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PubMed1994

Analysis of variations in mortality rates with small numbers.

OBJECTIVE: We present a Monte Carlo technique to evaluate if observed mortality rates differ from model-predicted rates for situations when the number of deaths is small. DATA SOURCES: We used Medicare hospital claims and model-predicted mortality rates from the Health Care Financing Administration (HCFA) for the 169 acute care hospitals in Georgia. The HCFA data provided model-predicted mortality rates at 30 days postadmission for 17 conditions and procedures of interest. The model-predicted rates calculated by HCFA were adjusted for patient factors, including demographic characteristics, principal diagnosis, and comorbidities. STUDY DESIGN: We test the hypothesis that model-predicted 30-day mortality rates at the 169 hospitals differ significantly from the observed 30-day mortality rates. Our approach uses a test statistic that resembles a chi-square statistic, and Monte Carlo simulations to estimate the distribution of the test statistic under the null hypothesis of no differences between the observed and predicted rates. We illustrate the method using two conceptually similar simulation models. We use results of the simulations to estimate p-values and compare these results with p-values associated with the nominal chi-square distribution. DATA EXTRACTION METHODS: We extracted 30-day observed and predicted mortality rates for Medicare beneficiaries for federal fiscal year 1990 for 17 conditions and procedures of interest. PRINCIPAL FINDINGS: If the number of deaths in some hospitals is small, p-values calculated using the nominal chi-square distribution can be misleading, thus supporting the usefulness of our simulation method. CONCLUSIONS: The Monte Carlo simulation is an appropriate approach to the analysis of hospital mortality or small area analysis for situations in which the number of deaths is small.

Analysis of Variance↗

PubMed2002

Modelling bacterial growth in quantitative microbiological risk assessment: is it possible?

Quantitative microbiological risk assessment (QMRA), predictive modelling and HACCP may be used as tools to increase food safety and can be integrated fruitfully for many purposes. However, when QMRA is applied for public health issues like the evaluation of the status of public health, existing predictive models may not be suited to model bacterial growth. In this context, precise quantification of risks is more important than in the context of food manufacturing alone. In this paper, the modular process risk model (MPRM) is briefly introduced as a QMRA modelling framework. This framework can be used to model the transmission of pathogens through any food pathway, by assigning one of six basic processes (modules) to each of the processing steps. Bacterial growth is one of these basic processes. For QMRA, models of bacterial growth need to be expressed in terms of probability, for example to predict the probability that a critical concentration is reached within a certain amount of time. In contrast, available predictive models are developed and validated to produce point estimates of population sizes and therefore do not fit with this requirement. Recent experience from a European risk assessment project is discussed to illustrate some of the problems that may arise when predictive growth models are used in QMRA. It is suggested that a new type of predictive models needs to be developed that incorporates modelling of variability and uncertainty in growth.

Bacteria↗

PubMed2004

Rescue surgery for unresectable colorectal liver metastases downstaged by chemotherapy: a model to predict long-term survival.

OBJECTIVE: To evaluate the long-term survival of patients resected for primarily unresectable colorectal liver metastases (CRLM) downstaged by systemic chemotherapy and to use prognostic factors of outcome for a model predictive of survival on a preoperative setting. SUMMARY BACKGROUND DATA: Surgery of primarily unresectable CRLM after downstaging chemotherapy is still questioned, and prognostic factors of outcome are lacking. METHODS: From a consecutive series of 1439 patients with CRLM managed in a single institution during an 11-year period (1988-1999), 1104 (77%) initially unresectable (NR) patients were treated by chemotherapy and 335 (23%) resectable were treated by primary liver resection. Chemotherapy mainly consisted of 5-fluorouracil and leucovorin combined to oxaliplatin (70%), irinotecan (7%), or both (4%) given as chronomodulated infusion (87%). NR patients were routinely reassessed every 4 courses. Surgery was reconsidered every time a documented response to chemotherapy was observed. Among 1104 NR patients, 138 "good responders" (12.5%) underwent secondary hepatic resection after an average of 10 courses of chemotherapy. At time of diagnosis, mean number of metastases was 4.4 (1-14) and mean maximum size was 5.2 cm (1-25). Extrahepatic tumor was present in 52 patients (38%). Multinodularity or extrahepatic tumor was the main cause of initial unresectability. All factors likely to be predictive of survival after liver resection were evaluated by uni- and multivariate analysis. Estimation of survival was adjusted on risk factors available preoperatively. RESULTS: Seventy-five percent of procedures were major hepatectomies (> or =3 segments) and 93% were potentially curative. Liver surgery was combined to portal embolization, to ablative treatment, or to a second-stage hepatectomy in 42 patients (30%) and to resection of extrahepatic tumor in 41 patients (30%). Operative mortality within 2 months was 0.7%, and postoperative morbidity was 28%. After a mean follow-up of 48.7 months, 111 of the 138 patients (80%) developed tumor recurrence, 40 of which were hepatic (29%), 12 extrahepatic (9%), and 59 both hepatic and extrahepatic (43%). Recurrence was treated in 52 patients by repeat hepatectomy (71 procedures) and in 42 patients by extrahepatic resection (77 procedures). Survival was 33% and 23% at 5 and 10 years with a disease-free survival of 22% and 17%, respectively. It was decreased as compared with that of patients primarily resected within the same period (48% and 30% respectively, P = 0.01). At the last follow-up, 99 patients had died (72%) and 39 (28%) were alive; 25 were disease free (18%) and 14 had recurrence (10%). At multivariate analysis, 4 preoperative factors were independently associated to decreased survival: rectal primary, > or =3 metastases, maximum tumor size >10 cm, and CA 19-9 >100 UI/L. Mean adjusted 5-year survival according to the presence of 0, 1, 2, 3, or 4 factors was 59%, 30%, 7%, 0%, and 0%. CONCLUSIONS: Modern chemotherapy allows 12.5% of patients with unresectable CRLM to be rescued by liver surgery. Despite a high rate of recurrence, 5-year survival is 33% overall, with a wide use of repeat hepatectomies and extrahepatic resections. Four preoperative risk factors could select the patients most likely to benefit from this strategy.

