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Prediction models in small area estimation.

Finite population estimation problems are formulated as prediction problems under superpopulation models. For linear regression models, a general theorem on optimal linear estimation is presented. The theorem is applied to simple cross-classification models to generate and analyze various statistics for estimating small area totals. These statistics include the synthetic and composite estimators, as well as some interesting alternatives.

Humans

Classification tree prediction models for dental caries from clinical, microbiological, and interview data.

Caries prediction by Classification And Regression Tree (CART) analysis is an appropriate and powerful alternative or complement to the commonly used classification methods of logistic regression and discriminant analysis, both parametric and nonparametric. The binary classification tree method discussed in this article is designed for complex data and does not require assumptions about the predictor variables or about the presence or absence of interactions among the predictor variables. Furthermore, the results give insight into the structures and interactions in the data and are easy to interpret and apply. In preliminary applications of the CART algorithms to data from The University of North Carolina Caries Risk Assessment Study, the method produced prediction rules having sensitivities and specificities that were similar to or slightly better than those associated with logistic and discriminant analyses. The classification trees constructed tended to involve far fewer predictor variables than required for adequate logistic and discriminant models. For example, for first-grade children in Aiken, South Carolina, nine variables were used to define a prediction rule having 64% sensitivity and 86% specificity. Ten-fold cross-validation estimates for future data were 58% and 79%, respectively. For first-grade children in Portland, Maine, two variables were used to define a prediction rule having 62% sensitivity and 77% specificity. The cross-validation estimates for future data were 58% and 78%, respectively. A brief, and previously unavailable, explanation of the CART method is given for the special case of a dichotomous outcome variable.

Child

Predictive models for human glucose-6-phosphate dehydrogenase deficiency.

The present paper has discussed available test systems for determination of the response of G-6-PD-deficient human erythrocytes to environmental agents. The limitations and advantages of each model have been examined, and the results of research using each model have been presented. The future development of suitable animal models or in vitro test systems may rely on advances in fields such as genetics and biochemistry. Genetic engineering may allow researchers to develop cells with a genetic deficiency of G-6-PD. These deficient cells could then be used to simulate human G-6-PD-deficient erythrocyte responses to various agents. Advances in biochemistry, in areas such as metabolism and enzymology, may also have an impact on future test systems. Due to the fact that present model systems are limited and their predictions often unreliable, the establishment of safe environmental health standards will depend upon advances in modern science and the converging of developments from various disciplines.

Animals

Analysis of the clinical findings used to diagnose coliform mastitis in dairy cows, and comparison to a prediction model.

Logistic regression was used to analyze the clinical findings (attributes) which predicted coliform mastitis in 113 dairy cattle, 36 of which had coliforms cultured from milk. Weakness of the cow, swelling of the udder, decreased body temperature and watery consistency of the milk were selected for the model. An analysis was then done to find the attributes which clinicians used when predicting that a cow would have a coliform cultured. Clinicians appeared to use water consistency of the milk, shivering, firmness of the udder, pulse rate, elevated body temperature, and respiratory rate. In a final analysis the clinicians' predictions were forced into the model to determine which attributes might be used by clinicians to increase diagnostic accuracy. Inclusion of weakness of the cow, swelling of the udder, decreased temperature of the cow, and duration of mastitis of less than 24 hours increased accuracy over clinical prediction alone. Accuracy of cowside diagnosis might be increased if more attention were paid to these attributes when making a diagnosis of coliform mastitis.

Animals

Predictive modelling of growth of Escherichia coli O157:H7: the effects of temperature, pH and sodium chloride.

The growth responses of Escherichia coli O157:H7 as affected by NaCl concentration, pH value and storage temperature were studied in laboratory medium. Growth curves at concentrations of NaCl in the range 0.5-6.5% (w/v), pH values in the range 4.0-7.0 and storage temperatures in the range 10-30 degrees C were fitted using the Gompertz routine and the derived parameters modelled. Growth curves could then be regenerated for any set of conditions within the matrix studied and values for growth rate, generation time, lag time and time to 1000-fold increase predicted. The model was validated against data from the literature and was found to give realistic estimates for generation time in media and a range of foods including meat and poultry, milk, cheese and tempeh. All predictions were consistently 'fail-safe'.

