https://www.journal-of-hepatology.eu/article/S0168-8278(05)00684-7/pdf

Natural history and prognostic indicators of survival in cirrhosis: a systematic review of 118 studies.

Physicians are often asked to make prognostic assessments but often worry that their assessments will prove inaccurate. Prognostic systems were developed to enhance the accuracy of such assessments. This paper describes an approach for evaluating prognostic systems based on the accuracy (calibration and discrimination) and generalizability (reproducibility and transportability) of the system's predictions. Reproducibility is the ability to produce accurate predictions among patients not included in the development of the system but from the same population. Transportability is the ability to produce accurate predictions among patients drawn from a different but plausibly related population. On the basis of the observation that the generalizability of a prognostic system is commonly limited to a single historical period, geographic location, methodologic approach, disease spectrum, or follow-up interval, we describe a working hierarchy of the cumulative generalizability of prognostic systems. This approach is illustrated in a structured review of the Dukes and Jass staging systems for colon and rectal cancer and applied to a young man with colon cancer. Because it treats the development of the system as a "black box" and evaluates only the performance of the predictions, the approach can be applied to any system that generates predicted probabilities. Although the Dukes and Jass staging systems are discrete, the approach can also be applied to systems that generate continuous predictions and, with some modification, to systems that predict over multiple time periods. Like any scientific hypothesis, the generalizability of a prognostic system is established by being tested and being found accurate across increasingly diverse settings. The more numerous and diverse the settings in which the system is tested and found accurate, the more likely it will generalize to an untested setting.

Assessing the Generalizability of Prognostic Information

1: Introduction.- 1.1. Systems Science.- 1.2. Systems Problem Solving.- 1.3. Hierarchy of Epistemological Levels of Systems.- 1.4. The Role of Mathematics.- 1.5. The Role of Computer Technology.- 1.6. Architecture of Systems Problem Solving.- Notes.- 2: Source and Data Systems.- 2.1. Objects and Object Systems.- 2.2. Variables and Supports.- 2.3. Methodological Distinctions.- 2.4. Discrete Versus Continuous.- 2.5. Image Systems and Source Systems.- 2.6. Data Systems.- Notes.- Exercises.- 3: Generative Systems.- 3.1. Empirical Investigation.- 3.2. Behavior Systems.- 3.3. Methodological Distinctions.- 3.4. From Data Systems to Behavior Systems.- 3.5. Measures of Uncertainty.- 3.6. Search for Admissible Behavior Systems.- 3.7. State-Transition Systems.- 3.8. Generative Systems.- 3.9. Simplification of Generative Systems.- 3.10. Systems Inquiry and Systems Design.- Notes.- Exercises.- 4: Structure Systems.- 4.1. Wholes and Parts.- 4.2. Systems, Subsystems, Supersystems.- 4.3. Structure Source Systems and Structure Data Systems.- 4.4. Structure Behavior Systems.- 4.5. Problems of Systems Design.- 4.6. Identification Problem.- 4.7. Reconstruction Problem.- 4.8. Reconstructability Analysis.- 4.9. Simulation Experiments.- 4.10. Inductive Reasoning.- 4.11. Inconsistent Structure Systems.- Notes.- Exercises.- 5: Metasystems.- 5.1. Change versus Invariance.- 5.2. Primary and Secondary Systems Traits.- 5.3. Metasystems.- 5.4. Metasystems versus Structure Systems.- 5.5. Multilevel Metasystems.- 5.6. Identification of Change.- Notes.- Exercises.- 6: Complexity.- 6.1. Complexity in Systems Problem Solving.- 6.2. Three Ranges of Complexity.- 6.3. Measures of Systems Complexity.- 6.4. Bremermann's Limit.- 6.5. Computational Complexity.- 6.6. Complexity Within GSPS.- Notes.- Exercises.- 7: Goal-Oriented Systems.- 7.1. Primitive, Basic, and Supplementary Concepts.- 7.2. Goal and Performance.- 7.3. Goal-Oriented Systems.- 7.4. Structure Systems as Paradigms of Goal-Oriented Behavior Systems.- 7.5. Design of Goal-Oriented Systems.- 7.6. Adaptive Systems.- 7.7. Autopoietic Systems.- Notes.- Exercises.- 8: Systems Similarity.- 8.1. Similarity.- 8.2. Similarity and Models of Systems.- 8.3. Models of Source Systems.- 8.4. Models of Data Systems.- 8.5. Models of Generative Systems.- 8.6. Models of Structure Systems.- 8.7. Models of Metasystems.- Notes.- Exercises.- 9: GSPS: Architecture, USE, Evolution.- 9.1. Epistemological Hierarchy of Systems: Formal Definition.- 9.2. Methodological Distinctions: A Summary.- 9.3. Problem Requirements.- 9.4. Systems Problems.- 9.5. GSPS Conceptual Framework: Formal Definition.- 9.6. Overview of GSPS Architecture.- 9.7. GSPS Use: Some Case Studies.- 9.8. GSPS Evolution.- Notes.- Exercises.- Appendices.- A: List of Symbols.- B: Glossary of Relevant Mathematical Terms.- C: Some Relevant Theorems.- D: Refinement Lattices.- E: Classes of Structures Relevant to Reconstructability Analysis.- References.- Author Index.

