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Competition Period
- Held online from April 2, 2024, to September 30, 2024.
Prizes (Awarded via Invoice for Final Solution)
- First Prize: $500 cash, a research internship* (conditional upon solution adoption), spotlight on Ingenii’s LinkedIn & Discord, and a research presentation opportunity.
- Second Prize: $300 cash, spotlight on Ingenii’s LinkedIn & Discord.
- Third Prize: $200 cash, spotlight on Ingenii’s LinkedIn & Discord.
Clinical trial optimization
Assigning subjects to treatment groups is is pivotal in experimental clinical trials for novel drugs. A critical component involves identifying distinct subject cohorts suitable for specific treatments. These cohorts should exhibit maximum similarity based on measurable covariates (or attributes), which influence individual responses to treatment, thus enabling the differentiation of treatment effects from confounding factors.
On average, clinical trials for newly approved drugs incur costs of $1 billion, with a failure rate of 70%. In 2010, global pharmaceutical companies allocated $32.5 billion to conduct clinical trials out of a total research and development expenditure of $46.4 billion. The financial and temporal constraints of this complex process requires accurate patient stratification to enhance the likelihood of success.
Setting
Each patient is associated with
r=3 covariates
wi=(wi1,wi2,wi3) that are relevant for predicting the patient's outcome. There are
n patients in total. The decision maker knows the total number of subjects of the experiment
n and the respective covariates
w=(w1,⋯,wn). The decision maker will assign
k:=N/m subjects to each of
m≥2 treatment groups. In this case, we will consider the scenario where only two groups are used (
m=2).
The binary decision variables are
x={xip∣i=1,⋯,N,p=1,2}, where
xip=1 if patient
i is assigned to group
p, and
xip=0 otherwise.
Objective
The objective of the assignment is to minimize the discrepancy between any two groups in the weighted sum of the first and second moments of the covariates.
That is, the discrepancy is calculated as follows:
d=s=1∑3∣Δμs∣+ρs=1∑3∣Δσss∣+2ρs=1∑3s′=s+1∑3∣Δσss′∣
where
Δμs=n1i=1∑nwis(xi1−xi2),∀s∈{1,2,3}
and
Δσss′=n1i=1∑nwiswis′(xi1−xi2),∀s∈{1,2,3},s′∈{s,