Title: New quantitative tools for precision medicine: overfitting correction in multivariate Cox analysis
Funder: Cancer Research UK

Abstract: Background: There is a need for more powerful statistical techniques in cancer research, specifically methods that enable us to extract clinical information reliably from high-dimensional data by addressing the problem of overfitting. Development and application of such methods, tailored to the needs of cancer research, are the theme of our proposal. This is a unique conjunction of wet-lab skills in the forefront of tumour immunology with mathematics and epidemiology expertise to provide novel insight into human tumour immunology. Aims: We propose to apply a new mathematical theory of overfitting in regression models for time-to-event cancer data. Our method will predict overfitting-induced deviations between true and reported regression parameters in multivariate Cox analysis and correct these parameters for overfitting effects. This enables reliable extraction of individualised predictive patterns from cancer data with much larger dimensions and increased accuracy, compared to what is feasible with standard tools. Methods: The new overfitting theory on which this project builds exploits the observation that, in contrast to finite sample noise, overfitting errors in Cox-type regression models are largely predictable. Using mathematical techniques from theoretical physics, it is possible to model imperfections of the regression process, leading to mathematical expressions from which to solve overfitting induced biases in associations and base hazard rates. We will apply the new method to data obtained in a recently finished pilot study investigating patterns of lymphoid stress surveillance to predict prostate cancer progression. The new method will help us evaluate heterogeneity in the capacity to monitor and eradicate malignant cells and/or their progenitors which may predict disease outcome and/or treatment response. We will work together to convert the new methodology, which has been published recently, into a well-documented statistical tool for general use and implement it in user-friendly software, tailored to the needs and conventions of cancer researchers. How the results will be used: The expected outcome of our proposal is an accurate mathematical/statistical method, implemented in software, which can correct reported parameters in Cox regression for overfitting. It will impact on cancer patients as we can apply it in a variety of clinical settings. For the current project this new methodology will help us understand how markers of lymphoid stress surveillance are predictive for prostate cancer progression and response to treatment. Overall, it will benefit the cancer field by enabling us to incorporate more patient information in our analyses, which will vastly improve the accuracy of individual outcome predictions.

Lay abstract: Background: There is a need for more powerful statistical techniques in cancer research, specifically methods that enable us to extract clinical information reliably from high-dimensional data by addressing the problem of overfitting. Development and application of such methods, tailored to the needs of cancer research, are the theme of our proposal. This is a unique conjunction of wet-lab skills in the forefront of tumour immunology with mathematics and epidemiology expertise to provide novel insight into human tumour immunology. Aims: We propose to apply a new mathematical theory of overfitting in regression models for time-to-event cancer data. Our method will predict overfitting-induced deviations between true and reported regression parameters in multivariate Cox analysis and correct these parameters for overfitting effects. This enables reliable extraction of individualised predictive patterns from cancer data with much larger dimensions and increased accuracy, compared to what is feasible with standard tools. Methods: The new overfitting theory on which this project builds exploits the observation that, in contrast to finite sample noise, overfitting errors in Cox-type regression models are largely predictable. Using mathematical techniques from theoretical physics, it is possible to model imperfections of the regression process, leading to mathematical expressions from which to solve overfitting induced biases in associations and base hazard rates. We will apply the new method to data obtained in a recently finished pilot study investigating patterns of lymphoid stress surveillance to predict prostate cancer progression. The new method will help us evaluate heterogeneity in the capacity to monitor and eradicate malignant cells and/or their progenitors which may predict disease outcome and/or treatment response. We will work together to convert the new methodology, which has been published recently, into a well-documented statistical tool for general use and implement it in user-friendly software, tailored to the needs and conventions of cancer researchers. How the results will be used: The expected outcome of our proposal is an accurate mathematical/statistical method, implemented in software, which can correct reported parameters in Cox regression for overfitting. It will impact on cancer patients as we can apply it in a variety of clinical settings. For the current project this new methodology will help us understand how markers of lymphoid stress surveillance are predictive for prostate cancer progression and response to treatment. Overall, it will benefit the cancer field by enabling us to incorporate more patient information in our analyses, which will vastly improve the accuracy of individual outcome predictions.

Research activity codes: 4.5 RESOURCES AND INFRASTRUCTURE (DETECTION);5.9 RESOURCES AND INFRASTRUCTURE (TREATMENT DEVELOPMENT)
Health categories: CANCER AND NEOPLASMS