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PubMed2006

Characteristics and modeling of Escherichia coli growth in pouched food.

Characteristics of the growth kinetics of Escherichia coli cells in pouched mashed potatoes under various conditions were studied with a mathematical model. Bacterial cells were inoculated in sterile mashed potatoes and then sealed in vinyl pouches, in which a very small amount of air was included. The growth curves of cells in the pouched mashed potatoes at constant temperature (12-34 degrees C) were sigmoidal with time on a semi-logarithmic plot and were successfully described with a new logistic model recently developed by us. The rate constant of growth showed a highly linear relationship to the temperature with the square-root model, and the lag period was longer at lower temperatures. The growth curve in glass tubes containing a large volume of air was similar to that in pouches, showing that the rate of growth was not affected by the volume of the surrounding air. The growth curves in pouched mashed potatoes were very similar to those in nutrient broth or on the surface of nutrient agar, which we previously reported. These results suggested that the growth kinetics of the bacterial cells under various conditions of rich nutrition might be almost identical, and can be described with a simple growth model like ours.

Escherichia coli↗

PubMed1977

On the treatment of grouped observations in life studies.

Assuming a model of proportional failure rates, Cox (1972) presents a systematic study of the use of covariates in the analysis of life time. The treatment of tied observations is a particularly troublesome point in both theory and application. It appears that grouping rather than discrete time is the right way to handle ties. This paper studies methodology for grouped observations. A logistic model, which makes explicit use of Cox's earlier binary data methods, is introduced and illustrated with a numerical example. The model leads back to Cox's proportional failure rates when the lengths of the grouping intervals approach zero. This limiting process provides some enlightenment on controversial issues such as ignoring intervals in which no failures occur, determining whether the covariates may be functions of time, and treating ties.

Humans↗

PubMed2003

Nuchal translucence incorporated into a one-stage multifactorial screening model for Down syndrome prediction at second-trimester pregnancy.

The aim of this study was to achieve one-stage screening for trisomy 21 using a combination of nuchal translucency (NuT) measurement and maternal serum alpha-fetoprotein (AFP) and free beta-human chorionic gonadotrophin (hCG) biochemistry levels in the second trimester among a high-risk study population. From January 1998 to June 2001, 45 cases of trisomy 21 were prenatally found and confirmed in the hospital-based cytogenetic diagnosis laboratory. A total of 867 normal singleton pregnancies were enrolled as controls from the antenatal care clinics in the hospital. All study and control subjects between 13 weeks and 18 weeks of gestation with a mean age of 15.2 +/- 1.3 weeks underwent one-stage nuchal translucence measurements and maternal serum biochemical screening for Down syndrome. The final logistic model contained beta-hCG (multiples of the gestational median or MoM), maternal age (matA), nuchal translucence (NuT MoM) and AFP (MoM) as covariates. Also, the estimated coefficients of the regression were highly significant. This model provided the estimated probability of Down syndrome as follows: Pr (Down syndrome) = exp (Z)/ [1 + exp (Z)], where Z = -11.18 + 0.64 x (beta-hCG MoM) + 0.25 x matA + 1.32 x NuT MoM -2.23 x AFP MoM. The logistic regression with estimated coefficients was installed in a Palm digital assistant (PDA) equipped with Excel (Microsoft). The risk probability of Down syndrome could be readily calculated after inputting data for all four predictor variables.

Adult↗

PubMed2002

Mixture models for linkage analysis of affected sibling pairs and covariates.

