Imperfect Information and Drug Diffusion

By Jon Atwell and Martha G. Alatriste Contreras

For this project we investigate the relationship between drug efficacy and the adoption of a new drug in a network structure. We assume that most drug treatments are unable to address all of the underlying causes of a medical condition but nonetheless might still be effective treatments. This less than perfect correspondence is a source of imperfect information in that the drug manufacturers are only able to communicate the efficacy of their drug for a subset of symptoms related to the condition.

Thus, when a person exhibits a condition and desires treatment, he/she lacks full information about the appropriateness of the drug and therefore the potential for side effects. Augmenting publicly available information about the drug are the recommendations of network neighbors. These recommendations are based on successful past experiences, defined as when a person who seeks treatment has more symptoms successfully addressed than the number of side effects they experience.

To pursue this simple setup, we assumed that there exists a list of characteristics with some possible relevance to the condition. One can think of this list as a portion of the genome of individuals. Only a subset of these characteristics or genes are effected by the condition or disease but for the most part drug manufactures don’t know the whole set of characteristics that define the condition. This in turn implies that the new drug may not be fully effective. The efficacy of the drug is a parameter defined in each simulation. We explored scenarios in which the efficacy of the drug varied from 0.6 to 1, meaning that the drug cures 60 percent of the symptoms or all of the symptoms, respectively. This drug has an opportunity to diffuse across a small-world network (Newman variation of the Watts-Strogatz model; 4 neighbors, .1 edge-probability) of either 500 or 1000 potential patients.

In this setting, the new drug will diffuse to new persons if either of the following two conditions are fulfilled: 1) the would-be patients symptoms are very close (Hamming distance <=2) to those of the condition described in the drug manual ; or 2) 20 percent of the would-be patient’s nearest neighbours had a successful experience and recommended the drug and the symptoms presented are close to those pointed out by the drug description (Hamming distance <=4).

We ran the model 50 times for parameter combinations of 500 and 1000 agents and drug efficacy of .60, .75, .9 and 1 (total sample = 400) and analysed the runs for possible relationships between drug efficacy, the number of recommendations and the percentage of the population that successfully used the drug.

First set of results are presented according to the efficacy of the drug. One can observe from the graph below that when the efficacy is low there is a lower percentage of patients successfully treated, and this success relies on recommendation coming from the agent’s nearest neighbours. When the efficacy of the drug increases to 0.75, a combination of efficacy and neighbor recommendations brings about a high percentage of successful treatments. Finally, when the efficacy of the drug is high (0.9 and 1.0), the percentage of patients successfully treated is also high but market penetration is lower because recommendations are far fewer.

Driving this dynamic appears to be the instances of unsuccessful treatments with the drugs of low efficacy. This can be seen in the following graph which plots the ratio of successful to unsuccessful treatments and the percent of the population having been treated. One can see that imperfect information about the appropriateness of the drug encourages experimentation with it as a possible treatment, but more cases are unsuccessful for efficacy of .60. A slightly high efficacy makes use of this tendency toward experimentation but minimizes the number of unsuccessful treatments, thereby making the drug very successful. For very high efficacy, there is little possibility for experimentation and therefore market penetration is far less.

The last graph shows the relationship between the number of side effects and the success of the drug.

There is not a one-to-one trade off between side effects and successful treatment because the more effective drugs still address underlying symptoms while producing side-effects. Drugs with an effectiveness of .75 still produce as many side effects as an effectiveness of .60, but remain more successful in the market.

In conclusion, we observe that there might be an optimal efficacy for drug that is not fully effective. This is because there is a trade-off between the potential for recommendations from neighbors and the rate of successful treatments. This suggests a positive but diminishing rate of return to neighbor recommendations and a positive but diminishing rate of return to drug efficacy, which while stronger than the return to recommendation, suggests an optimal level of drug efficacy for a given recommendation mechanism.

There are obviously limits to such a simple model and fully understanding the dynamics and sensitivity to assumptions would take significant effort. Nonetheless, the basic insight might prove valuable for future studies. Extensions of the model include modeling feedback of successful treatment to medical doctors that prescribe the new drug. This feedback could potentially reinforce the successful treatments and have an effect on the importance of recommendations. This type of model could also be applied to the diffusion of other products where the mechanism of adoption relies on recommendations and proximity to individual characteristics.