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Toward validation of process criteria for high-pressure processing of orange juice with predictive models.

Mathematical models were developed to predict time to inactivation (TTI) by high-pressure processing of Salmonella in Australian Valencia orange juice (pH 4.3) and navel orange juice (pH 3.7) as a function of pressure magnitude (300 to 600 MPa) and inoculum level (3 to 7 log CFU/ml). For each model, the TTI was found to increase with increasing inoculum level and decrease with increasing pressure magnitude. The U.S. Food and Drug Administration Juice Hazard Analysis and Critical Control Point Regulation requires fruit juice processors to include control measures that produce a 5-log reduction of the pertinent microorganism of public health significance in the juice. To achieve a 5-log reduction of Salmonella in navel orange juice at 20 degrees C, the models predicted hold times of 198, 19, and 5 s at 300, 450, and 600 MPa, respectively. In Valencia orange juice at 20 degrees C, a 5-log reduction of Salmonella was achieved in 369, 25, and 5 s at 300, 450, and 600 MPa, respectively. At pressures below 400 MPa, Salmonella was more sensitive to pressure in the more acidic conditions of the navel orange juice and TTIs were shorter. At higher pressures, little difference in the predicted TTI was observed. Refrigerated storage (4 degrees C) of inoculated navel orange juice treated at selected pressure/time/inoculum combinations showed that under conditions in which viable Salmonella was recovered immediately after high-pressure processing, pressure-treated Salmonella was susceptible to the acidic environment of orange juice or to chill storage temperature. These TTI models can assist fruit juice processors in selecting processing criteria to achieve an appropriate performance criterion with regard to the reduction of Salmonella in orange juice, while allowing for processing flexibility and optimization of high-pressure juice processing.

Beverages↗

Development of a clinical prediction model for an ordinal outcome: the World Health Organization Multicentre Study of Clinical Signs and Etiological agents of Pneumonia, Sepsis and Meningitis in Young Infants. WHO/ARI Young Infant Multicentre Study Group.

This paper describes the methodologies used to develop a prediction model to assist health workers in developing countries in facing one of the most difficult health problems in all parts of the world: the presentation of an acutely ill young infant. Statistical approaches for developing the clinical prediction model faced at least two major difficulties. First, the number of predictor variables, especially clinical signs and symptoms, is very large, necessitating the use of data reduction techniques that are blinded to the outcome. Second, there is no uniquely accepted continuous outcome measure or final binary diagnostic criterion. For example, the diagnosis of neonatal sepsis is ill-defined. Clinical decision makers must identify infants likely to have positive cultures as well as to grade the severity of illness. In the WHO/ARI Young Infant Multicentre Study we have found an ordinal outcome scale made up of a mixture of laboratory and diagnostic markers to have several clinical advantages as well as to increase the power of tests for risk factors. Such a mixed ordinal scale does present statistical challenges because it may violate constant slope assumptions of ordinal regression models. In this paper we develop and validate an ordinal predictive model after choosing a data reduction technique. We show how ordinality of the outcome is checked against each predictor. We describe new but simple techniques for graphically examining residuals from ordinal logistic models to detect problems with variable transformations as well as to detect non-proportional odds and other lack of fit. We examine an alternative type of ordinal logistic model, the continuation ratio model, to determine if it provides a better fit. We find that it does not but that this model is easily modified to allow the regression coefficients to vary with cut-offs of the response variable. Complex terms in this extended model are penalized to allow only as much complexity as the data will support. We approximate the extended continuation ratio model with a model with fewer terms to allow us to draw a nomogram for obtaining various predictions. The model is validated for calibration and discrimination using the bootstrap. We apply much of the modelling strategy described in Harrell, Lee and Mark (Statist. Med. 15, 361-387 (1998)) for survival analysis, adapting it to ordinal logistic regression and further emphasizing penalized maximum likelihood estimation and data reduction.

Chi-Square Distribution↗

Development of a predictive model for biodegradability based on BIODEG, the evaluated biodegradation data base.

A file of evaluated biodegradation data was used to develop a model for predicting aerobic biodegradability from chemical structure alone. Chemicals were initially divided into three groups: (i) chemicals that degrade rapidly under most environmental conditions without requiring acclimation; (ii) chemicals that degrade slowly or not at all; and (iii) chemicals that are biodegradable, but only after an acclimation period. Chemicals in the first two groups were then used to develop a model for classifying chemicals as rapidly or not rapidly biodegradable. The model is based on linear regression against 34 preselected substructures, and correctly classifies 92% (211 or 229) of the chemicals in the final training set.

