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Register a new userOptimal Experimental Design for Mathematical Models of Hematopoiesis
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The hematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. Feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in hematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. Developing a proper experimental design for these studies is an extremely challenging task. To address this issue, we have developed a novel Bayesian framework for optimal design of perturbation experiments. We model the numbers of hematopoietic stem and progenitor cells in mice that are exposed to a low dose of radiation. We use a differential equations model that accounts for feedback and feedforward regulation. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. This model is embedded in a hierarchical framework with latent variables that capture unobserved cellular population levels. We select the optimum design based on the amount of information gain, measured by the Kullback-Leibler divergence between the probability distributions before and after observing the data. We evaluate our approach using synthetic and experimental data. We show that a proper design can lead to better estimates of model parameters even with relatively few subjects. Additionally, we demonstrate that the model parameters show a wide range of sensitivities to design options. Our method should allow scientists to find the optimal design by focusing on their specific parameters of interest and provide insight to hematopoiesis. Our approach can be extended to more complex models where latent components are used.
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Estimating causal effects for survival outcomes in the high-dimensional setting is an extremely important topic for many biomedical applications as well as areas of social sciences. We propose a new orthogonal score method for treatment effect estimation and inference that results in asymptotically valid confidence intervals assuming only good estimation properties of the hazard outcome model and the conditional probability of treatment. This guarantee allows us to provide valid inference for the conditional treatment effect under the high-dimensional additive hazards model under considerably more generality than existing approaches. In addition, we develop a new Hazards Difference (HDi), estimator. We showcase that our approach has double-robustness properties in high dimensions: with cross-fitting, the HDi estimate is consistent under a wide variety of treatment assignment models; the HDi estimate is also consistent when the hazards model is misspecified and instead the true data generating mechanism follows a partially linear additive hazards model. We further develop a novel sparsity doubly robust result, where either the outcome or the treatment model can be a fully dense high-dimensional model. We apply our methods to study the treatment effect of radical prostatectomy versus conservative management for prostate cancer patients using the SEER-Medicare Linked Data.
A new class of survival frailty models based on the Generalized Inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model. Furthermore, our proposed class is robust and does not present some computational issues experienced by the gamma model. By assuming a piecewise-exponential baseline hazard function, which gives a semiparametric flavour for our frailty class, we propose an EM-algorithm for estimating the model parameters and provide an explicit expression for the information matrix. Simulated results are addressed to check the finite sample behavior of the EM-estimators and also to study the performance of the GIG models under misspecification. We apply our methodology to a TARGET (Therapeutically Applicable Research to Generate Effective Treatments) data about survival time of patients with neuroblastoma cancer and show some advantages of the GIG frailties over existing models in the literature.
Inferring the causal structure of a system typically requires interventional data, rather than just observational data. Since interventional experiments can be costly, it is preferable to select interventions that yield the maximum amount of information about a system. We propose a novel Bayesian method for optimal experimental design by sequentially selecting interventions that minimize the expected posterior entropy as rapidly as possible. A key feature is that the method can be implemented by computing simple summaries of the current posterior, avoiding the computationally burdensome task of repeatedly performing posterior inference on hypothetical future datasets drawn from the posterior predictive. After deriving the method in a general setting, we apply it to the problem of inferring causal networks. We present a series of simulation studies in which we find that the proposed method performs favorably compared to existing alternative methods. Finally, we apply the method to real and simulated data from a protein-signaling network.
We studied how lagged linear regression can be used to detect the physiologic effects of drugs from data in the electronic health record (EHR). We systematically examined the effect of methodological variations ((i) time series construction, (ii) temporal parameterization, (iii) intra-subject normalization, (iv) differencing (lagged rates of change achieved by taking differences between consecutive measurements), (v) explanatory variables, and (vi) regression models) on performance of lagged linear methods in this context. We generated two gold standards (one knowledge-base derived, one expert-curated) for expected pairwise relationships between 7 drugs and 4 labs, and evaluated how the 64 unique combinations of methodological perturbations reproduce gold standards. Our 28 cohorts included patients in Columbia University Medical Center/NewYork-Presbyterian Hospital clinical database. The most accurate methods achieved AUROC of 0.794 for knowledge-base derived gold standard (95%CI [0.741, 0.847]) and 0.705 for expert-curated gold standard (95% CI [0.629, 0.781]). We observed a 0.633 mean AUROC (95%CI [0.610, 0.657], expert-curated gold standard) across all methods that re-parameterize time according to sequence and use either a joint autoregressive model with differencing or an independent lag model without differencing. The complement of this set of methods achieved a mean AUROC close to 0.5, indicating the importance of these choices. We conclude that time- series analysis of EHR data will likely rely on some of the beneficial pre-processing and modeling methodologies identified, and will certainly benefit from continued careful analysis of methodological perturbations. This study found that methodological variations, such as pre-processing and representations, significantly affect results, exposing the importance of evaluating these components when comparing machine-learning methods.
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a true research hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal policies become more complex. In this paper we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the policies. This leads us to formulate the optimal policy problem as an explicit optimization problem with objective and constraints which describe its specific desiderata. We describe a complete solution for deriving optimal policies for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal policies that are identical to existing policies, such as Hommels procedure or the procedure of Bittman et al. (2009), while for others it yields completely novel and more powerful policies than existing ones. We demonstrate the nature of our novel policies and their improved power extensively in simulation and on the APEX study (Cohen et al., 2016).
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