Significance tests for cancer screening trials

The goal of a cancer screening program is to reduce cancer mortality by detecting tumors at earlier stages of their development. For some types of cancer, screening tests may allow the preclinical detection of benign precursors of a tumor, and thus a screening program could result in reductions in both cancer incidence and mortality. For other types of cancer, a screening program will not reduce cancer incidence, and thus the expected outcome in a randomized cancer screening trial would be equal cancer incidence rates in control and study groups, but reduced cancer mortality in the study group. For the latter situation, we employ a variety of Poisson models for cancer incidence and mortality to derive optimal tests for equality of cancer mortality rates in a cancer screening trial, and we compare the asymptotic relative efficiencies of the test statistics under various alternatives. We demonstrate that testing equality of case mortality rates using Fisher's exact test or its Pearson chi-square approximation is nearly optimal when cancer incidence rates are equal and is fully efficient when cancer incidence rates are unequal. When valid, this comparison of case mortality rates in the study and control groups can be considerably more powerful than the standard comparison of population mortality rates. We illustrate the results using data from a clinical trial of a breast cancer screening program.     

Role of optimal control theory in cancer chemotherapy

This paper presents a review of the ways in which optimal control theory interacts with cancer chemotherapy. There are three broad areas of investigation. One involves miscellaneous growth kinetic models, the second involves cell cycle models, and the third is a classification of "other models." Both normal and tumor cell populations are included in a number of the models. The concepts of deterministic optimal control theory are applied to each model in such a way as to present a cohesive picture. There are applications to both experimental and clinical tumors. Suggestions for designing better chemotherapy strategies are presented.     

Optimal Tuberculosis Prevention and Control Strategy from a Mathematical Model Based on Real Data

A mathematical control model for the transmission dynamics of tuberculosis (TB) in South Korea is developed on the basis of the reported active-TB and relapse-TB incidence data. In this work, optimal control theory is used to propose optimal TB prevention and control strategy and rearrange the government TB budget for the best TB elimination plan. The impact of distancing, case finding, and/or case holding controls are investigated when the number of infected and infectious individuals are minimized, while the intervention costs are kept low. The implementation of optimal control measures shows that the distancing control, such as isolation of infectious people, early TB patient detection, and educational program/campaign for healthy control, is the most effective control factor for the prevention of TB transmission in South Korea.     

Present state and possibilities for improvement of cancer prevention and early detection in the Osijek-Baranya county

Cancer morbidity and mortality are on a steady increase in Croatia. Technologic possibilities for appropriate management are available for four cancer sites, i.e. cancer of the breast, cervix uteri, colorectum and prostate, and include cancer prevention and early detection in individuals yet free from manifest signs of the disease. The magnitude of the problem, the experience acquired to date, health care personnel available, and additional resources required to launch a systematic program of early detection of the disease are presented. The program should be initially launched in a county with greatest experience in early detection of cancer, where health care service is ready to immediately start its implementation. The role of family physician, gynecologic service at primary health care level, and polyclinic-consultation hospital service in program implementation is described. The following three possible options for early detection of cancer are analyzed and proposed: minimal program (early detection every 3 years), medium program (the same individuals examined every 2 years), and optimal program proposed by the American Cancer Society and other national and international organizations.     

An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance

An evolutionary program, based on a real-code genetic algorithm (GA), is applied to calculate optimal control policies for bioreactors. The GA is used as a nonlinear optimizer in combination with simulation software and constraint handling procedures. A new class of GA-operators is introduced to obtain smooth control trajectories, which leads also to a drastic reduction in computational load. The proposed method is easy to understand and has no restrictions on the model type and structure. The performance and optimal trajectories obtained by the extended GA are compared with those calculated with two common methods: (i) dynamic programming, and (ii) a Hamiltonian based gradient algorithm. The GA proved to be a good and often superior alternative for solving optimal control problems.     

The somatic mutation theory of cancer: growing problems with the paradigm?

The somatic mutation theory has been the prevailing paradigm in cancer research for the last 50 years. Its premises are: (1) cancer is derived from a single somatic cell that has accumulated multiple DNA mutations, (2) the default state of cell proliferation in metazoa is quiescence, and (3) cancer is a disease of cell proliferation caused by mutations in genes that control proliferation and the cell cycle. From this compelling simplicity, an increasingly complicated picture has emerged as more than 100 oncogenes and 30 tumor suppressor genes have been identified. To accommodate this complexity, additional ad hoc explanations have been postulated. After a critical review of the data gathered from this perspective, an alternative research program has been proposed. It is based on the tissue organization field theory, the premises of which are that carcinogenesis represents a problem of tissue organization, comparable to organogenesis, and that proliferation is the default state of all cells. The merits of these competing theories are evaluated herein.     

Optimal coordination and control of posture and locomotion.

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory, and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and stance model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses.     

Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis

Tumor anti-angiogenesis is a cancer treatment approach that aims at preventing the primary tumor from developing its own vascular network needed for further growth. In this paper the problem of how to schedule an a priori given amount of angiogenic inhibitors in order to minimize the tumor volume is considered for three related mathematical formulations of a biologically validated model developed by Hahnfeldt et al. [1999. Tumor development under angiogenic signalling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 59, 4770-4775]. Easily implementable piecewise constant protocols are compared with the mathematically optimal solutions. It is shown that a constant dosage protocol with rate given by the averaged optimal control is an excellent suboptimal protocol for the original model that achieves tumor values that lie within 1% of the theoretically optimal values. It is also observed that the averaged optimal dose is decreasing as a function of the initial tumor volume.     

Optimal coordination and control of posture and movements

This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton–Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.     

Bioeconomic dynamics of a fishery modeled as an S-system

A bioeconomic model of a single species fishery is developed by using a realistic catch-rate function and assuming that a regulatory agency controls exploitation of the fishery by imposing a suitable tax on the catch. The existence of a nontrivial steady state and its stability are examined. The optimal harvesting policy is discussed from the viewpoints of variational calculus and control theory. The fishery is then modeled as an S-system by following the recasting techniques of Savageau and Voit. Numerical examples of the optimal control curves and the yield-effort curves are obtained by executing the ESSYNS algorithm.     

Combining optimal control theory and molecular dynamics for protein folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the Cα atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the Cα atoms. In turn, MD simulation provides an all-atom conformation whose Cα positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the Cα atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization-MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages.     

Evolution of life history strategies for an asexual annual plant model

At any given moment in time a plant is partitioning total growth mass into its various component parts such as leaves, roots, reproductive material, etc. The view is taken that the plant has evolved a life history strategy to control this partitioning process. This paper illustrates the utility of optimal control theory for use in determining life history strategies which maximize fitness for a given asexual plant model. The optimal control methods are first used on a model previously analyzed by Professor Dan Cohen, who used a different method. His results of a change from 100% vegetable growth to 100% reproductive growth at a fixed switching time is again obtained. This 100% switching result is shown to be more generally applicable by using a qualitatively described model. However the switching time in general is shown to be a function of both leaf mass and time remaining to the end of the growing season. The allocation to toxin production is also considered. It is shown that under this model an inequality between system parameters must be satisfied before the plant should allocate growth to toxin production. Although the particular model explored here may rarely be realistic in nature, these same methods of optimal control theory can be applied in a similar fashion to many other proposed models of plant resource allocation.     

Combinatorial codons: a computer program to approximate amino acid probabilities with biased nucleotide usage

Using techniques from optimization theory, we have developed a computer program that approximates a desired probability distribution for amino acids by imposing a probability distribution on the four nucleotides in each of the three codon positions. These base probabilities allow for the generation of biased codons for use in mutational studies and in the design of biologically encoded libraries. The dependencies between codons in the genetic code often makes the exact generation of the desired probability distribution for amino acids impossible. Compromises are often necessary. The program, therefore, not only solves for the "optimal" approximation to the desired distribution (where the definition of "optimal" is influenced by several types of parameters entered by the user), but also solves for a number of "sub-optimal" solutions that are classified into families of similar solutions. A representative of each family is presented to the program user, who can then choose the type of approximation that is best for the intended application. The Combinatorial Codons program is available for use over the web from http://www.wi.mit.edu/kim/computing.html.     

Combining several screening tests: optimality of the risk score

The development of biomarkers for cancer screening is an active area of research. While several biomarkers exist, none is sufficiently sensitive and specific on its own for population screening. It is likely that successful screening programs will require combinations of multiple markers. We consider how to combine multiple disease markers for optimal performance of a screening program. We show that the risk score, defined as the probability of disease given data on multiple markers, is the optimal function in the sense that the receiver operating characteristic (ROC) curve is maximized at every point. Arguments draw on the Neyman-Pearson lemma. This contrasts with the corresponding optimality result of classic decision theory, which is set in a Bayesian framework and is based on minimizing an expected loss function associated with decision errors. Ours is an optimality result defined from a strictly frequentist point of view and does not rely on the notion of associating costs with misclassifications. The implication for data analysis is that binary regression methods can be used to yield appropriate relative weightings of different biomarkers, at least in large samples. We propose some modifications to standard binary regression methods for application to the disease screening problem. A flexible biologically motivated simulation model for cancer biomarkers is presented and we evaluate our methods by application to it. An application to real data concerning two ovarian cancer biomarkers is also presented. Our results are equally relevant to the more general medical diagnostic testing problem, where results of multiple tests or predictors are combined to yield a composite diagnostic test. Moreover, our methods justify the development of clinical prediction scores based on binary regression.     

Optimal blood sugar control in labile diabetics using a portable open-loop insulin infusion system with a flexible program.

11 labile diabetics were well controlled after 2 days of an i.v., open-loop insulin infusion program consisting of constant, empirically determined, basal infusion rates (mean: 1.1 U/h) and superimposed rectangular one-hour insulin infusions between 2 and 8 U/h during the main meals. The steering unit switches automatically back to the basal infusion rate after one hour. An almost optimal blood sugar profile was already obtained on the third day of the infusion program. We believe that such a flexible, open-loop insulin infusion program would render long-term optimal blood sugar control in "labile" diabetics possible if the technological development ever allows implantation of the infusion pumps.     

Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity

We derive and analyse a deterministic model for the transmission of malaria disease with mass action form of infection. Firstly, we calculate the basic reproduction number, R(0), and investigate the existence and stability of equilibria. The system is found to exhibit backward bifurcation. The implication of this occurrence is that the classical epidemiological requirement for effective eradication of malaria, R(0)<1, is no longer sufficient, even though necessary. Secondly, by using optimal control theory we derive the conditions under which it is optimal to eradicate the disease and examine the impact of a possible combined vaccination and treatment strategy on the disease transmission. When eradication is impossible, we derive the necessary conditions for optimal control of the disease using Pontryagin's Maximum Principle. The results obtained from the numerical simulations of the model show that a possible vaccination combined with effective treatment regime would reduce the spread of the disease appreciably.     

Self-Interest versus Group-Interest in Antiviral Control

Antiviral agents have been hailed to hold considerable promise for the treatment and prevention of emerging viral diseases like H5N1 avian influenza and SARS. However, antiviral drugs are not completely harmless, and the conditions under which individuals are willing to participate in a large-scale antiviral drug treatment program are as yet unknown. We provide population dynamical and game theoretical analyses of large-scale prophylactic antiviral treatment programs. Throughout we compare the antiviral control strategy that is optimal from the public health perspective with the control strategy that would evolve if individuals make their own, rational decisions. To this end we investigate the conditions under which a large-scale antiviral control program can prevent an epidemic, and we analyze at what point in an unfolding epidemic the risk of infection starts to outweigh the cost of antiviral treatment. This enables investigation of how the optimal control strategy is moulded by the efficacy of antiviral drugs, the risk of mortality by antiviral prophylaxis, and the transmissibility of the pathogen. Our analyses show that there can be a strong incentive for an individual to take less antiviral drugs than is optimal from the public health perspective. In particular, when public health asks for early and aggressive control to prevent or curb an emerging pathogen, for the individual antiviral drug treatment is attractive only when the risk of infection has become non-negligible. It is even possible that from a public health perspective a situation in which everybody takes antiviral drugs is optimal, while the process of individual choice leads to a situation where nobody is willing to take antiviral drugs.     

Optimal Vaccination Policies for an SIR Model with Limited Resources

The purpose of the paper is to use analytical method and optimization tool to suggest a vaccination program intensity for a basic SIR epidemic model with limited resources for vaccination. We show that there are two different scenarios for optimal vaccination strategies, and obtain analytical solutions for the optimal control problem that minimizes the total cost of disease under the assumption of daily vaccine supply being limited. These solutions and their corresponding optimal control policies are derived explicitly in terms of initial conditions, model parameters and resources for vaccination. With sufficient resources, the optimal control strategy is the normal Bang–Bang control. However, with limited resources, the optimal control strategy requires to switch to time-variant vaccination.     

低能Ti+注入棉花种子的深度-浓度分布的模拟计算

国内许多单位开展了低能离子注入植物种子的实验研究, 但在生物诱变机理方面却尚未有定论, 其中低能离子注入植物种子的深度-浓度分布成为研究的一个焦点问题。许多人直接用LSS理论得到的TRIM程序, 从理论上计算了低能重离子注入植物种子的深度-浓度的分布, 却发现计算结果与实验测量结果相差甚远, 于是得出LSS理论及TRIM程序不能直接用于计算离子注入非均匀、非致密、有孔道的植物种子这种特殊的靶材料的结论。针对这一研究课题, 在目前尚未有更加成熟完善的理论模型和计算方法的前提下, 为了便于计算, 本文根据植物种子的结构特点, 对靶材料棉花种子进行了处理,并对LSS理论进行了修正, 用蒙特卡罗方法计算了初始能量为20keV的Ti+注入棉花种子的深度-浓度分布, 得到了与实验结果符合较好的分布曲线, 初步的确定了低能离子注入植物种子深度-浓度分布的一种理论计算方法。     

Algebraic stability indicators for ranked lists in molecular profiling

MOTIVATION: We propose a method for studying the stability of biomarker lists obtained from functional genomics studies. It is common to adopt resampling methods to tune and evaluate marker-based diagnostic and prognostic systems in order to prevent selection bias. Such caution promotes honest estimation of class prediction, but leads to alternative sets of solutions. In microarray studies, the difference in lists may be bewildering, also due to the presence of modules of functionally related genes. Methods for assessing stability understand the dependency of the markers on the data or on the predictor's type and help selecting solutions. RESULTS: A computational framework for comparing sets of ranked biomarker lists is presented. Notions and algorithms are based on concepts from permutation group theory. We introduce several algebraic indicators and metric methods for symmetric groups, including the Canberra distance, a weighted version of Spearman's footrule. We also consider distances between partial lists and an aggregation of sets of lists into an optimal list based on voting theory (Borda count). The stability indicators are applied in practical situations to several synthetic, cancer microarray and proteomics datasets. The addressed issues are predictive classification, presence of modules, comparison of alternative biomarker lists, outlier removal, control of selection bias by randomization techniques and enrichment analysis. AVAILABILITY: Supplementary Material and software are available at the address http://biodcv.fbk.eu/listspy.html