Aerobiosis↗

Modeling a multivariable reactor and on-line model predictive control.

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.

Algorithms↗

A generalized HLA prediction model for related donor matches.

This article derives a generalized probabilistic model for predicting HLA matches from a population of family members consisting of all blood-related descendants of one pair of patient's grandparents, excluding parents and siblings, for three subsequent generations. This consists of the patient's children, blood-related aunts/uncles, first cousins, first cousins once removed and nephews/nieces. (It is assumed that the patient's siblings and parents were tested prior but did not produce a match.) The model uses family pedigree information and haplotype frequency data to estimate the likelihood of a match. Results are given for many ethnic groupings. These results indicate that such a family search frequently approximates or exceeds the 0.25 success rate of a single sibling search when the patient possesses a common haplotype within the patient's ethnic population, and the family members are also of the same ethnic origin. Families of the same lineage averaging more than two children/nuclear family substantially exceed the 0.25 rate. The results degrade only modestly for the two children/nuclear family scenario when first cousins once removed are excluded from the search. Among the study's larger nations of Japan, the United States and the United Kingdom, approximately 15-20% of the population can potentially benefit from such searches. These percentages are much higher for the study's smaller countries.

HLA Antigens↗

A detailed predictive model of the mammalian circadian clock.

Experimental data on the circadian (approximately 24-h) clock in mammalian cells are vast, diverse, and detailed. Mathematical models are therefore needed to piece these data together and to study overall clock behavior. Previous models have focused on Neurospora or Drosophila or can be converted to a Drosophila model simply by renaming variables. Those models used Hill-type terms for transcription regulation and Michaelis-Menten type or delay terms for posttranslation regulation. Recent mammalian experimental data call into question some of the assumptions in these approaches. Moreover, gene duplication has led to more proteins in the mammalian system than in lower organisms. Here we develop a detailed distinctly mammalian model by using mass action kinetics. Parameters for our model are found from experimental data by using a coordinate search method. The model accurately predicts the phase of entrainment, amplitude of oscillation, and shape of time profiles of clock mRNAs and proteins and is also robust to parameter changes and mutations.

Animals↗

Validation of a predictive model for postoperative pulmonary complications.

OBJECTIVE: To test or validate a previously reported model for predicting postoperative pulmonary complications (PPCs) after elective abdominal surgical procedures. DESIGN: Prospective, descriptive. SETTING: Four midwestern hospitals serving a diverse population of patients. PATIENTS: Two hundred seventy-six adult patients who had undergone abdominal surgery (51% men, 49% women; mean age 54.1 +/- 5.3 years). OUTCOME MEASURES: PPC developed in 26.4%. DATA COLLECTION: Data were collected preoperatively during a brief interview and a pulmonary physical examination and on the first 6 postoperative days. RESULTS: A six risk-factor model was tested in this sample of subjects. The model validated relatively well in the sample of 276 subjects with use of the basic criteria of correct classification, sensitivity, and specificity. However, when a new model was developed from this sample, differing risk factors emerged as significant independent predictors. CONCLUSIONS: Further research is needed to assess the stability of the risk factors and test the models in differing settings and populations of patients.

Abdomen↗

A predictive model for delirium in hospitalized elderly medical patients based on admission characteristics.

OBJECTIVE: To prospectively develop and validate a predictive model for the occurrence of new delirium in hospitalized elderly medical patients based on characteristics present at admission. DESIGN: Two prospective cohort studies done in tandem. SETTING: University teaching hospital. PATIENTS: The development cohort included 107 hospitalized general medical patients 70 years or older who did not have dementia or delirium at admission. The validation cohort included 174 comparable patients. MEASUREMENTS: Patients were assessed daily for delirium using a standardized, validated instrument. The predictive model developed in the initial cohort was then validated in a separate cohort of patients. RESULTS: Delirium developed in 27 of 107 patients (25%) in the development cohort. Four independent baseline risk factors for delirium were identified using proportional hazards analysis: These included vision impairment (adjusted relative risk, 3.5; 95% Cl, 1.2 to 10.7); severe illness (relative risk, 3.5; Cl, 1.5 to 8.2); cognitive impairment (relative risk, 2.8; Cl, 1.2 to 6.7); and a high blood urea nitrogen/creatinine ratio (relative risk, 2.0; Cl, 0.9 to 4.6). A risk stratification system was developed by assigning 1 point for each risk factor present. Rates of delirium for low- (0 points), intermediate- (1 to 2 points), and high-risk (3 to 4 points) groups were 9%, 23%, and 83% (P < 0.0001), respectively. The corresponding rates in the validation cohort, in which 29 of 174 patients (17%) developed delirium, were 3%, 16%, and 32% (P < 0.002). The rates of death or nursing home placement, outcomes potentially related to delirium, were 9%, 16%, and 42% (P = 0.02) in the development cohort and 3%, 14%, and 26% (P = 0.007) in the validation cohort. CONCLUSIONS: Delirium among elderly hospitalized patients is common, and a simple predictive model based on four risk factors can be used at admission to identify elderly persons at the greatest risk.