Adult↗

PubMedDate not supplied

Statistical models for prediction of arterial oxygen and carbon dioxide tensions during mechanical ventilation.

The possibility of constructing statistical models for prediction of alveolar oxygen and carbon dioxide tensions has been investigated in 20 mechanically ventilated patients in acute respiratory failure (ARF). Linear multiple regression analysis using PaCO2 and PaO2 as dependent variables was used to construct (a) models for individual patients, (b) models for specific diagnostic groups and (c) general models (all patients). The coefficient of determination (R2) was highest for the individual patient models (0.38-0.99) and lowest for the general models (0.28-0.49). In order to achieve a high predictive accuracy, models matching individual patients should be constructed on the basis of initial invasive blood gas measurement. Statistically derived models may bring better understanding of the behaviour of factors influencing arterial gas tensions in ARF and may be of value in the management of patients on mechanical ventilation.

Adult↗

PubMed2004

A simple model to predict the sensitivity to change of visual acuity measurements.

BACKGROUND: Estimates of test-retest variability (TRV) in the form of a 95% range have been suggested as providing a cutoff value (or "change-criterion") against which measured acuity changes can be judged to decide whether they are indicative of a clinically important change. This approach is based on ensuring that the specificity of the procedure is 95% in individuals with no real change. In an earlier article we investigated empirically the ability of the procedure to detect varying degrees of change (its sensitivity). In this article, we develop a simple statistical model to examine further the sensitivity of the approach. METHODS: A statistical model was developed, and predictions from the model were compared with empirical visual acuity data. RESULTS: The model predicts that for changes equal in size to the magnitude of the change-criterion, sensitivity will be 50%. For changes 1.65 times the change-criterion, sensitivity is 90% and increasing to 95% for changes 1.84 times the size of the change-criterion. Predicted sensitivities agreed well with those measured empirically. CONCLUSIONS: The 95% range for TRV is often used to decide whether measured changes are indicative of clinically important changes. Evaluating the performance of visual acuity charts using a method analogous to that of estimating the sensitivity and specificity of a screening test highlights some limitations of this method. Use of the 95% range as a change-criterion ensures a high specificity, but a simple statistical model indicates that changes must approach twice the size of the change-criterion before they will be detected with sensitivity in excess of 95%. This has implications for the clinician attempting to assess the reliability of visual acuity charts, and in other similar tests, to detect change.

Humans↗

PubMed2002

A model to predict long-term performance of vapor-phase bioreactors: a cellular automaton approach.

A novel numerical model was constructed to predict performance of vapor-phase bioreactors (VPBs) operated over extended periods. This model incorporates two unique features to simulate changes in pollutant removal efficiency and biomass accumulation: (1) total biomass is divided into two microbial components, active and inactive biomass, and (2) biomass growth and biofilm thickness changes are simulated by means of a cellular automaton (CA) approach. The CA approach, a differential-discrete algorithm, numerically allows the excess quantity of biomass in each numerical element to move toward the biofilm surface as biomass accumulates. One set of experimental bioreactor data was used to estimate unknown model parameters. A 90-day simulation using the estimated parameters agreed with pollutant removal and biomass accumulation profiles determined experimentally. Four additional model simulations using the same estimated model parameters were generally consistent with experimental data collected from a series of toluene-degrading VPBs operated over a range of conditions. Model predictions imply that the decline in bioreactor performance observed over extended operation was caused by a decline in the active biomass fraction and a decrease in the biofilm specific surface area. This CA model provides insight into biomass accumulation during complex bioreactor operation and improves our capability to predict long-term VPB performance.