To determine the genetic etiology of complex diseases, a common study design is to recruit affected sib/relative pairs (ASP/ARP) and evaluate their genome-wide distribution of identical by descent (IBD) sharing using a set of highly polymorphic markers. Other attributes or environmental exposures of the ASP/ARP, which are thought to affect liability to disease, are sometimes collected. Conceivably, these covariates could refine the linkage analysis. Most published methods for ASP/ARP linkage with covariates can be conceptualized as logistic models in which IBD status of the ASP is predicted by pair-specific covariates. We develop a different approach to the problem of ASP analysis in the presence of covariates, one that extends naturally to ARP under certain conditions. For ASP linkage analysis, we formulate a mixture model in which a disease mutation is segregating in only a fraction alpha of the sibships, with 1 - alpha sibships being unlinked. Covariate information is used to predict membership within groups; in this report, the two groups correspond to the linked and unlinked sibships. For an ASP with covariate(s) Z = z and multilocus genotype X = x, the mixture model is alpha(z)g(x; lambda) + [1 - alpha(z)]g(0)(x), in which g(0)(x) follows the distribution of genotypes under the null IBD distribution and g(x; lambda) allows for increased IBD sharing. Two mixture models are developed. The pre-clustering model uses covariate information to form probabilistic clusters and then tests for excess IBD sharing independent of the covariates. The Cov-IBD model determines probabilistic group membership by joint consideration of covariate and IBD values. Simulations show that incorporating covariates into linkage analysis can enhance power substantially. A feature of our conceptualization of ASP linkage analysis, with covariates, is that it is apparent how data analysis might evaluate covariates prior to the linkage analysis, thus avoiding the loss of power described by Leal and Ott [2000] when data are stratified.

Algorithms↗

PubMed2001

Reduction in mortality after inappropriate early discharge from intensive care unit: logistic regression triage model.

OBJECTIVE: To develop a predictive model to triage patients for discharge from intensive care units to reduce mortality after discharge. DESIGN: Logistic regression analyses and modelling of data from patients who were discharged from intensive care units. SETTING: Guy's hospital intensive care unit and 19 other UK intensive care units from 1989 to 1998. PARTICIPANTS: 5475 patients for the development of the model and 8449 for validation. MAIN OUTCOME MEASURES: Mortality after discharge and power of triage model. RESULTS: Mortality after discharge from intensive care was up to 12.4%. The triage model identified patients at risk from death on the ward with a sensitivity of 65.5% and specificity of 87.6%, and an area under the receiver operating curve of 0.86. Variables in the model were age, end stage disease, length of stay in unit, cardiothoracic surgery, and physiology. In the validation dataset the 34% of the patients identified as at risk had a discharge mortality of 25% compared with a 4% mortality among those not at risk. CONCLUSIONS: The discharge mortality of at risk patients may be reduced by 39% if they remain in intensive care units for another 48 hours. The discharge triage model to identify patients at risk from too early and inappropriate discharge from intensive care may help doctors to make the difficult clinical decision of whom to discharge to make room for a patient requiring urgent admission to the unit. If confirmed, this study has implications on the provision of resources.

APACHE↗

PubMed1998

A linear model method for rank measures of association from longitudinal studies with fixed conditions (visits) for data collection and more than two groups.

Several statistical methods are available for the analysis of responses with ordinal categories or continuous distributions for the respective visits in longitudinal studies. This paper discusses an alternative nonparametric strategy for studies with more than two groups through Mann-Whitney rank measures of association for all pairs of groups. The proposed method is based on U-statistic theory, and it applies a linear or linear logistic model to the Mann-Whitney estimators for the probabilities of better response for each group relative to each of the others. In addition, the ways of adjusting for covariables and managing stratification factors are explained. Analysis of parallel dose-response relationships for two treatments is illustrated for the proposed method with data from a multicenter study with repeated measurements. A nonparametric estimator for relative potency is provided from the method.

Algorithms↗

PubMed1995

Predicting common bile duct lithiasis: determination and prospective validation of a model predicting low risk.