Architecture of Systems Problem Solving

A measure of uncertainly and information for possibility theory is introduced in this paper The measure is called the U-uncertainty or, alternatively, the U-information. Due to its properties, the U-uncertainty/information can be viewed as a possibilistic counterpart or the Shannon entropy and, at the same time, a generalization or the Hartley uncertainty/information. A conditional U-uncertainty is also derived in this paper, it depends on the U-uncertainties or the joint and marginal possibility distributions in exactly the same way as the conditional Shannon entropy depends on the entropies or the joint and marginal probability distributions. The conditional U-uncertainty is derived without the use of the notion of conditional possibilities, thus avoiding a current controversy in possibility theory. The proposed measures of U-uncertainty and conditional U-uncertainty provide a foundation for developing an alternative theory of information, one based on possibility theory rather than probability...

Measures of uncertainty and information based on possibility distributions

All self-respecting nonlinear scientists know self-organization when they see it: except when we disagree. For this reason, if no other, it is important to put some mathematical spine into our floppy intuitive notion of self-organization. Only a few measures of self-organization have been proposed; none can be adopted in good intellectual conscience. 
To find a decent formalization of self-organization, we need to pin down what we mean by organization. The best answer is that the organization of a process is its causal architecture—its internal, possibly hidden, causal states and their interconnections. Computational mechanics is a method for inferring causal architecture—represented by a mathematical object called the e-machine—from observed behavior. The e-machine captures all patterns in the process which have any predictive power, so computational mechanics is also a method for pattern discovery. In this work, I develop computational mechanics for four increasingly sophisticated types of process—memoryless transducers, time series, transducers with memory, and cellular automata. In each case I prove the optimality and uniqueness of the e-machine's representation of the causal architecture, and give reliable algorithms for pattern discovery. 
The e-machine is the organization of the process, or at least of the part of it which is relevant to our measurements. It leads to a natural measure of the statistical complexity of processes, namely the amount of information needed to specify the state of the E-machine. Self-organization is a self-generated increase in statistical complexity. This fulfills various hunches which have been advanced in the literature, seems to accord with people's intuitions, and is both mathematically precise and operational.

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Causal architecture, complexity and self-organization in time series and cellular automata

The structure of n-dimensional information theory is well adapted to the study of complex systems of many parts interacting in a nonsimple way, since it allows quantifications of the degree to which the parts are interdependent, i.e., are in communication with each other. It is particularly well suited to hierarchical systems. Even when calculations are impossible, informal interpretations of informational equations shed interesting light on the behavior of systems. These informal interpretations are emphasized. It is shown that the requirements on a system for selection of appropriate information (and therefore blockage of irrelevant information), internal coordination of parts, and throughput are essentially additive and therefore compete for the computational resources of the system. This observation has implications for system architecture. It is shown that under certain assumptions (valid, for example, for networks of parallel processors) systems are constraintlosing as well as information-losing. The importance and usefulness of the loss of information by a system is discussed briefly.

Laws of Information which Govern Systems

Relations between information flows and structure are discussed for two major classes of systems which have information-processing functions. It is shown that for both classes hierarchical structure is ideally suited for efficiency in the information processing. A partition law of information flow is developed which shows that the sum of the information flows through atomic components of a deterministic system can be partitioned into flow within the system devoted to system coordination, input flow which affects the output (throughput), and input flow which is blocked by the system.

Information flows in hierarchical systems

An informational analysis of the inter-male behaviour of the grasshopper chortophaga viridifasciata

Several fundamental relations between regulation and informational quantities are given. These show that regulation is a phenomenon closely tied to the transinformation between the regulator and the system which might be called its opponent. Two basic types of regulators are distinguished. The first, error-controlled regulators, are shown to be essentially coding devices which operate by taking advantage of constraints in the input sequence. The second, cause-controlled regulators, are shown to be free of some limitations inherent in error-controlled regulators. The importance of the regulator's channel capacity in cause-controlled regulation is established.

The Information Transfer Required in Regulatory Processes

The structure of a system of N variables is defined to be the set of N dependency relationships giving, for each variable, the set of other variables upon which it is statistically dependent. Because statistical dependence is indicated by the transmission measure of information theory, this set can be found by finding the smallest subset of variables for which T (subset : variable) is a maximum. Sampling considerations of this method are discussed, and the results of 21 experiments with it are given. The results are compatible with those of other structural modelling methods.

Roger C. Conant

Papers

Laws of Information which Govern Systems

Information flows in hierarchical systems

An informational analysis of the inter-male behaviour of the grasshopper chortophaga viridifasciata

The Information Transfer Required in Regulatory Processes

Structural modelling using a simple information measure