Cancer is a common but very heterogeneous disease. If there is such a thing as a “war” on cancer, it seems to be an attritional campaign of hand-to-hand battles along a vast front, while scientists work behind the scenes to find the fabled “silver bullet.”

Global cancer incidence is rising. Some projections suggest a rise of more than 30% between 2019 and 2030 (Zhao et al., 2023), with modifiable risk factors including diet, alcohol consumption, and obesity playing a substantial role; indeed, nearly half of cancer deaths have been attributed to such factors (GBD 2019 Cancer Risk Factors Collaborators, 2022). Early-onset cancers (in persons under age 50 years) are a particular concern and remain poorly understood; a recent study in England points again to obesity as a significant risk factor (Garcia-Closas et al., 2026), likely reflecting a combination of behavioral, environmental, and diagnostic factors. Drivers of cancer also appear to vary by region; in countries such as South Korea, population aging is a primary contributor to increasing cancer burden, while in others, such as parts of Africa, lifestyle and environmental risk factors are increasingly implicated (Austin, 2026).

Cancer mortality is equally heterogeneous, with five-year survival ranging from around 5% in pancreatic carcinoma (Cancer Research UK, 2026b) to almost 90% in breast cancer in England (Cancer Research UK, 2026a). There have been some successes; cancer mortality has been declining in some countries, including the US (Shiels et al., 2023), reflecting improvements in screening and treatment.

Overall, these observations mark a growing appreciation of underlying complexity. Interpreting them is complicated by two opposing forces operating across different ages, geographies, and stages of development. On the one hand, advances in medicine have progressively eliminated or deferred competing causes of death, effectively unmasking cancer as a natural cause of death at older ages – a competing risks phenomenon. On the other hand, new lifestyle and environmental exposures may be accelerating cancer onset in younger populations by introducing physiological drivers – a challenge of a fundamentally different, public health character. Disentangling these mechanisms is essential for understanding why cancer burdens are shifting in ways that aggregate statistics alone cannot easily explain.

This epidemiological complexity – marked by diverging trends in incidence and mortality, heterogeneous risk profiles, and rapidly evolving treatment landscapes – underscores the importance of robust modeling frameworks and motivates engagement from a range of disciplines. Cancer risk means different things to different professionals. To an actuary, it is a quantity to be priced and reserved against; to an oncologist, it is a challenge to be minimized through the best available treatment; to a public health expert, it is a signal of population-level burden requiring intervention. These differing objectives bring with them different presumptions, jargon, and research traditions – a communication challenge recognized explicitly when the Institute and Faculty of Actuaries established a mortality working group some two decades ago, with the aim of surfacing how divergent professional viewpoints shape modeling assumptions (Macdonald, Reference Macdonald2009). Despite these differing objectives, all three perspectives rely on a common set of statistical modeling frameworks to understand and project cancer dynamics – and bridging across them remains as important today as it was then.

Nonparametric approaches, most notably the Kaplan–Meier estimator (Kaplan & Meier, Reference Kaplan and Meier1958), remain a cornerstone for estimating survival functions without imposing strong structural assumptions. When the focus shifts to understanding the role of risk factors, semi-parametric models – particularly the Cox proportional hazards model (Cox, Reference Cox1972) – become central, allowing for covariate effects to be quantified while preserving flexibility in the underlying hazard structure. It is worth noting that these methods are widely used because they often work well, but also because they are familiar – a distinction that could matter when assessing how robustly modeling conclusions translate across different settings.

