People in general, and physicians in particular, are not always comfortable with exponential thinking. This is because we live life linearly. We grow older year after year. We learn first to crawl, then walk, then run. We learn to invest month after month to grow our net worth (though it is here that most people learn the value of compounding), and in medicine, we learn step by step, often one patient at a time.
This way of thinking has been at the root of apprenticeship-like medical training. Experience is linear, so is mentorship, and the backbone of health care delivery.
The same might be said of our approach to the natural history of disease. For most illnesses, we speak of progression in stages, and even in the case of infections, we describe phases that progress over time from incubation to prodrome, through illness, decline, and convalescence.
We have learned through bitter experience, however, that many infectious diseases: measles, Ebola, influenza, and COVID-19, for example, spread exponentially. We have also learned of the dangers of something known as exponential growth bias, which is defined as “the pervasive tendency to linearize exponential functions when assessing them intuitively.”
Our public health systems and millions of patients bear the consequences of such misunderstanding.
Exponential growth is usually defined as a process in which change accelerates in proportion to what already exists (the classic J-shaped curve on a graph). In other words, the larger something becomes, the faster it grows. This contrasts with linear growth, whereby a quantity increases at a constant rate over an equal interval of time (the classic straight line on a graph).
In science, medicine, technology, and finance, linear thinking underestimates the acceleration of anything that grows exponentially. At its core, exponential thinking demands attention to rates of change rather than the quantity of change.
Tumor growth presents a humbling illustration. Tumor cells, for example, are known to increase in number in proportion to their existing volume. In pulmonary medicine and oncology, we use tumor doubling time (DT) and volume doubling time (VDT) to assess pulmonary nodules and malignancies. Because malignant growth often follows near-exponential kinetics in its early phases, a lesion that appears small in diameter and stable over a short interval of time may already be progressing along a steep growth curve and doubling in volume.
Failure to appreciate this dynamic reflects a misunderstanding of the difference between linear and exponential growth. This invites complacency and exposes both patients and their health care providers to the risks of delayed diagnostic or therapeutic intervention.
Today, artificial intelligence introduces similar nonlinear dynamics into interventional pulmonology. Navigation systems refine accuracy through iterative learning. Imaging segmentation algorithms improve multiplicatively as datasets expand. Risk stratification models enhance predictive power across tens of thousands of cases. What once required the slow accumulation of individual procedural experiences now crosses continents and health care institutions with the click of a computer mouse.
We must understand that many clinical processes, technological advances, scientific discoveries, and healthcare system failures are not gradual. They often follow a nonlinear curve and accelerate dangerously once a critical threshold is reached. Thinking exponentially helps us recognize these nonlinear dynamics before a crisis appears.
Acting before a threshold is reached, rather than reacting after it has been crossed, is a mark of responsible, ethical, and forward-thinking leadership.
- Berg SH, Lungu DA, Brønnick K, et al. Exponential Growth Bias of Infectious Diseases: Protocol for a Systematic Review. JMIR Res Protoc 2022;24;11(10):e37441. doi: 10.2196/37441.
- Beibei J, Daiwei H, Carlijn M. et al., Lung cancer volume doubling time by computed tomography: A systematic review and meta-analysis. European Journal of Cancer 2024;212:114339. 10.1016/j.ejca.2024.114339.
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