## Abstract

### Background

### Objectives

### Methods

### Results

### Conclusions

## Keywords

## Introduction

*Uptake*is defined, for the purposes of this article, as the number of units of a technology purchased through the health system relating to a specific medical indication, whereas

*diffusion*is defined as the process of uptake growth over time. Both uptake and diffusion can also refer to the presentation of the number of adoptions as a proportion of the number of attainable or desirable adoptions. The phenomenon of experience curves describes the impact of increasing uptake of technologies on price. We performed a literature review of studies citing experience curve literature [

## Methods

### The Experience Curve Model

*N*

_{t}is the cumulative uptake or sales volume up to period

*t*, with ${P}_{{N}_{t}}$ being the price at

*N*

_{t}; ${P}_{{N}_{0}}$ is the price that was set at initial quantity

*N*

_{0}, which is maintained until

*N*

_{t}≥ 2

*N*

_{0};

*α*is the experience curve parameter or the percentage of the technology’s initial price, with 0 <

*α*< 1; and

*β*is the number of times that the initial quantity doubled, with $\beta ={\mathrm{log}}_{2}\left[\frac{{N}_{t}}{{N}_{0}}\right]$. Table 1 provides a definition of all parameters and the equation is graphed with different parameter values in Figure 2 and explained in the Results section.

Parameter | Definition |
---|---|

${P}_{{N}_{t}}$ | Price at cumulative sales volume quantity N_{t} |

α | Experience curve parameter, the proportion of initial price that price is reduced to |

β | Number of times that sales volume quantity doubles |

n | Number of new per-period adoptions |

M | Total number of attainable adoptions |

M* | Number of desirable adoptions |

t | Period of time |

N_{t − 1} | Cumulative number of adoptions up to t − 1 |

p | Coefficient of external influence or innovation |

q | Coefficient of internal influence or imitation |

c_{j} | Costs of intervention j |

e_{j} | Benefits of intervention j |

T^{T1} | Technology life horizon of technology T1 |

δ | Term for discounting |

r | Discounting factor |

NB | Net monetary benefit |

θ | Vector of uncertain parameters |

λ | Willingness-to-pay threshold |

T^{VOI} | VOI time horizon |

*β*, the number of times that the initial quantity had doubled, rather than on time. This highlights the need for another piece of information: technology uptake over time.

### The Uptake Model

*n*(

*t*) is the number of new adoptions in period

*t*, with

*n*(

*t*) ≥ 0,

*t*> 0;

*p*is the coefficient of innovation;

*q*is the coefficient of imitation, with $\frac{q}{p}>1$ to ensure the s-shape [

*M*> 0; and ${N}_{t-1}$ is the cumulative number of adoptions up to

*t*– 1. To our knowledge, restrictions on

*p*and

*q*are not clearly defined in the diffusion curve literature. We found that the model worked best at values of $0<p<0.1\phantom{\rule{.25em}{0ex}}\mathrm{and}\phantom{\rule{.25em}{0ex}}0<q<1$. This model is graphed in Figure 3 and explained further in the Results section.

### The Dynamic Cost-Effectiveness Model

*i*and

*j*, with $c,e\ge 0$.

*t*are now dependent on price and cumulative uptake up to period

*t*through the experience curve model. It is important to note that we consider future incident cohorts in the modeling of future periods. The reason we refer to periods instead of cohorts is because price changes will also affect the first incident cohort in future periods in technologies in which consumption occurs in each period. In some cases, medical devices are associated with one-off costs in the first period, in which case a future period equals a future cohort.

*t*, as a function of price and uptake, and $e(t)\phantom{\rule{.25em}{0ex}}$are effects in each period of time, both summed up over the number of periods up to technology life horizon ${T}^{{T}_{j}}$ and discounted at a discount factor of $\delta =\frac{1}{{(1+r)}^{t}}$ (where

*r*is the discount rate), with $c\left({P}_{{N}_{t}}\right),e\left(t\right)\ge 0,r\ge 0$.

#### The effect of the dynamic model on VOI analysis

*λ*is the willingness-to-pay threshold with $\lambda >0$.

*j*given the uncertain model input parameters

*θ*.

Grimm S, Dixon S, Stevens JW. Are we over-estimating the value of further research? A review of methods used to estimate uptake in population expected value of information analyses. Health Economics and Decision Science (HEDS) discussion papers [Internet]. December 4, 2013. Available from: 〈http://www.shef.ac.uk/polopoly_fs/1.329389!/file/1.pdf〉. [Accessed June 15, 2016].

*j*in period

*t*as a proportion of the desirable number of adoptions ${M}^{\u204e}$, $\delta \pi $ is the discounted affected patient population, and ${T}^{\mathrm{VOI}}$ is the VOI time horizon.

## Application in Illustrative Example

*p*and

*q*available [

*α*= 90%), or perform expert elicitation on this. We explored the effects of different values for diffusion parameters on the shape of the diffusion curve and of the experience curve parameters on the format of price changes.