Culture Media

How well does a three-sphere model predict positions of dipoles in a realistically shaped head?

The electrical potential produced by a dipole in the temporal or frontal lobe was calculated for a realistically shaped scalp, skull, and brain. This potential distribution was then used with a 3-sphere model to predict the position, orientation, and strength of the dipole source. The original and predicted dipole positions differed by an average of 1.97 cm, with a difference of more than 4 cm in some cases. Control calculations demonstrated that this difference was not caused by numerical artifacts in the computation, but instead was due to a true difference between the 3-sphere and realistically shaped head models.

Brain

A weather-based prediction model for the life-cycle of the sheep tick, Ixodes ricinus L.

The incidence of sheep tick activity depends not only on the climatic conditions within the tick habitat, but also on the rates of fecundity, development, activity, engorgement and mortality of each stage of the life-cycle. Use of existing experimental results on the effect of these factors enables a model of the life-cycle to be formulated for the purpose of predicting the occurrence of tick activity in the field where climatic conditions vary. The components of such a model are described and the predicted results compared with field studies carried out in Ireland. It is hoped that the model presented will show the potential of formulating a system for predicting tick activity. Such a system could be used to enhance the control of tick-transmitted diseases.

Animals

Model predicting survival in stage I melanoma based on tumor progression.

We used the lesional steps in tumor progression and multivariable logistic regression to develop a prognostic model for primary, clinical stage I cutaneous melanoma. This model is 89% accurate in predicting survival. Using histologic criteria, we assigned melanomas to tumor progression steps by ascertaining their particular growth phase. These phases were the in situ and invasive radial growth phase and the vertical growth phase (the focal formation of a dermal tumor nodule or dermal tumor plaque within the radial growth phase or such dermal growth without an evident radial growth phase). After a minimum follow-up of 100.6 months and a median follow-up of 150.2 months, 122 invasive radial-growth-phase tumors were found to be without metastases. Eight-year survival among the 264 patients whose tumors had entered the vertical growth phase was 71.2%. Survival prediction in these patients was enhanced by the use of a multivariable logistic regression model. Twenty-three attributes were tested for entry into this model. Six had independently predictive prognostic information: (a) mitotic rate per square millimeter, (b) tumor-infiltrating lymphocytes, (c) tumor thickness, (d) anatomic site of primary melanoma, (e) sex of the patient, and (f) histologic regression. When mitotic rate per square millimeter, tumor-infiltrating lymphocytes, primary site, sex, and histologic regression are added to a logistic regression model containing tumor thickness alone, they are independent predictors of 8-year survival (P less than .0005).

Female

Species distribution models predict genome-wide polymorphism and gene flow in an endangered amphibian.

Species distribution models (SDMs) are widely used to predict habitat suitability but their usefulness and accuracy for inferring population health is still debated. Here, we evaluate whether SDM-derived relative habitat suitability (RHS) predicts genome-wide genetic diversity and connectivity-which are key proxies for population health and the functional integrity of landscapes. We addressed this issue in the Yellow-bellied toad (Bombina variegata), an endangered amphibian species with limited dispersal. We combined hierarchical SDMs, integrating both continental-level bioclimatic data and regional-level landscape variables, with genome-wide SNP data from 404 individuals sampled across 92 sites in southeastern France. We then used a multi-scale modelling framework to test the effect of bioclimatic (BRHS) and landscape (LRHS) habitat suitability on observed heterozygosity and pairwise genetic differentiation, accounting for heterogeneous genetic drift using gravity models. Our results show that both BRHS and LRHS are significant predictors of heterozygosity, with their effects expressed at different spatial scales-11 km and 3 km for BRHS and LRHS, respectively. Connectivity patterns also widely varied depending on scale and were best explained by gravity models integrating LRHS, BRHS, and local heterozygosity, underscoring the combined role of landscape resistance and population size in shaping patterns of genetic differentiation. These findings show that SDMs, when carefully calibrated and interpreted, can provide proxies for genetic diversity and landscape resistance in species with limited dispersal.

