Last day of stats lessons!? Maybe? At least, this’ll be the last time I try explaining one of the algorithms. Today’s focus was on multistage regimes (quite the party) and concerned the new variable H for history of treatments a patient receives. Here’s the equation:
Remember:
- Y = outcome
- X = patient characteristics
- Q = quality, or type of function
- A = treatment
- A bar = sequence of A
- E = expected outcome
- ∏ = product operator
- t = time
- T = subscript just to indicate transposing of data to fit the code
Dr. Laber explained how this function defines a potential outcome under some regime [Y*(pi)] as a summation of all “a” values within the function defined by the sequence of treatments received. Then this is multiplied by the product operator acting from t = 1 where the regime at some t value by the sequence of “a” treatments with the history of such treatments before the trial took place. Ultimately, the entire right side of the equation can be negated if the sequence provides a 0 or all 1s. Woohoo! The final equation below just explains that the expected outcome of an optimal pi regime must have a greater or equal utility value that any other outcome (making it the most favorable). My parents said I’d better want to be a stats major after all this, and I’m starting to agree.
In the second part of the day, Suki and I worked in the BOM and helped design levels for a new board game – Boredoom. Based off a board game and the word “boredom” due to the tediousness of creating it, the game has a 3D printed goat trying to evade rotating trees that (in theory) shoot pine needles on a classic chess board layout. While Louie was off having the board be carved out of wood, Suki and I were planning out 12 different levels, annotating the correct move set, and transcribing it to sheets of paper. It was both arduous and exasperating to keep track of all the pieces, but we’re happy to be helping the Laber Labs team. Plus, we’ll be featured in the credits!
