Prognostic models models

There has been a tremendous development of various types of prognostic models of the carbon cycle during the past decades with increased refinement of both oceanic processes (see Siegenthaler and Sarmiento, 1993 Sarmiento et ah, 1992, 1998), terrestrial processes (Bonan,... 

Sebastian P, Ramoni ME, Nolan V, Baldwin CT, Steinberg MH. Genetic dissection and prognostic modeling of overt stroke in sickle cell anemia. Nat Genet 2005 37 435-40. 

Harrell E, Lee K, Mark D. Multivariable prognostic models issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. StatMed 1996 15 361-87. 

Astrup C, Noreik K. Functional psychoses diagnostic and prognostic models. Springfield, IL Charles C Thomas, 1966. 

Olivotto lA, Bajdik CD, Ravdin PM et al. Population-based validation of the prognostic model ADJUVANT for early breast cancer. Oncol 2005 23 2716-2725. 

By combining static and prognostic models it is possible to predict the levels of 03 concentration in real time. However, in this case it is necessary to describe photochemical reactions with other components of the atmosphere and, to a greater extent, by taking N02 into account (Agirre-Basurko et al., 2006). Some other ozone models were reviewed by Kondratyev and Varotsos (2000). 

Figure 2. Prognostic model on cereal diseases. (Reproduced with permission from Ref. 10. Copyright 1981 Organization Europeenne et Mediterraneenne pour la Protection des Plantes.)...

In the middle 1970s, the first results of diagnostic and prognostic numerical modeling of the BSGC were published [8,9]. Because of the coarse spatial resolution of the model grids and the insufficient reliability of the initial and boundary conditions, only their most general features corresponded to the concepts of the current pattern in the Black Sea that existed at that time. 

In contrast to diagnostic modeling, which is aimed at the construction of reliable current fields from the specified density fields, the principal goal of the so-called prognostic modeling lies in the understanding of the mechanisms of formation of the circulation in seas and oceans and their possible reproduction in numerical models. Only if thickness problem is resolved, one can speak about the hydrodynamic current forecasting. 

Prognostic models reproduce the process of evolution of the initial condition of the current, temperature, and salinity (density) fields under the action of the boundary conditions (momentum, heat, moisture, and mass fluxes) without any correction for the observational data. Usually, the climatic annual cycle of the variabilities in the circulation and thermohaline water structure is modeled. The calculations are performed until the parameters of this cycle stabilize, i.e. the differences between two successive become lower than a certain specified value. Then, the results obtained (model current, temperature, and salinity fields energy, dynamic, and thermodynamic budgets, etc.) un-... 

The results of prognostic modeling depend on numerous factors such as the completeness of the processes considered in the model, the parameterization of subgrid processes that are not reproduced explicitly, the quality of the numerical approximation of the model equations, the spatial and temporal resolutions in the calculation domain, and the reliability of the initial and boundary conditions and model constants. 

The modern prognostic models have reached their maximum in the fullness of the equations of the momentum, heat, and salt balance considered and in their numerical approximation. They may be joined into multilevel model and quasi-isopycnic model groups. The former models deal with a grid domain fixed in space and time, while the latter models involve layers with fixed water density values varying with respect to depth and time. Below, we present the results of the applications of these two groups of models to the studies of the BSGC separately. 

Multilevel prognostic models may be divided into two groups with respect to the mode of consideration of the vertical coordinate. One group uses the traditional Cartesian vertical coordinate with horizontal levels the other considers a vertical coordinate normalized with respect to the sea depth at the site (the so-called a-coordinate). Let us start the discussion of the results with the first group of models, because they prevail in the studies of the BSGC. 

The first prognostic models of the BSGC [8,9] were mentioned in the introduction to this chapter. They reproduced only the most general features of the BSGC. 

In addition to the results presented above, we should also note the studies of the climatic BSGC [56] based on the basic Russian prognostic model [57]. The distinctive features of [56] were related to the dependence of the coefficients of horizontal turbulence on lateral velocity shears and to the specifying of the monthly climatic temperature and salinity field at the surface [29] instead of the heat and moisture fluxes. Despite the relatively coarse horizontal calculation grid (about 22 km), this allowed the authors to reproduce [56] a relatively distinct MRC jet and the known NSAEs off the Turkish and Caucasian coasts and off the Danube River mouth. The results of the tuning in [56] of the Munk-Anderson s formula for the coefficient of the vertical turbulent exchange from the point of view of reproduction of the actual CIL were used in [53,54]. 

Table 14.1. Prerequisites for the clinical credibility of a prognostic model...

A prognostic model is the mathematical combination of two or more patient or disease characteristics to predict outcome. Confusingly, prognostic models are also termed prognostic indexes, risk scores, probability models, risk stratification schemes or clinical prediction rules (Reilly and Evans 2006). To be useful, they must be shown to predict clinically relevant outcomes reliably. They must, therefore, be derived from a representative cohort in which outcome has been measured accurately. Next, they must be validated, not just in the data from which they were derived (internal validation) but also on data from independent cohorts (external validation) (Wyatt and Altman 1995 Justice et al. 1999 Altman and Royston 2000). Lastly, a model must be simple to use and have clinical credibility, otherwise it is unlikely to be taken up in routine clinical practice (Table 14.1). 

A prognostic model or score must always be independently validated. Simply because a model seems to include appropriately modeled powerful predictors does not mean that it will necessarily validate well, because associations might just occur by chance, and predictors may not be as powerful as they appear. 

External validation of a model means determining whether it performs well in groups of patients other than those on whom it was derived that is, how is it likely to do in real clinical practice. These other groups almost certainly will differ in case mix, referral patterns, treatment protocols, methods of measurement of variables and definition of outcomes. Nevertheless, if a prognostic model includes powerful predictive variables, appropriately modeled, it should vaUdate reasonably well in other groups of patients. For example. Fig. 14.1 shows the vaUdation of the ABCD score on pooled individual patient data from six independent groups of patients with TIA (Johnston et al. 2007) (Ch. 15). 

Counsell C, Dennis M (2001). Systematic review of prognostic models in patients with acute stroke. Cerebrovascular Diseases 12 159-170 Dahlof B, Lindhohn LIT, Flansson L etal. (1991). Morbidity and mortality in the Swedish trial in old patients with hypertension (STOP-hypertension). Lancet 338 1281-1285 Feinstein AR (1996). Multivariable Analysis ... 

Harrell FE Jr., Lee KL, Mark DB (1996). Multivariable prognostic models issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in Medicine 15 361-387 Hart RG (2007). Antithrombotic therapy to prevent stroke in patients with atrial fibrillation. In Treating Individuals From Randomized Trials to Personalised Medicine, Rothwell PM (ed.) pp. 265-278. London Elsevier... 

Jacob M, Lewsey JD, Sharpin C et al. (2005). Systematic review and validation of prognostic models in liver transplantation. Liver Transplantation 11 814-825... 

Wyatt JC, Altman DG (1995). Commentary. Prognostic models clinically useful or quickly forgotten British Medical Journal 311 1539-1541... 

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