Is there any research/study/survey/... that tried to assess the time elapsed between the publication of medical advances and when they start to be used in practice?
Title of this publication speaks it all: The answer is 17 years, what is the question: understanding time lags in translational research (2011). Some quotes:
This process of conversion of basic science to patient benefit is often called ‘translation’
Using different endpoints, different domains and different approaches, Balas and Bohen and Grant et al. both estimate the time lag in health research being 17 years. Wratschko also suggested 17 years as the highest limit for the time taken from drug discovery to commercialization.
Innovative surgical devices have preceded many of the major advances in surgical practice. However, the process by which devices arising from academia find their way to translation remains poorly understood. (...) The probability of a first-in-human at 10 years was 9.8%.
The median time from discovery to recommendation statement was 14.7 years.
There are people trying to lower those lag times, see for example Faster by a power of 10: a PLAN for accelerating national adoption of evidence-based practices (2015):
We propose an ambitious goal: to increase the speed of adoption of evidence-based practices by a power of 10, from 17 years to 1.7 years, and present a 4-step PLAN to achieve this.
So maybe in the future things will be better.