Translating such evidence into actuarial applications often requires a more structured representation of disease progression and competing risks. In this setting, multi-state models provide a natural framework for capturing transitions between health states. A canonical example is the three-state (healthy-ill-dead) Markov model (Sverdrup, 1965; Hoem, 1988). Many variants of this have been applied in cancer insurance pricing, while extensions to four-state frameworks incorporating cause-specific mortality have been explored in the context of critical illness insurance (Baione & Levantesi, Reference Baione and Levantesi2018; Reynolds & Faye, Reference Reynolds and Faye2016). Such models allow for the explicit incorporation of duration dependence and disease history, features that are particularly relevant for cancer outcomes. Recent studies have further highlighted their ability to incorporate diagnostic and treatment pathways (Arık et al., Reference Arık, Cairns, Dodd, Macdonald and Streftaris2024). Further applications in critical illness and cancer insurance pricing continue to demonstrate the breadth of this modeling tradition (Dȩbicka & Zmyślona, Reference Dȩbicka and Zmyślona2019; Soetewey et al., Reference Soetewey, Legrand, Denuit and Silversmit2022; Arık et al., Reference Arik, Cairns and Streftaris2025).

Alongside these applied developments, there has been growing methodological interest in non-Markov modeling, and semi-Markov models in particular. Semi-Markov models appear natural when disease onset is a well-defined event that starts its own clock running. They are theoretically tractable insofar as they can be represented as Markov in an extended state space but historically have been challenging to implement; see CMI (1991) for an early example. Recent theoretical work and sheer computing power are now making such models practicable (Adékambi & Christiansen, Reference Adékambi and Christiansen2017; Bladt et al., Reference Bladt, Minca and Peralta2026), but the modeler will often find real data to be either missing or messy. Possible next steps might be to model imperfect data directly (Christiansen & Furrer, Reference Christiansen and Furrer2021) or general non-Markov models with minimal assumptions on intertemporal structure, robust to mis-specification (van Houwelingen & Putter, Reference van Houwelingen and Putter2012; Christiansen, Reference Christiansen2021; Ahmad et al., Reference Ahmad, Bladt and Furrer2023). Such advances are particularly timely for cancer insurance pricing, where the complexity of disease trajectories demands modeling frameworks that are both statistically rich and computationally feasible.

Complementing these multi-state approaches, Bayesian methods provide a further methodological strand for modeling cancer risk, particularly in capturing parameter uncertainty and integrating heterogeneous data sources. This approach offers a coherent basis for inference and projection at the population level and has seen increasing application in actuarial research, including studies incorporating health behaviors such as smoking (Arik et al., Reference Arik, Cairns and Streftaris2025).

More recently, artificial intelligence and data-driven methodologies, particularly machine learning techniques, have attracted growing attention in cancer risk modeling within actuarial and statistical science (Richter & Khoshgoftaar, Reference Richter and Khoshgoftaar2018). Methods such as random forests, gradient boosting, neural networks, and survival-based machine learning models offer new opportunities to capture complex nonlinear relationships, high-dimensional covariate structures, and interactions among genetic, behavioral, clinical, and environmental risk factors (Deepa & Gunavathi, Reference Deepa and Gunavathi2022). These approaches have the potential to enhance prediction accuracy and support more personalized assessments of cancer incidence, progression, and survival (Kaur et al., Reference Kaur, Doja and Ahmad2022; O’Donnell et al., Reference O’Donnell, Cronin, Moghaddam and Wolsztynski2025). Their integration into actuarial applications raises important questions regarding interpretability, fairness, transparency, and the balance between predictive performance and regulatory accountability in insurance decision-making (Kuo & Lupton, Reference Kuo and Lupton2023). Beneath these practical concerns lies a harder question: predictive power and explanatory insight do not always travel together. Whether commercial pressures may push actuarial profession toward pure prediction, at the expense of understanding underlying drivers, is an open question.

This evolving and uncertain landscape presents significant challenges for the insurance industry. Cancer is a major source of claims, particularly in products such as critical illness insurance, where issues of affordability and accessibility are closely tied to adverse selection and underwriting practices. Meanwhile, improving survival rates – particularly for cancers such as breast cancer – and evolving regulatory frameworks, including “right to be forgotten” initiatives in Europe (European Society for Medical Oncology, 2026), are creating new possibilities for insurers to develop more inclusive products for those with a cancer history.

Actuaries increasingly rely on medical and epidemiological evidence to assess risk, yet translating these insights into robust and equitable insurance solutions remains far from straightforward.