BACKGROUND: The aim of this two-part prospective study was: (1) to identify simple, noninvasive, preoperative factors associated with low or very low risk of common bile duct lithiasis (CBDL); and (2) to test the validity of the statistical model obtained during Part One by the postcholecystectomy follow-up of patients classified into a low-risk group. PATIENTS AND METHODS: In Part One of the study, preoperative clinical, biologic, and ultrasonographic data, and intraoperative cholangiographic findings were collected from 503 consecutive patients undergoing cholecystectomy for symptomatic lithiasis from 1985 to 1989. Using the data obtained in Part One, a linear logistic model was used prospectively in Part Two to determine the prediction of absence of CBDL in 279 consecutive patients. No jaundice, normal transaminase levels, common bile duct (CBD) diameter < 8 mm, and no intrahepatic duct enlargement defined the low-risk group of CBDL. RESULTS: In Part One, CBDL was present in 84 (17%) of all patients. Five parameters were used to classify 73% of all patients as low risk of CBDL and 27% as high risk. In the low-risk groups, CBDL was present in 1% of 116 cases with acute gallbladder complications, and 5% of 250 cases with no acute gallbladder complications. In Part Two, 171 (61%) patients were classified in the low-risk group (Group 1), and CBD stones were not sought by any additional preoperative investigations or intraoperative cholangiography (IOC). One hundred eight patients (39%) were considered at risk of CBDL (Group 2). Mean follow-up was 20.6 months (median 19); 2 patients (1%) in the low-risk group presented a symptomatic retained stone. CONCLUSIONS: This study validated this simple model for predicting risk of CBDL and avoiding invasive preoperative investigations--as well as IOC--in more than 60% of symptomatic cholelithiases. In addition, this model seemed useful for defining patients in whom further exploration for CBDL was justified, since 42 (39%) of the 108 Group 2 patients were proved to have CBDL.

Analysis of Variance↗

PubMed1994

[Epidemiological study on risk factors of cervical cancer].

The relationship between cervical cancer and risk factors including virus infection of cervix was studied with methods of molecular and serological epidemiology. DNA extracted from cervical biopsies taken from 57 cases and 51 controls were tested for HPV6/11, HPV16/18 by Dot-blot hybridization and for HSV-2 by PCR. Sera were detected for HCMV-IgM by ELISA. The results and risk factors were analyzed by logistic regression model. The multiple logistic regression model results showed that HPV16/18 infection was an important risk factor, the infection rate was significantly higher in the group of cervical cancer, the OR was 31.96. Other risk factors were the educational level and the number of birth, the OR were 0.57 and 1.85, respectively. The difference of HSV-2 infection of cervix and HCMV-IgM in serum was not significant between the two groups.

Case-Control Studies↗

PubMed2005

A comparison of fitting growth models with a genetic algorithm and nonlinear regression.

A genetic algorithm (GA), an optimization procedure based on the theory of evolution, was compared with nonlinear regression for the ability of the 2 algorithms to fit the coefficients of poultry growth models. It was hypothesized that the nonlinear approach of using GA to define the parameters of growth equations would better fit the growth equations than the use of nonlinear regression. Two sets of growth data from the literature, consisting of male broiler BW grown for 168 and 170 d, were used in the study. The growth data were fit to 2 forms of the logistic model, the Gompertz, the Gompertz-Laird, and the saturated kinetic models using the SAS nonlinear algorithm (NLIN) procedure and a GA. There were no statistical differences for the comparison of the residuals (the difference between observed and predicted BWs) of growth models fit by a GA or nonlinear regression. The plotted residuals for the nonlinear regression and GA-determined growth values confirmed observations of others that the residuals have oscillations resembling sine waves that are not represented by the growth models. It was found that GA could successfully determine the coefficients of growth equations. A disadvantage of slowness in converging to the solution was found for the GA. The advantage of GA over traditional nonlinear regression is that only ranges need be specified for the parameters of the growth equations, whereas estimates of the coefficients need to be determined, and in some programs the derivatives of the growth equations need to be identified. Depending on the goal of the research, solving multivariable complex functions with an algorithm that considers several solutions at the same time in an evolutionary mode can be considered an advantage especially where there is a chance for the solution to converge on a local optimum when a global optimum is desired. It was concluded that the fitting of the growth equations was not so much a problem with the fitting methodology as it is with the form of the equation.

Algorithms↗

PubMed1996

Mapping quantitative trait loci for complex binary diseases using line crosses.

A composite interval gene mapping procedure for complex binary disease traits is proposed in this paper. The binary trait of interest is assumed to be controlled by an underlying liability that is normally distributed. The liability is treated as a typical quantitative character and thus described by the usual quantitative genetics model. Translation from the liability into a binary (disease) phenotype is through the physiological threshold model. Logistic regression analysis is employed to estimate the effects and locations of putative quantitative trait loci (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). Simulation studies show that properties of this mapping procedure mimic those of the composite interval mapping for normally distributed data. Potential utilization of the QTL mapping procedure for resolving alternative genetic models (e.g., single- or two-trait-locus model) is discussed.

