Introduction 

Cancer surveillance directly affects patient outcomes, and the tests chosen for this process is critical. The three crucial factors of the test – sensitivity, specificity and cost – need to be balanced to yield the best outcome.  

Sensitivity refers to the ability to identify true positives, contributing to early detection. Specificity measures the ability to avoid false positives, reducing unnecessary tests and the burden on healthcare system. Cost is also critical because it influences both equity of access and health system budgets: even the most accurate test have limited impact if it is too expensive for widespread use. Trade-offs exist between all three parameters, thus only when all three are balanced can a test truly improve survival rates, reduce healthcare burdens and be adopted in real world settings.

My research project focuses on colorectal cancer, the third most common cancer globally. Under the mentorship of Dr Reza Skandari, Assistant Professor of Health Operations at Imperial College Business School, I aim to design an optimisation framework using partially observable Markov decision process (POMDP). Built using Python, this model aims to identify the optimal balance of sensitivity, specificity and cost for circulating tumour DNA (ctDNA) testing, while also identifying relationships and trends between these parameters.

The purpose of this article is to reflect on the process of developing this model, focusing on the intellectual challenges of bridging clinical medicine and operations research, the methodological choices made, and the personal and academic growth gained from engaging with a real-world, complex project.

Project Conception and Engaging with the Literature

This project resonates with my interest in applying analytical methods to real world medical problems. The challenge of balancing clinical benefit, patient wellbeing and healthcare costs in surveillance strategies for cancer recurrence sits at the intersection of programming, health economics, and clinical decision making, making it an ideal context for an optimisation-based approach.

Upon reviewing literature, it became clear that current policies are fragmented. Although guidelines on post-treatment cancer surveillance are widely established, there is little consensus reached on how to balance sensitivity, specificity and cost in the design or approval of new tests. Existing cost-effectiveness models often take the form of static comparisons between a handful of predefined strategies, such as fixed imaging schedules or fixed cut-offs on biomarker assays. While informative, these approaches fail to explore the full decision space.

My contribution is to address this gap by building a flexible decision analytic model based on partially observable Markov decision processes (POMDPs). I am to simulate the sequential nature of surveillance decisions, incorporate uncertainty in disease progression and test performance, and optimise outcomes across sensitivity, specificity, and cost simultaneously. This approach focuses on actively generating optimal policies under different clinical and economic assumptions.

Methodological Choices and Rationale

I selected to model cancer surveillance using POMDP model because it allows me to simulate surveillance as a sequence of repeated decision points under uncertainty, where outcomes of one test influence subsequent actions. This approach incorporates sensitivity, specificity and cost as tenable parameters, enabling systematic exploration of trade-offs and identification of profit-maximising strategies. The model allows me to define health states such as ‘cancer free’, ‘undetected cancer’, ‘has cancer’ and ‘dead’, thus the model effectively captures the chronic, state-based nature of colorectal cancer and is computationally tractable for long term horizon modelling.

The reward structure of the model was designed to optimise net profit from the patient and health system perspective, accounting for not only direct testing costs, but also downstream costs such confirmatory colonoscopies following positive results, and the penalties associated with missed detections. Framing the outcome in terms of overall profit is meaningful, as it captures both clinical and economic consequences of surveillance strategies, and aligns with how decision makers in health policy evaluate new technologies.

While building this model, I reviewed published literature and databases like SEER for key parameters such as pre-insurance cost of CT scan and ctDNA testing, treatment costs and the current cancer surveillance guidelines. Initially, sourcing these parameters presented challenge because these numbers varied greatly from source to source, region to region. After careful comparison, I decided to parameterise the model using US based data, as this was the most comprehensive and consistently reported. While this decision narrows the scope geographically, it does not reduce the conceptual validity of the model because the framework itself is transferable: other regions could recalibrate the parameters using their own data, and the optimisation process would remain the same.

Navigate Challenges and Problem-Solving

A major challenge was the lack of high quality, granular data for transition probabilities between health states, often forcing reliance on aggregated or older studies. I learned to plan for probabilistic sensitivity analysis to account for this uncertainty and developed smaller scripts within the model to check the validity of the parameter inputs, which proved to be crucial in making the model’s outputs robust.

Balancing the model realism and simplicity was a recurring difficulty. When starting the project, I aimed to create the most realistic model, thus attempted to account for non-monetary elements such as family anxiety, opportunity costs, and change in productivity after test results. However, these dimensions caused my model to behave unpredictably, distracting the outcome away from the real focus – profit optimisation. I also faced great challenge when ethically grappling with reducing human health outcomes into numerical utilities (QALYs) and costs, which is an inherent limitation and an ongoing challenge of quantitative modelling in medicine.

After extensive tuning of the model and discussions with my supervisor, I narrowed the model’s scope to only monetary costs and benefits, framed from a societal perspective rather than an individual one. This shift provided clarity: the model was then able to demonstrate coherent trade-offs between sensitivity, specificity, and cost, and to identify an optimal policy. Nonetheless, I acknowledge that non-monetary factors, particularly psychological burden, are very relevant in cancer surveillance, thus my long term goal is to extend the framework to incorporate these dimensions, once the economic model is validated and stable.

Synthesis of Learning and Self-Reflection

Through this research project, I advanced my skills in Python programming and mathematical modelling. More importantly, I developed resilience in problem-solving, learned to manage a complex project independently, and improved my ability to navigate ambiguous problems. In classroom settings, I am usually presented with problems with known outcomes; the task is to work systematically towards that solution. In contrast, this research project placed me in an environment of genuine uncertainty, where I had to make methodological choices without knowing exactly what direction they would lead to. Learning to remain adaptable in the face of this uncertainty was one of the most valuable aspects of the experience.

The theme of balance ran not only through the content of my project—optimising the balance between sensitivity, specificity, and cost in cancer surveillance—but also through the process of research itself. I had to constantly weigh the simplicity of the model against the desire for realism and accept that sacrificing some certainty of outcome was necessary to achieve efficiency and clarity. This tension pushed me to refine my judgement and taught me that effective research often lies in recognising the right level of complexity for the problem at hand.

Ultimately, this project has deepened my appreciation of how analytical tools can bridge the gap between theory and real-world medical decision-making. It has also shown me that research is as much about intellectual rigour as it is about personal growth—cultivating patience, adaptability, and the confidence to navigate uncertainties.

Conclusion: Looking Forward

This project has taken me on a journey from a complex clinical problem—balancing sensitivity, specificity, and cost in colorectal cancer surveillance—to the development of a quantitative optimisation model using POMDPs. Along the way, I not only learned new technical skills but also gained valuable insights into the challenges of modelling real-world healthcare decisions.

At this stage, the model structure is defined, and parameters have been identified, but calibration and validation remain. The immediate next step is to write smaller programs to verify the model’s individual components and comparing outputs against base cases to refine parameter values. Once calibrated, the model will be able to generate more reliable and concrete insights into cancer surveillance.

While still in progress, this project has provided an invaluable framework for understanding how analytical rigour can be applied to improve patient outcomes. I am excited to continue developing the model and see what insight it will bring.