Biofilms↗

PubMed2002

Application of a model to predict cyanobacterial growth patterns in response to climatic change at Farmoor reservoir, Oxfordshire, UK.

The cyanobacterial growth for the next 90 years at Farmoor Reservoir, Oxfordshire is predicted using the cyanobacterial growth model, CLAMM, with data obtained from HADCM2 climate change model. It is predicted that solar radiation at the water-body surface will decrease slightly due to increased cloud cover. Predictions of cyanobacterial growth indicate little change in total production although the main summer growing season may be extended. It is also suggested that increased wind velocities may affect the frequency of 'blooming incidents'.

Biomass↗

PubMed2001

A model for predicting endotoxin concentrations in metalworking fluid sumps in small machine shops.

METHODS: In British Columbia, Canada, nineteen small machine shops which used water-based metalworking fluids (MWF) were examined. One bulk MWF sample was taken from each independent sump (N=140) and tested for endotoxin using the Limulus Amoebocyte Lysate assay. Factors that might influence the MWF sump endotoxin concentration were investigated using mixed effect multiple regression modelling to control for repeated measures within shops. RESULTS: The geometric mean (GM) endotoxin concentration was 6791 EU/ml. Contamination of MWF with tramp oil, MWF pH, MWF temperature, and MWF type were significant predictors of sump fluid endotoxin concentration (model P=0.0001, ordinary least squares R(2) =0.36). Concentrations of endotoxin in sump fluids were increased by MWF contamination with tramp oils such as hydraulic oils, preservative oils, spindle oils, slidway lubricants, gear lubricants, and greases (model predicted GM=17400 EU/ml vs. 1600 EU/ml without tramp oil). Concentrations were also elevated where pH was lower than 8.5 (predicted GM=10600, vs 3600 EU/ml for pH 8.5 to 9.5), where soluble fluids were used (predicted GM=11800 vs. 2800 EU/ml for synthetic fluids), and where sump fluid temperatures were higher (predicted GM=2600 EU/ml at 11 degrees C vs. 21500 EU/ml at 32 degrees C). The within-shop correlation of sump bulk fluid endotoxin concentrations was 38%. CONCLUSIONS: Minimizing tramp oil contamination, using synthetic fluids, and monitoring pH and temperature would be valuable tools for controlling endotoxin contamination in MWF sumps. In addition, since there was correlation within-shop, contamination of one sump in a shop may suggest changing the fluids in all.

Endotoxins↗

PubMed1991

Intracerebral hemorrhage: external validation and extension of a model for prediction of 30-day survival.

We report validation of a previously reported logistic regression model for predicting 30-day survival after supratentorial intracerebral hemorrhage using independent, prospectively collected data. The original model, using initial Glasgow Coma Scale score, hemorrhage size, and pulse pressure, accounted for mortality or survival at 30 days in 92% of patients in the Pilot Stroke Data Bank with a sensitivity of 0.84 and a specificity of 0.96. For external validation, the model was used to predict 30-day status for each patient in the Main Phase Stroke Data Bank for whom complete risk factor information was available. Overall, 90% of patients' outcomes were correctly predicted with a sensitivity of 0.85 and a specificity of 0.92. Two factors not collected in the Pilot Stroke Data Bank, hyperglycemia and intraventricular hemorrhage extension, were assessed to determine if they provided additional predictive information on 30-day mortality. Intraventricular hemorrhage extension contributed significant predictive information in a logistic regression, whereas hyperglycemia did not. The resulting four-factor model with an interaction term (intraventricular hemorrhage extension and Glasgow Coma Scale score) correctly classified the survival status of 94% of patients at 30 days. A more general outcome, death or failure to achieve a "good" Activities of Daily Living Score by one year, was analyzed with respect to the same four factors. The resulting model correctly classified 95% of the patients in the cohort.

Blood Glucose↗

PubMed2007

A mathematical model for predicting controlled release of bioactive agents from composite fiber structures.

