Bayesian nonparametric statistics: A new toolkit for discovery in cancer research

Abstract

Many commonly used statistical methods for data analysis or clinical trial design rely on incorrect assumptions, or assume an over-simplified framework that ignores important information. Such statistical practices may lead to incorrect conclusions about treatment effects, or clinical trial designs that are impractical or that do not accurately reflect the investigator’s goals. Bayesian nonparametric (BNP) models and methods are a very flexible new class of statistical tools that can overcome such limitations. This is because BNP models can accurately approximate any distribution or function, and can accommodate a broad range of statistical problems, including density estimation, regression, survival analysis, graphical modeling, neural networks, classification, clustering, population models, forecasting and prediction, spatio-temporal models, and causal inference. This paper describes three illustrative applications of BNP methods, including a randomized clinical trial to compare treatments for intraoperative air leaks after pulmonary resection, estimating survival time with different multi-stage chemotherapy regimes for acute leukemia, and evaluating joint effects of targeted treatment and an intermediate biological outcome on progression-free survival time in prostate cancer.

A Causal Framework for Making Individualized Treatment Decisions in Oncology

“…For example, if goodness-of-fit analyses show that the proportional hazards assumption is not valid for a survival-time dataset, then the Cox model should not be used [ 63 ]. Bayesian nonparametric (BNP) regression models for P(Y | X, Z) are a family of robust models that can accurately approximate any distribution, due to the property of “full support” [ 55 , 64 , 65 ]. Moreover, BNP regression models can be used to correct for bias.…”

“…HTEs may take much more complex forms than the treatment–covariate interactions in the LIN given above. In such a case, more flexible statistical methods such as a regression tree [ 77 , 78 ], neural net [ 79 ], or BNP regression model [ 64 ] may be applied to capture complicated patterns, such as high-order interactions among X and elements of a vector (Z, B) of variables that includes both patient prognostic covariates Z and a biomarker B. These models lack a uniform component that can be called LIN.…”

“…Note that these numerical computations mimic the theoretical derivation, given earlier, of an unbiased causal effect estimate based on a patient’s two potential outcomes when comparing treatments. An important general point is that being able to compute a 95% CI, or a 95% credible interval under a Bayesian model [ 58 , 64 ], around the estimated ARR to account for uncertainty would make it much more useful. For example, the estimate 13.5% with 95% CI [−2.0%, 28.0%] would be far less reliable than if the 95% CI were [10.0%, 16.0%].…”

Utility-Based Bayesian Personalized Treatment Selection for Advanced Breast Cancer

“…BNP models have been applied to a broad range of statistical problems, including density estimation, regression, clustering and survival analysis. See, for example, Müller et al (2015) for general applications, Mitra and Müller (2015) for applications in biostatistics, or Müller and Mitra (2013); Thall et al (2017) for overviews and illustrations. Given a Bayesian model f ( y | τ , x , θ ) and utility function U ( y , x ), we use posterior predictive utility distributions as a basis for deciding between treatments for a new patient with prognostic variables x .…”

Hydra: A mixture modeling framework for subtyping pediatric cancer cohorts using multimodal gene expression signatures

“…The number of clusters is then inferred while fitting the mixture model using Markov chain Monte Carlo (MCMC) sampling [26]. This approach has not been widely used in clinical cancer research because these algorithms are still computationally expensive, but recent advances in Bayesian variational inference have made this approach scalable for precision oncology applications [27].…”