Journal Article

Comparison between pore model predictions and sheep lung fluid and protein transport.

The multiple pore model of T. R. Harris and R. J. Roselli (1981, J. Appl. Physiol: Respir. Environ. Exercise Physiol. 50, 1-14), was used to simulate lung lymph flow and protein transport at various levels of microvascular pressure. Response of the three-pore structure determined in that study was found to be in excellent agreement with the experimental sheep lung lymph measurements of R. E. Parker, R. J. Roselli, T. R. Harris, and K. L. Brigham (1981, Circ. Res. 49, 1164-1172). Optimal one- and two-pore model structures were also determined and their responses compared with the experimental data. The two-pore model behavior was found to be very similar to that of the three-pore model but a homoporous model which reproduced the experimental findings could not be found. All simulations required interstitial fluid pressure to increase as microvascular pressure was elevated. True filtration-independent conditions could only be simulated when lung vascular pressures were raised to physiologically unrealistic values.

Animals

Assessment of milk transfer coefficients for use in prediction models of radioactivity transport.

The transfer coefficient (Fm) which is widely used to predict the fraction of ingested radionuclides found in milk is an important parameter for modelling. The accuracy of estimates can be improved by considering the following factors that influence the Fm; (1) the physical-chemical form of the radionuclide in the feed of cows, (2) the hay to concentrate ratio of cows diets and (3) correcting for a steady state situation for feed intake and milk concentrations. Factors such as stable element intake, soil intake, milk production rate, metabolic rate and inhalation do not appear to have significant effects upon the transfer coefficient.

Accidents

Clinical validation of a predictive modeling equation for sodium.

Changes in plasma sodium (Na) concentration during hemodialysis were predicted by changes in Na concentration of the dialysate at equilibrium with the plasma, according to the formula C't = CD - (CD - C'0) [(V0 - QFt)/V0]A/QF, where C'0 and C't are the Na concentration of the dialysate at equilibrium with the plasma at times 0 and t, respectively; QF is the ultrafiltration flow rate; V0 is the initial total body water; and CD is the Na dialysate concentration. This modeling involves only one parameter, A, which is the effective sodium dialysance and depends on the dialyzer, the QF, the plasma water flow rate, and the actual Donnan coefficient. Parameter A was evaluated after 1 h of dialysis. Seven routine 4-h dialysis sessions were performed in which the Na concentration of dialysate at equilibrium with the plasma was measured at varying times. The mean (+/- SEM) difference between predicted and measured values was delta C = 0.5 +/- 0.2 mmol/L. These data support the validity of the model that allows the monitoring of Na dialysate concentration to obtain a prescribed Na plasma concentration at the end of a dialysis session.

Humans

Cat lung hemodynamics: comparison of experimental results and model predictions.

Commonly, attempts have been made to learn about the structure and function of the pulmonary vascular bed from measurements of arterial and venous pressures and blood flow rate under steady-state conditions (e.g., from pressure vs. flow data) or dynamic conditions (e.g., from vascular occlusion data). Zhuang et al. (J. Appl. Physiol. 55: 1341-1348, 1983) have presented a detailed model of steady-state cat lung hemodynamics based on direct measurements of anatomical and elasticity data. This model provides an opportunity to better understand the information content of the hemodynamic data. Therefore, in the present study we carried out a series of steady-state and dynamic experiments on isolated cat lungs. We then compared the results with those predicted by the model. We found that the model provided a good fit to the steady-state data. However, to fit the dynamic data, some modifications were necessary to account for the viscous behavior of the vessel walls and to move the first moment of the distribution of vascular resistance toward the arterial end of the vascular bed relative to that of the distribution of vascular compliance. Due to the sensitivity of the vascular resistance to small changes in vessel diameters and branching ratio, the modifications in morphometry represent small changes in morphometric data and are probably within the range of uncertainty in such data. The modifications had little effect on the steady-state model simulations but substantially improved the dynamic model simulations, suggesting that the dynamic data are quite sensitive to small changes in the relative distributions of vessel diameters and elasticity.