Aged↗

Predictive model for plasma concentration-versus-time profiles of investigational anticancer drugs in patients.

We report a model that provides a strong correlation between mouse toxicity data [mouse lethal dose 10% (LD10)] and human plasma concentration-versus-time (CXT) data for 22 commonly used anticancer agents. Mouse toxicity data (LD10) from two dosing schedules, daily times one and daily times seven, were evaluated for the two mouse strains BDF/1 and Swiss. Data from BDF/1 mice were selected for analysis because they were more abundant. Strong correlations were found between LD10 and human plasma CXT data for both daily times one and daily times seven dosing schedules--ln (CXT) = -1.6504 + [0.8408 X ln (LD10)], r = .84, P less than .0001, and ln (CXT) = -0.0754 + [0.8954 X ln (LD10)], r = .90, P less than .0001, respectively. These correlations may serve as useful models to predict the maximally tolerated dose of an investigational anticancer agent prior to entry into clinical trials and to assist in the selection of clinically relevant in vitro CXTs for new-agent screening against human tumors.

Animals↗

Elements of a predictive model for determining beach closures on a real time basis: the case of 63rd Street Beach Chicago.

Data on hydrometeorological conditions and E. coli concentration were simultaneously collected on 57 occasions during the summer of 2000 at 63rd Street Beach, Chicago, Illinois. The data were used to identify and calibrate a statistical regression model aimed at predicting when the bacterial concentration of the beach water was above or below the level considered safe for full body contact. A wide range of hydrological, meteorological, and water quality variables were evaluated as possible predictive variables. These included wind speed and direction, incoming solar radiation (insolation), various time frames of rainfall, air temperature, lake stage and wave height, and water temperature, specific conductance, dissolved oxygen, pH, and turbidity. The best-fit model combined real-time measurements of wind direction and speed (onshore component of resultant wind vector), rainfall, insolation, lake stage, water temperature and turbidity to predict the geometric mean E. coli concentration in the swimming zone of the beach. The model, which contained both additive and multiplicative (interaction) terms, accounted for 71% of the observed variability in the log E. coli concentrations. A comparison between model predictions of when the beach should be closed and when the actual bacterial concentrations were above or below the 235 cfu 100 ml(-1) threshold value, indicated that the model accurately predicted openings versus closures 88% of the time.

Bathing Beaches↗

A predictive model for matrix and analyte effects in electrospray ionization of singly-charged ionic analytes.

In electrospray ionization (ESI), droplets with a surface excess charge are created. The rate of production of surface excess charge is a constant and is equal to the rate of ion production. The ions appearing in the mass spectrum are postulated to be those that formed the surface excess charge at the time of droplet formation (or their collision products). An equilibrium model based on competition among the ions in the solution for the limited number of excess charge sites has been developed. This model accurately predicts the response curves of singly-charged ionic analytes as a function of the concentration of electrolyte and other analytes and provides an explanation for the selective effectiveness of ESI. At low concentrations of total analyte (micromolar and less), the response curves are linear, indifferent to the presence of other low concentration analytes, and suppressed by electrolyte concentrations in excess of the minimum required. At higher analyte concentrations, the response becomes independent of analyte concentration but highly affected by the presence of other analytes.

Mass Spectrometry↗

Predictive modelling: applications in the dairy industry.

Predictive modelling has been used in the dairy industry for determining the keeping quality of raw milk and pasteurized products. More recently, predictive equations describing growth and toxin production for a number of bacteria of concern to dairy microbiologists have been developed. A more mathematical approach is also being adopted for determining effective pasteurization conditions for organisms present in milk.