Chromosome Mapping↗

PubMed1987

Making the most of multiple measurements in estimating carrier probability in Duchenne muscular dystrophy: the Bayesian incorporation of repeated measurements using logistic discrimination.

In carrier detection studies, females-at-risk are usually tested several times if the results are ambiguous, whereas subjects in the control and obligate carrier reference groups may not be tested as often. The question is how to incorporate the multiple measurements most effectively with information in the family pedigree into combined carrier risks. Sets of measurements on individuals are not independent, but are related with the correlation coefficient 0 less than rho less than 1. We have developed a procedure for incorporating repeated measurements on individuals and their a priori chance of having the disease into logistic models. This procedure utilizes the set of measurements and an estimate of rho. We describe application of this procedure to carrier detection in Duchenne muscular dystrophy (DMD) using serum creatine kinase (CK) measurements as the biochemical indicator of carrier status. Estimates of rho for controls and obligate DMD carriers did not differ significantly from 0.5. Repeated testing with use of rho = 0.5 significantly decreased the median logistic carrier probability for controls and increased it for carriers. In some cases four to six rather than the three CK tests conventionally used in genetic counseling were necessary to obtain a stable logistic carrier probability for a subject.

Creatine Kinase↗

PubMed1997

The crankshaft phenomenon after posterior Harrington fusion in skeletally immature patients with thoracic or thoracolumbar idiopathic scoliosis followed to maturity.

STUDY DESIGN: This retrospective study evaluated the progression of deformity after posterior fusion by reviewing 63 consecutive patients with idiopathic scoliosis who were all in Risser sign 0 at the time of surgery. All patients were observed beyond the time of skeletal maturity. Average follow-up time was 9 years and 8 months (range, 5-16 years). OBJECTIVES: To investigate the risk factors for the crankshaft phenomenon after posterior fusion and to build a model for predicting the probability of curve progression until maturation of growth. SUMMARY OF BACKGROUND DATA: There remains considerable controversy concerning the incidence, risk factors, and necessity of combined anterior fusion to prevent the crankshaft phenomenon in patients who are skeletally immature. METHODS: Serial radiographs were measured for Cobb angle, apical rotation according to Perdriolle, and apical rib-vertebra angle of Mehta. Multivariate and univariate logistic regression analysis was performed using seven potential predictors as independent variables and Cobb angle progression and rotational progression as dependent variables. RESULTS: Average progression of deformity was 3 degrees Cobb angle (range, -8-16 degrees) and 3 degrees Perdriolle rotation (range, -9-17 degrees). Progression of deformity more than 5 degrees of either Cobb angle or rotation was observed in 22 (35%) of 63 curves with 7 (11%) of 63 curves greater than 10 degrees. Chronologic age and skeletal age were found to be significantly associated with progression of deformity in univariate analysis. In multivariate analysis, only skeletal age seemed to be independently prognostic. The authors tried to build the logistic model using the three factors of chronologic age, skeletal age, and apical rib-vertebra angle. This model correctly classified 81% of all patients as progressive or nonprogressive. The positive predictive value was 90%. CONCLUSIONS: The results showed that patients with chronologic age of 11 years of younger, especially those with a skeletal age of 10 years or younger, had a high estimated probability of progression of deformity. The progression was fairly moderate, however, with an average Cobb angle of 9 degrees and average rotation of 7 degrees, which neither the patients nor the surgeon believed was of such magnitude as to warrant routine combined anterior fusion.

Adolescent↗

PubMed1993

A model to predict survival at time of postcardiotomy intraaortic balloon pump insertion.

