Innovative cardiological technologies: a model of technology adoption, diffusion and competition

Abstract

Technology diffusion of medical innovations is a complex evolutionary process. The specificities on the demand as well as on the supply side have a crucial impact on their diffusion paths. This paper aims to investigate the diffusion process of two competing innovative technologies in the health care sector. The case of percutaneous aortic valve replacement in heart medicine serves as an example. A simple model illustrates the decision-making process of adopters and suppliers that shape the evolution of a new market. Thereby, network externalities and individual learning bias the market outcome such as increasing returns to adoption and may lead to technological ‘lock-ins’.

Keywords:

• technological change
• adoption decisions
• diffusion processes
• competing technologies
• network externalities
• medical equipment

Acknowledgements

We want to thank Uwe Cantner for a continuous discussion and helpful comments. Furthermore, we thank Stan Metcalfe, Andrea Mina, Davide Consoli and two unknown referees for helping to improve our paper. Of course, the responsibility for the contents of this paper remains with the authors.

Notes

Percuaneous transluminal coronary angioplasty (PTCA) was one of the major breakthroughs in cardiology. Before those days an open heart operation was necessary in order to lay a by-pass that replaced the stenosed coronary heart valve. With a transcatheter procedure, the coronary vessel can be reopened safely, pain reducing and without a heart–lung machine.

Glaucoma is a disease that gradually reduces the field of vision and eventually may even lead to blindness.

Consoli et al. (2005) address this issue in detail.

In greater detail, we define a threshold parameter L between zero and one, before drawing pseudo-random numbers for each agent a _i who decided to adopt V (). If the random number exceeds the defined threshold, a _i immediately adopts technology V. Otherwise, actual adoption is postponed for at least another period since the decision process will then be repeated.

The parameters and initial values for the illustrated diffusion process are as follows: N=300, θ _i random numbers drawn from uniform distribution (range from 0 to 100); T=97; μ _i random numbers drawn from normal distribution with and standard . Inertia parameter L=0.75 indicating that the probability to finally adopt V after deciding for it in Equation (1) () is 25% for each actor. Furthermore, the setting of θ _i and T means that the share of early adopters in t=1 is around 3%. Finally, one has to point out that Figure 1 does not reflect the results of a single simulation run, but the average values of 100 different runs to – at least partly – account for random events.

In equilibrium a firm could only determine one parameter because of the other being endogenous.

For modeling reasons, we use this simplifying assumption on the coordination of demand and supply. Concerning the evolution of demand see Greenhalgh et al. (2004) for a detailed discussion. Moreover, Antonelli (2006) shows how the process of creative adoption drives technology diffusion.

See Arro (1962) and Jovanovic and Nyarko (1996) for further details on individual learning curve effects.

This price-cost relation is a rough approximation since the reimbursement procedure hospitals receives for a conventional heart valve implementation, which serves as an upper boundary of pricing, are about five times higher than the expected production costs for one unit of the innovative technology.

On average the market share of technology version D was 50.13% when market saturation was reached. At maximum D captured 58.66% of the market, while its lowest market share observed in our 100 simulations was about 42.33%; standard deviation among the market share distributions of D amounted to 3.89% points.

The precise average value for the market share of D over 100 simulation runs is 79.37%, the minimum value was 71% and the maximum could be found at 85.33%. The distribution of market shares was narrower in this case compared to our initial setting, since the standard deviation decreased to 2.86% points.

These observations are of course heavily dependent on the distribution of preferences among our set of potential technology adopters. When shifting the preference even stronger towards D (e.g. ρ ^D =30 vs. ρ ^E =10) technology version E almost completely drops out of the market with even lower increases of δ. But since still some agents opt for E instead of D until δ crosses a certain threshold (comparable to the one above) relatively strong preferences for E might still be enough to forgo possible benefits the alternative technology may reveal due to network effects.

For the different levels of δ at 0.5%, 0.25% and 0.1% we obtain average market shares for D of 76.87%, 75.76% and 75.12%, respectively.

The maximum difference between D and E remains slightly below 1.5 price units and accounts for only 0.3% of the price actually charged in the respective period.

Simulation runs with β at 0.10, 0.20 and 0.50 led to temporary price differences at most of 3.0, 5.8 and 13.6%, respectively. Expressed in price units this means that prices for D were at most 15–72 units bigger than those of E. The consequential loss in market shares for D was nevertheless not bigger than 1.55% points.

For the sake of clarity we dropped the supply curves here. The supply evolves again similarly to demand, only shifted a bit to the right.

On average D obtained a market share of 54.5%, while standard deviation among these market shares was very low amounting to only 1.06% points, indicating that randomness became less important in the simulation runs.

The prices for commodity D are for more than 10 periods at least 200 price units higher than for the competing technology version.

On average D holds a market share of almost 80%. As the variance among the market shares for D is in this setting almost as high as in our basic scenario, we could find the maximum market share within our 100 simulation runs at 87% and the minimum share slightly below 72%.

The reason for this observation is simply the existence of a minimum pricing level equal to marginal costs which also constitutes a maximum for the divergence in prices between D and E.

Given 100 simulation runs; about two thirds out of 300 agents choose on average technology version D in the final period.

However, a scenario resulting in a final market share of 100% for one of the firms can – under the current parameter setting – only be achieved when the price charged by the competing supplier is at least more than 60 times higher. Therefore, this is a rather hypothetical situation.