Animals

A predictive model for combined temperature and water activity on microbial growth during the growth phase.

An empirical and generalized model is presented, based on a modified Arrhenius equation, for predicting the combined effect of temperature and water activity on the growth rate of bacteria. When it was applied to seven separate sets of wide ranging published results, spanning some 50 years and including a spore-former and a silage micro-organism, predictions explained between 92.9 and 99.0% of the variation in the results with an overall mean of 96.6%. Advantages over existing models are that it is relatively easy to fit to data using least squares regression and requires only five coefficients. These, together with its simplicity and demonstrated wide application, will facilitate its practical use.

Bacteria

Grading scores and survivorship functions in liver cirrhosis: a comparative statistical analysis of various predictive models.

In a group of followed-up liver cirrhotics we evaluated the reliability of prognostic estimates predicted on the basis of a previously described multivariate statistical model (MSM). In the same subjects we also compared theoretical survival estimates obtained by fitting some other liver cirrhosis grading scores (Child-Turcotte's, McCormick's and Orrego's) to prognostic purposes. No statistical difference between actual and MSM-estimated survivorship functions was found (employing a life-table method with Logrank test), thus confirming the prognostic reliability of this multivariate classification model. Such a global and prognosis-correlated index may be recommendable both for comparing different groups of patients, and for assessing treatment effectiveness. Or results also substantially confirm the other investigated classificative methods such as reliable liver cirrhosis severity indexes, although their use for prognostic purposes seems to be less suitable.

Actuarial Analysis

Importance of glucose per se to intravenous glucose tolerance. Comparison of the minimal-model prediction with direct measurements.

Glucose disappearance after an oral or intravenous challenge is a function of the effects of both endogenously secreted insulin and of glucose itself. We previously introduced the term "glucose effectiveness," or SG, defined as the ability of glucose per se to enhance its own disappearance independent of an increment in plasma insulin. The present investigation, performed in conscious dogs, was undertaken to quantify this glucose effect by minimal-model-based analysis of insulin and glucose dynamics after a frequently sampled intravenous glucose tolerance test (FSIGT). The values from the standard FSIGT were then compared with direct measurements obtained from experiments in which the dynamic insulin response to glucose was suppressed with somatostatin (SRIF). In addition, we examined SG values from the modified FSIGT protocol, which involves both glucose and tolbutamide injections. Protocol l (N = 9): FSIGTs were performed and the glucose and insulin data were analyzed by computer. KG was 2.65 +/- 0.28 min-1, S1 was 4.09 +/- 0.34 X 10(4) min-1/(microU/ml), and SG was 0.033 +/- 0.004 min-1. Protocol II (N = 6): FSIGTs were performed on animals in which SRIF was infused (0.8 micrograms/min X kg) to obliterate the dynamic insulin response to glucose injection. Before the FSIGt, insulin and glucagon were infused intraportally to reattain basal glycemia. Without dynamic insulin, KG was reduced to 0.96 +/- 0.18 min-1 (P less than 0.0001). However, SG, estimated from the exponential rate of fall of plasma glucose in the absence of dynamic insulin, was similar to the standard FSIGTs: 0.025 +/- 0.004 (P greater than 0.25). Protocol III (N = 6): modified FSIGTs were performed using glucose and tolbutamide injections for a better estimate of model parameters. Model parameters Sl and SG, and the KG were not different from standard FSIGTs (P greater than 0.3). In fact, the value of SG (0.028 +/- 0.003 min-1) was nearly identical to the direct measure from protocol II. Therefore, the effect of glucose per se on glucose decline, estimated by modeling the standard and modified FSIGTs, was confirmed by a direct measurement with the endogenous insulin response suppressed with SRIF. Also, the time course of the insulin effect to enhance net glucose disappearance from plasma [Ieff(t)] was calculated from the data of protocol II, and was the same as the time course predicted by the model. These studies demonstrate the ability of the computer modeling approach to separate insulin-dependent and glucose-dependent glucose disappearance, and represent a direct confirmation of the minimal model.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals