You need to replicate the simulations discussed in the paper for scenarios A, B and C only (see attachment). Once you understand the algorithm, the R code is actually simple (you can use any built-in functions in R), not more than 300 lines (this is an overestimation). You need to submit your R code, and a 3-page typed report that describes:

How to use your R code

An example of running your script or calling your function

A table to summarize the simulation results as described in the paper.

What is the recommended dose combination

Additional Notes:

How do we simulate the response of a patient? Consider scenario A. Suppose it is decided that the patient will receive dose combination (2,4). This combination has a probability of 0.26 of causing a dose-limiting toxicity (DLT), and 0.74 of no DLT. Therefore, the response of the patient is a Bernoulli random variable with success probability 0.26, where success means there is a DLT. Simulating the response of a patient then requires the simulation of a realization of Bernoulli(0.26) random variable.

Notes to help:

Find starting dose then apply to patient bayesian.

Initially assign dose randomly, no bayesian involved.

Keep track of patients that survived and died.

Stop when toxicity, this is starting dose.
1.use prior
2. use cost

simulated according prior entries, 2 simulations total. Prior will get updated.

Every patient used give only one dose

Random escalation

Update posterior matrix based on toxicity, pij will be recalculated.

Bayesian estimate while trying to find best dose combo.

Every updated matrix will be the prior for the next one.

Attachment:- Assignment.zip