Pharmaceutical companies versus the exponential function

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Rafał Samborski, CEO 16.1.2019 | 6 min read
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A few words on bacteria

Many phenomena in the world around us are described using the exponential function. Take a look at this film showing five hours of a bacterial colony growing, compressed into seven seconds [1].



If we plot a graph of the numbers of these bacteria over time, we get the characteristic shape of the exponential function.



The problem with presenting exponential relationships in this way is that it is difficult to compare growth in the initial and final period. Although over the first 110 minutes, the population of bacteria increased ten-fold: from 1 to 10, it is difficult to observe on an almost flat graph. In cases like this exponential relationships are often presented using a logarithmic scale. On a logarithmic axis we can see the small numbers in the initial phase of the process at the same time as seeing the large numbers of the end of the process. Exponential functions presented using a logarithmic axis typically appear as straight lines.



Transistors as bacteria

As it happens, more than just biological processes are described using exponential relations. In 1965, Gordon Moore, one of the founders of Intel, observed that the number of transistors in a typical integrated circuit doubles every 18 months. This estimation was later corrected, and it is now taken that the number of transistors doubles every 24 months. This progression proved to repeat so reliably that it is now known as Moore’s law. In the graph charted below, which uses a logarithmic axis, you can see how dependably Moore’s law has been working for half a century – the dots show successive generations of processors, and the line shows an exponential trend in the integrated circuits industry. In the lower left corner there is a point indicating the Intel 4004 processor from 1971 that contained two thousand transistors, and in the upper right corner of the chart are products from the last few months containing more than 10 billion transistors.



Eroom’s law

There is also a certain trend in the pharmaceutical industry that is exponential. It relates to the number of new drugs that can be developed for a billion dollars. Unfortunately, in contrast to the exponential functions presented above, this one is declining [2].



The contrast between this trend and Moore’s law described earlier is so clear that it has been called Eroom’s law (“Moore” spelled backwards). If Eroom’s law does not cease to apply (and there is no indication that it will), in little more than a decade the cost of developing a new drug will hit the $10 billion mark.

There are many theories trying to explain the root of this tendency. It is caused by, among others, increasingly stringent regulations. The fact is, however, that the medications that are easiest (and hence cheapest) to develop have already been created. Introducing something significantly better than existing solutions onto the market must be more expensive. As a good analogy, take a coal mine, where the surface-most deposits can be extracted quickly and cheaply. After a few decades, extraction from deposits lying several thousand metres down is expensive; it requires far more advanced technologies, and there is an associated risk of failure.

It is natural, therefore, that pharmaceutical companies look – and will increasingly – for support in industries that have not been affected by Eroom’s law. The technology industry, with ready-made solutions for sensors, communication, remote care and data processing, is an ideal partner here.

Of course, a collision of worlds between technology and pharma companies brings with it challenges, and a need for mutual understanding. Pharmaceutical companies, accustomed as they are to high margins (especially on blockbusters), will have to make compromises here, but they will certainly be very pleasantly surprised by product development times being reduced by orders of magnitude. This process is just beginning, but it’s worth starting to follow it right now.


  1. Aging and Death in an Organism That Reproduces by Morphologically Symmetric Division; Eric J Stewart , Richard Madden, Gregory Paul, François Taddei; PLOS Biology (2005)
  2. Diagnosing the decline in pharmaceutical R&D efficiency; Jack W. Scannell, Alex Blanckley, Helen Boldon & Brian Warrington; Nature Reviews Drug Discovery (2012)