Animals↗

Discovery of predictive models in an injury surveillance database: an application of data mining in clinical research.

A new, evolutionary computation-based approach to discovering prediction models in surveillance data was developed and evaluated. This approach was operationalized in EpiCS, a type of learning classifier system specially adapted to model clinical data. In applying EpiCS to a large, prospective injury surveillance database, EpiCS was found to create accurate predictive models quickly that were highly robust, being able to classify > 99% of cases early during training. After training, EpiCS classified novel data more accurately (p < 0.001) than either logistic regression or decision tree induction (C4.5), two traditional methods for discovering or building predictive models.

Artificial Intelligence↗

Predictive models for cochlear implantation in elderly candidates.

OBJECTIVE: An aging American population carries a high prevalence of profound sensorineural hearing loss. We examined the performance of multichannel cochlear implant recipients in a large database of adult subjects. DESIGN: Nonconcurrent prospective study of a national cohort with multivariate regression analysis of preoperative and postoperative performance variables in multichannel cochlear implant recipients. We applied models of prediction established in previous studies to the observed results. SETTING: Referral centers with active cochlear implant programs. PATIENTS: Adolescents and adults with profound hearing loss (N = 749; age range, 14-91 years). MAIN OUTCOME MEASURE: Postoperative monosyllabic word recognition. RESULTS: The population 65 years and older demonstrated a clinically insignificant 4.6%-smaller postoperative word score compared with the population younger than 65 years. When duration of deafness exceeded 25 years, elderly recipients demonstrated higher word scores than their younger counterparts. A more significant factor affecting outcomes is the ratio of duration of deafness to age at implantation. CONCLUSIONS: Age at implantation carried relatively little predictive value for postoperative performance in subjects 65 years and older. Although a small decrement in mean speech recognition scores was evident, the clinical significance of this difference is questionable when all of the results observed in elderly patients are considered. A shorter percentage of life spent in severe-to-profound sensorineural hearing loss suggests a foundation of acoustic/auditory processing in the elderly cohort that may mitigate potential physiological effects associated with advanced age. This study confirms and extends previous observations that duration of profound deafness and residual speech recognition carry higher predictive value than the age at which an individual receives an implant.

Adolescent↗

Ca(2+)-dependent binding of endonexin (annexin IV) to membranes: analysis of the effects of membrane lipid composition and development of a predictive model for the binding interaction.

Endonexin (annexin IV) is a member of the annexin family of homologous proteins that bind membranes and aggregate vesicles in a calcium-dependent fashion. This study examines the lipid modulation and mechanism of the binding of endonexin to membranes using a fluorescence energy transfer assay to measure bovine endonexin binding to well-defined large unilamellar vesicles. The calcium sensitivity for endonexin-membrane binding is observed to be highly dependent on the types of membrane lipids present. As with most annexins, negatively charged lipids best promote endonexin binding to phosphatidylcholine (PC) containing membranes. However, a comparison of 11 different types of lipids reveals that other factors such as the type of ion contributing the charge and head-group size are also important. The concentrations of calcium required for half-maximal binding of endonexin to PC vesicles containing 30% phosphatidylserine (PS) or 30% phosphatidylinositol (PI), both lipids with net charge-1, are 48 +/- 6 and 114 +/- 19 microM, respectively, while half-maximal binding to 30% phosphatidylinositol bisphosphate (PIP2), with a greater net charge of -3 to -5, occurs at 65 microM calcium, similar to the calcium requirement for binding to PS. The apparent affinities of endonexin for seven different types of lipids parallel those reported for annexin V [Andree, H. A. M., Reutelingsperger, C. P. M., Hauptmann, R., Hemker, H. C., Hermans, W. T., & Willems, G. M. (1990) J. Biol. Chem. 265, 4923-4928], except for a greater preference of endonexin for membranes containing phosphatidic acid. Mixing PS and phosphatidylethanolamine (PE) or PS and PI in the same PC vesicle synergistically enhances endonexin-membrane binding, indicating that even lipids with no net charge such as PE may dramatically affect endonexin binding to mixed-lipid membranes. The maximum amount of endonexin able to bind to PS/PC vesicles at 1 mM calcium increases with mole % PS. A simple and general model that treats protein-membrane binding as a two-step process, with adsorption to a membrane surface followed by interaction with specific lipid molecules [Lentz, B. R., & Hermans, J. (1989) Biochemistry 28, 7459-7461], is extended to include the coupled binding of calcium with binding of specific lipid molecules. This extended model accurately predicts trends observed when protein and calcium titrations of endonexin binding to PS/PC vesicles are performed under a wide variety of conditions and suggests that 3-5 calcium ions and 9-18 PS molecules participate in each endonexin-membrane complex.(ABSTRACT TRUNCATED AT 400 WORDS)

Annexin A4↗

Identification of interacting mixed cultures of lactic acid bacteria by their exclusion from a model predicting the acidifying activity of non-interacting mixed cultures.

