# Using Markov Chains to predict market share for prescription drugs

I wish to understand if the approach I am researching holds up to analytical rigor.

I am planning to use historical data of 4 prescription drugs to forecast the market share of the same 4 drugs some time in the future using Markov Chains.

From the transactional database I have pulled all claims for the 4 drugs of interest.

I have ranked the claims per member from most recent to oldest and pulled claims where rank = 1 & 2 where rank = 1 is the latest claim and rank = 2 is their previous claim. Also the date of the rank = 1 claim is in the month of interest (ensures the most recent data for accuracy purposes).

I then pivot the data to capture the number of claims per drug which went from rank = 2 to rank = 1

An example of the transition counts looks as follows:

   A   B   C   D
A  2   1   0   0
B  0   0   0   0
C  0   0   1   1
D  0   0   0   0


In the example above 2 members who took Drug A (from on L.H.S) at t-1 also took Drug A (to on top) at t0, 1 person who took Drug A at t-1 moved to Drug B at t0 etc.

Probabilities are then calculated across rows from the count values above and represent P (the stochastic matrix)

Then, taking the last claim for all members I then calculated the market share for each drug, this will be used as the x(0)

x0 = [0.2 0.3 0.5]


I then plan to use these two data points to predict what the market share will be for these 4 drugs will be at t+3,4,5,6 etc.

I would be delighted to hear from anyone with detailed knowledge of this approach and if any suggestions/guidance can be offered.

Thanks