To facilitate timely application of new forms of cardiac support to patients at highest risk after cardiotomy despite conventional support with the intraaortic balloon pump, an accurate prediction of survival must be available at the time of weaning from cardiopulmonary bypass. We, therefore, acquired 240 demographic, disease, and perioperative characteristics of 322 patients (mortality rate, 48.4%) who required IABP support to separate from bypass. Four variables available before or within 10 minutes of the first attempt at weaning from bypass significantly predicted mortality by stepwise logistic regression: complete heart block as demonstrated by need for temporary pacing at weaning (p < 0.001), advanced age (p < 0.002), preoperative blood urea nitrogen concentration (p = 0.036), and female sex (p = 0.048). An equation generated by the logistic model predicted a 72.2% survival rate in the 25% of patients at least risk (actual survival rate, 71.6%); in the 25% at greatest risk, death was predicted in 73.0%, and the actual mortality rate was 74.1%. The equation was then prospectively applied to 330 intraaortic balloon pump-supported patients managed at another institution. The overall mortality rate there was 41.2%; in the 25% at least risk, predicted survival rate was 70.5% (actual survival rate, 77.1%), and in the 25% at greatest risk, predicted mortality rate was 75.7% (actual mortality rate, 62.7%). Thus, retrospectively at one institution and prospectively at another, the equation generated by this model based only on data available at the time of weaning from bypass was able to define one subgroup of patients 2.6 to 2.7 times as likely to die as another subgroup from within similar cohorts.(ABSTRACT TRUNCATED AT 250 WORDS)

Aged↗

PubMed1998

Pregnancy and other risk behaviors among adolescent girls in Ohio.

PURPOSE: The purpose of this study was to determine whether teenage girls who had been pregnant were more likely to engage in other risk or problem behaviors than girls who had had sexual intercourse without becoming pregnant. METHODS: The 1993 Ohio Youth Risk Behavior Survey was administered to a random sample of 2461 high school students. A subset of 592 girls (mean age 16.1 +/- 1.1 years, 69.2% Caucasian, 24.1% African-American, 2.4% Hispanic, 4.3% other) reported sexual activity (SA) on the anonymous survey. Demographic factors plus risk and problem behaviors were compared between 98 girls who had been pregnant and 494 girls who had never been pregnant using Chi-square analysis. Risk and problem behaviors were classified into four distinct groups: recent risk behaviors, age of onset of behavior, lifetime behavior, and general behavior. Variables which were univariately significant at p < 0.15 were considered in one of four stepwise multiple logistic regression models based on behavior type, with demographic factors considered in all four models. The final logistic regression model was developed using variables which were significant at p < 0.01. Variables which were significantly associated with pregnancy were summarized as odds ratios (OR) and 99% confidence intervals (CI); these ORs were adjusted for the effects of the other variables in the model. RESULTS: Pregnancy was more common in girls of color than in Caucasian girls (OR 99% and CI, 2.09, 1.06-4.11) and in older girls than in younger girls (1.52, 1.12-2.08). Among SA girls, weapon carrying in the past 30 days (4.06, 1.75-9.42) was significantly associated with pregnancy, whereas alcohol use in the past 30 days (0.37, 0.18-0.76) was less likely to be associated with pregnancy. The risk of pregnancy increased 1.75 times (1.26-2.43) for each additional sexual partner. Girls who had tried cocaine were 4.88 times (1.40-16.95) more likely to have been pregnant, and the risk of having been pregnant increased 1.43 times (1.14-1.80) for each additional year of SA. Past history of sexually transmitted disease (3.50, 1.28-9.55) was associated with increased pregnancy risk. CONCLUSIONS: Girls who had been pregnant also had engaged in other risk behaviors, including recent weapon carrying and cocaine use. A history of previous sexually transmitted diseases plus increasing numbers of partners add to the risk of pregnancy. Counseling and educational efforts should continue to identify teens at risk both to prevent pregnancy and to decrease associated risks.

Adolescent↗

PubMed1996

PRISM score evaluation to predict outcome in pediatric patients on admission at an emergency department.