A model predicting the acidifying activity of mixed cultures of lactic acid bacteria and based on the lack of interaction between the strains has been investigated to identify interacting cultures. Three mixed cultures with Streptococcus thermophilus TH3 and ST7 and Lactobacillus delbrueckii ssp. bulgaricus LB10 were grown on milk. The acidifying activities of the two mixed cultures TH3/LB10 and TH3/ST7 were predicted accurately by the model, with mean prediction errors of 7.7% and 14.1%, respectively. However, the model underestimated the acidifying activity of the mixed culture ST7/LB10, with a mean prediction error of 43.5%, which provides evidence of positive interaction between the strains ST7 and LB10 during acidification.

Animals↗

Prognostic index score and clinical prediction model of local regional recurrence after mastectomy in breast cancer patients.

PURPOSE: To develop clinical prediction models for local regional recurrence (LRR) of breast carcinoma after mastectomy that will be superior to the conventional measures of tumor size and nodal status. METHODS AND MATERIALS: Clinical information from 1,010 invasive breast cancer patients who had primary modified radical mastectomy formed the database of the training and testing of clinical prognostic and prediction models of LRR. Cox proportional hazards analysis and Bayesian tree analysis were the core methodologies from which these models were built. To generate a prognostic index model, 15 clinical variables were examined for their impact on LRR. Patients were stratified by lymph node involvement (<4 vs. >or =4) and local regional status (recurrent vs. control) and then, within strata, randomly split into training and test data sets of equal size. To establish prediction tree models, 255 patients were selected by the criteria of having had LRR (53 patients) or no evidence of LRR without postmastectomy radiotherapy (PMRT) (202 patients). RESULTS: With these models, patients can be divided into low-, intermediate-, and high-risk groups on the basis of axillary nodal status, estrogen receptor status, lymphovascular invasion, and age at diagnosis. In the low-risk group, there is no influence of PMRT on either LRR or survival. For intermediate-risk patients, PMRT improves LR control but not metastases-free or overall survival. For the high-risk patients, however, PMRT improves both LR control and metastasis-free and overall survival. CONCLUSION: The prognostic score and predictive index are useful methods to estimate the risk of LRR in breast cancer patients after mastectomy and for estimating the potential benefits of PMRT. These models provide additional information criteria for selection of patients for PMRT, compared with the traditional selection criteria of nodal status and tumor size.

Adult↗

A new and accurate prediction model for growth response to growth hormone treatment in children with growth hormone deficiency.

OBJECTIVE: To identify parameters which predict individual growth response to recombinant human GH (rhGH) therapy and to combine these parameters in a prediction model. DESIGN: Fifty-eight prepubertal patients with GH deficiency (17 females) participated in this prospective multicenter trial with 1 year of follow-up. METHODS: Auxological measurements, parameters of GH status and markers of bone metabolism were measured at baseline and at 1, 3 and 6 months after the start of rhGH treatment. Correlations with height velocity during the first 12 months of treatment (HV+12) were calculated. Prediction models were derived by multiple regression analysis. RESULTS: The model which best predicted HV+12 combined the following parameters: pretreatment bone age retardation as a fraction of chronological age, pretreatment serum levels of IGF-I, urinary levels of deoxypyridinoline (a marker of bone resorption) after 1 month of treatment and height velocity after 3 months of treatment. This model explained 89% of the variation in HV+12 with a standard deviation of the residuals of 0.93 cm/year. Defining successful rhGH therapy as a doubling of pretreatment height velocity, the model had a specificity of 90% and a sensitivity of 100% in predicting therapeutic success. CONCLUSIONS: This model is an accurate and practicable tool to predict growth response in GH-deficient children. It may help to optimize rhGH therapy by individual dose adjustment and contribute to improved overall outcomes.

Adolescent↗