## Results

*α*in Equation 1) of 80% could reduce future price to less than half of its starting value once 140 adoptions are reached, which in the case study example is at approximately 10 years. An

*α*of 95%, in contrast, would reduce the future price to just more than 80% of its starting value. The effect of different values for diffusion parameters

*p*and

*q*is shown in Figure 3: we used the minimum, maximum, and mean values that resulted from 1000 simulations inverting the elicited quantities to yield parameters

*p*and

*q*, and plotted resulting diffusion curves for parameter

*p*in Figure 3A, holding parameter

*q*constant, and for parameter

*q*in Figure 3B, holding parameter

*p*constant. Both parameters could significantly change the speed of diffusion, which would result in price changes occurring faster or more slowly.

## Discussion

## Conclusions

## References

- Whose costs and benefits? Why economic evaluations should simulate both prevalent and all future incident patient cohorts.
*Med Decis Making.*2010; 30: 426-437 - Historical lifetimes of drugs in England: application to value of information and cost-effectiveness analyses.
*Value Health.*2010; 13: 885-892 - Accounting for the drug life cycle and future drug prices in cost-effectiveness analysis.
*Pharmacoeconomics.*2011; 29: 1-15 - The half-life of truth: what are appropriate time horizons for research decisions?.
*Med Decis Making.*2008; 28: 287-299 - Future drug prices and cost-effectiveness analyses.
*Pharmacoeconomics.*2008; 26: 589-602 - Marketing innovation: medical device prices follow the experience curve.
*J Med Mark.*2007; 7: 203-212 - A dynamic perspective on pharmaceutical competition, drug development and cost effectiveness.
*Health Policy.*2011; 100: 18-24 - Application of the experience curve to price trends in medical devices: implications for product development and marketing strategies.
*J Med Mark.*2008; 8: 241-255 - Diffusion of Innovations. 5th ed. Free Press, New York, NY2003
- Modelling and forecasting the diffusion of innovation—a 25-year review.
*Int J Forecast.*2006; 22: 519-545 - Innovation Health and Wealth, Accelerating Adoption and Diffusion in the NHS.Department of Health, NHS Improvement and Efficiency Directorate, Innovation and Service Improvement, Quarry House - 2N16, Quarry Hill Leeds, West Yorkshire, 2011
- Implementing the findings of health technology assessments. If the CAT got out of the bag, can the TAIL wag the dog?.
*Int J Technol Assess Health Care.*2000; 16: 1-12 - A new product growth model for consumer durables.
*Manage Sci.*1969; 15: 215-227 - Priority setting for research in health care: an application of value of information analysis to glycoprotein IIb/IIIa antagonists in non-ST elevation acute coronary syndrome.
*Int J Technol Assess Health Care.*2006; 22: 379-387 - Minimal modelling approaches to value of information analysis for health research.
*Med Decis Making.*2011; 31: E1-22 Hoomans T, Seidenfeld J, Basu A, Meltzer D. Systematizing the Use of Value of Information Analysis in Prioritizing Systematic Reviews. Rockville, MD: Agency for Healthcare Research and Quality, 2012.

Grimm S, Dixon S, Stevens JW. Are we over-estimating the value of further research? A review of methods used to estimate uptake in population expected value of information analyses. Health Economics and Decision Science (HEDS) discussion papers [Internet]. December 4, 2013. Available from: 〈http://www.shef.ac.uk/polopoly_fs/1.329389!/file/1.pdf〉. [Accessed June 15, 2016].

- Universal cervical-length screening to prevent preterm birth: a cost-effectiveness analysis.
*Ultrasound Obstet Gynecol.*2011; 38: 32-37 - Screening to prevent spontaneous preterm birth: systematic reviews of accuracy and effectiveness literature with economic modelling.
*Health Technol Assess.*2009; 13: 1-627 - Estimating multiparameter partial expected value of perfect information from a probabilistic sensitivity analysis sample: a nonparametric regression approach.
*Med Decis Making.*2014; 34: 311-326 - A meta-analysis of applications of diffusion models.
*J Mark Res.*1990; 27: 70-77 - Forecasting for Biomedical Device Companies: Application of Techniques for a New Neuromonitoring Device.San Jose State University, San Jose, CA2009
- Forecasting the adoption of new medical technology using the Bass model.
*J Health Care Market.*1992; 12: 42-51 - Are the UK systems of innovation and evaluation of medical devices compatible? The role of NICE’s Medical Technologies Evaluation Programme (MTEP).
*Appl Health Econ Health Policy.*2014; 12: 347-357 - Modeling good research practices—overview: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-1.
*Value Health.*2012; 15: 796-803 - The value of implementation and the value of information: combined and uneven development.
*Med Decis Making.*2008; 28: 21-32 - Value of information and value of implementation: application of an analytic framework to inform resource allocation decisions in metastatic hormone-refractory prostate cancer.
*Value Health.*2009; 12: 315-324 - Optimal clinical trial design using value of information methods with imperfect implementation.
*Health Econ.*2010; 19: 549-561

## Article Info

### Publication History

### Identification

### Copyright

### User License

Elsevier user license |## Permitted

### For non-commercial purposes:

- Read, print & download
- Text & data mine
- Translate the article

## Not Permitted

- Reuse portions or extracts from the article in other works
- Redistribute or republish the final article
- Sell or re-use for commercial purposes

Elsevier's open access license policy