This study was undertaken in order to evaluate for the first time the usefulness of PRISM score to predict outcome in pediatric patients in the Intensive Care Area of the Emergency Department at the Instituto Nacional de Pediatría in Mexico City. A prolective evaluation of PRISM score was done using 100 consecutive pediatric patients admitted to INP-ED between July and November 1992 and considered critically ill by the attending pediatricians to calculate by a lineal logistic model the expected mortality and compare with the observed one. Using a cut-off of r = 0, we evaluated at the same time the sensitivity, specificity and efficiency of this score. Fifty-eight patients were male and 42 were female. The mean age was 51 months with a range of 3 days -192 months. PRISM score for survivors was in general 8.7 +/- 7.2 and 25.8 +/- 14 for nonsurvivors (p < 0.001). Based on the logistic regression coefficients defined by Pollack et al., our sample of 100 patients was estimated to expect 12.91 deaths whereas in fact 11 were observed. Inspection of the survival rates across the different categories of expected mortality showed agreement and consistency in relation to original reports (9). The sensitivity, specificity and efficiency in general were 1.0, 0.98 and 0.98, respectively. The PRISM is an objective and efficient method which helps physicians to predict patients' outcome and risk of mortality, providing the medical staff with an epidemiological criteria. Additionally, it may be helpful in decision-making for ICU admissions and correct identification of patients who can benefit from that level of care.

Adolescent↗

PubMed1990

In-vitro fertilization: influence of women's age on pregnancy rates.

An analysis of the influence of women's age on the results of in-vitro fertilization was performed, using 5590 attempts collected during the year 1986. Increasing age was found to be related to decreased success rates from 19.8% per attempt below the age of 25 years, to 9% per attempt at 40 years or more. A cut-off point was found between the ages of 36 and 37 years, using a mathematical model. The decrease was related to a reduction in oocyte production (4.3 +/- 2.8 at 25 years or less and 3.3 +/- 2.1 at 40 years or more, P less than 0.001), and to a reduced implantation rate, whatever the number of transferred embryos. These findings were not due to spouse's age, rank of attempt, infertility diagnosis or oocyte stimulation regimen, since the effect of age remained significant when a logistical model including these confounders was applied. Finally, a woman's age must be considered as a prognostic factor when IVF is proposed to infertile couples.

Adult↗

PubMed2001

Comparison of maximum specific growth rates and lag times estimated from absorbance and viable count data by different mathematical models.

Maximum specific growth rate (mu(max)) and lag time (lambda) were estimated from viable count and absorbance data and compared for different microorganisms, incubation systems and growth conditions. Data from 176 growth curves and 120 absorbance detection times of serially diluted cultures were evaluated using different mathematical growth models. Accurate estimates of mu(max) and lambda were obtained from individual absorbance growth curves by using the Richard model, with values of the parameter m fixed to 0.5, 1.0 or 2.0 to describing different degrees of growth dampening, as well as from absorbance detection times of serially diluted cultures. It is suggested to apply the two techniques complementarily for accurate, rapid and inexpensive estimation of microbial growth parameter values from absorbance data. In contrast, considerable limitations were demonstrated for the ability of the Exponential, the Gompertz and the Logistic models to estimate mu(max) and lambda values accurately from absorbance data. Limitations of these models were revealed due the wide range of growth conditions studies.

Bacteria↗

PubMed2004

Testing a maternal attachment model of behavior problems in early childhood.

BACKGROUND: The purpose of the present study was to test a maternal attachment model of behavior problems in early childhood using phase I data from the NICHD Study of Early Child Care, a prospective study of 1,364 children from birth through sixth grade. METHODS: Mothers' and caregivers' ratings of children's internalizing and externalizing problems at age three were regressed separately on a set of fifteen predictors that included security and disorganization scores from 15, 24, and 36 months using hierarchical and logistical modeling. RESULTS: There were three main findings. First, Q-set mother-child attachment security, based on home observations at 24 months, provided the best evidence that attachment was associated with behavior problems, especially above-average levels of problems. Second, insecurity in the 36-month modified Strange Situation predicted mothers' and caregivers' ratings of internalizing problems for boys and girls as well as their ratings of externalizing problems for boys. Third, maternal depressive symptoms predicted mothers' ratings of internalizing and externalizing problems. CONCLUSIONS: There are meaningful associations between attachment insecurity and behavior problems as assessed not only by mothers but also by caregivers.

Child↗