one may sound foolish), being prepared to admit that you don’t know what someone means, and being tactful. Helping the physicians – who are not statisticians – quickly understand complex ideas, such as measurement error, was very important. For example, although an eye doctor assesses your eyesight using an eye chart, measurement error may occur if a patient, unsure of a letter, manages to guess it correctly rather than acknowledge that they cannot see it clearly.

Measurement error became a major area of focus of Wallace’s work starting with his PhD thesis. Wallace looks at what might happen if measurement error is present, but not accounted for in statistical analysis. This could lead to incorrect decisions, or even the conclusion that an effective treatment is viewed as harmful. This is important in personalized medicine where health practitioners look to identify the right treatment for an individual, and not a broad population.

“There is a huge amount of data in statistics available in health,” said Wallace. “When you have a large group of patients responding to treatment, personalized medicine will look at why one group of patients responded a certain way, while another group of patients had a different response. When you look at the differences between groups of patients like this, it can be a complicated statistical problem.”

Michael Wallace - Writing on BlackboardA particular challenge Wallace highlighted is in the observational data, such as from hospital records or other scenarios where the statistician has little control over which patients receive which treatments. When health practitioners are trying to determine what treatment to give patients, they will look at data such as your age and symptoms. Often their decision will be based on these properties, which can make things harder for statisticians.

Take for example, two options for treatment. One is more aggressive and expensive, so they prescribe that treatment for patients with more severe symptoms. In the end, those patients don’t fare very well, but is it the treatment, or because their symptoms were so severe? People start to draw correlations, but causation isn’t always there.

Wallace often thinks about the assumptions that people make about data. For example, it’s common to assume that patients in a study are ‘independent’, so if one patient receives a treatment it won’t affect how well another patient in the study fares. Often such an assumption is violated, however, if patients are related or share a hospital ward. We have to consider what happens if our assumptions are wrong because this is what happens in the real world. 

Recognizing and understanding that statistics are much more important than people realize, is one of the key concepts Wallace introduces when he teaches statistics courses at the undergraduate level. He talks to students about the idea of causality and how you can build up networks of cause and effects, and then picks apart a set of variables and the consequences of assumptions we make.

"Data are everywhere, and inform many aspects of our lives. From personal choices such as diet and exercise, to more broad issues like where our governments spend money. Statistics are - or at least should be - at the basis of our decision making.” said Wallace. “It’s essential that we are equipped to understand them."

Michael Wallace