A mathematical model for predicting bioactive agent release profiles from core/shell fiber structures was developed and studied. These new composite fibers, which combine good mechanical properties with desired protein release profiles, are designed for use in tissue regeneration and other biomedical applications. These fibers are composed of an inner dense polymeric core surrounded by a porous bioresorbable shell, which encapsulates the bioactive agent molecules. The model is based on Fick's second law of diffusion, and on two major assumptions: (a) first-order degradation kinetics of the porous shell, and (b) a nonconstant diffusion coefficient for the bioactive agent, which increases with time because of degradation of the host polymer. Three factors are evaluated and included in this model: a porosity factor, a tortuosity factor, and a polymer concentration factor. Our study indicates that the model correlates well with in vitro release results, exhibiting a mean error of less than 2.2% for most studied cases. In this study, the model was used for predicting protein release profiles from fibers with shells of various initial molecular weights and for predicting the release of proteins with various molecular weights. This new model exhibits a potential for simulating fibrous systems for a wide variety of biomedical applications.

Biocompatible Materials↗

PubMed1988

Mathematical models to predict behaviour of tumours?

Mathematical modeling is an important tool in science that allows the investigator to examine phenomena that are not easily studied by direct experiment. The growth of neoplasms and their response to treatment are processes that appear particularly well suited for study by this approach. The ready availability of inexpensive powerful microcomputers and sophisticated software makes this research avenue open to all experimental and clinical oncologists.

Drug Resistance↗

PubMed2004

Visual perception of extent and the geometry of visual space.

The question of how perceived extents are related to the corresponding physical extents is a very old question that has not been satisfactorily answered. The common model is that perceived extent is proportional to the product of image size and perceived distance. We describe an experiment that shows that perceived extents are substantially larger than this model predicts. We propose a model that accounts for our results and a large set of other results. The principal assumption of the model is that, in the computation of perceived extent, the visual angle signal undergoes a magnifying transform. Extent is often perceived more accurately than the common model predicts, so the computation is adaptive. The model implies that, although the perception of location and the perception of extent are related, they not related by Euclidean geometry, nor by any metric geometry. Nevertheless, it is possible to describe the perception of location and extent using a simple model.

Humans↗

PubMed1986

A model for predicting utilization of psychiatric facilities.

This paper develops a parsimonious model for predicting utilization of a regional system of psychiatric facilities based on census data. The model combines conceptual simplicity with readily-available data sources. In practical terms, the model removes the need to undertake comprehensive and expensive utilization surveys. In theoretical terms, the model indicates that the fundamental relationship between utilization rates and key social indicators is stable through time. Although further testing is necessary, it would seem that these key indicators can provide reasonable estimates of psychiatric morbidity for up to ten years in the future.

Forecasting↗

PubMed2004

The burden of treatment failure in type 2 diabetes.

OBJECTIVE: In type 2 diabetes, therapies to maintain blood glucose control usually fail after several years. We estimated the glycemic burden that accumulates from treatment failure and describe the time course and predictors of failure. RESEARCH DESIGN AND METHODS: A prospective, population-based study using retrospective observational data. We identified all 7208 complete courses of treatment with nondrug therapy, sulfonylurea monotherapy, metformin monotherapy, and combination oral antihyperglycemic therapy between 1994 and 2002, inclusive, among members of the Kaiser Permanente Northwest Region. We calculated mean cumulative glycemic burden, defined as HbA(1c)-months >8.0 or 7.0% for each treatment. We then measured the likelihood that the next HbA(1c) would exceed 8.0 and 7.0% after HbA(1c) exceeded each of ten hypothetical treatment thresholds. Finally, we estimated multivariate logistic regression models to predict when HbA(1c) would continue to deteriorate. RESULTS: In this well-controlled population, the average patient accumulated nearly 5 HbA(1c)-years of excess glycemic burden >8.0% from diagnosis until starting insulin and about 10 HbA(1c)-years of burden >7.0%. Whenever patients crossed the American Diabetes Association-recommended treatment threshold of 8.0%, their next HbA(1c) result was as likely to be <8.0 as >8.0%. Multivariate prediction models had highly statistically significant coefficients, but predicted <10% of the variation in future HbA(1c) results. CONCLUSIONS: Clinicians should change glucose-lowering treatments in type 2 diabetes much sooner or use treatments that are less likely to fail. An action point at 7.0% or lower is more likely to prevent additional deterioration than the traditional action point of 8.0%.

Blood Glucose↗

PubMedDate not supplied

[A selection model for predicting poultry meat productivity].

A model for estimating growth intensity parametres in poultry in early ontogenesis has been worked out. The growth intensity parametres were studied; high efficiency of using the model for prognosis of meat productivity in poultry at the age of 49-56 days are shown. The application techniques of the model offered for increasing poultry growth energy were examined.

Animals↗

PubMed1987

Are hospital managers served by current models for predicting financial distress?

During the last decade there have been major competitive changes in the health care industry. This more dynamic environment has forced hospitals to emphasize efficiency in their operations. One consequence is an increased concern with financial condition and, subsequently, with the ability to predict financial distress. This paper synthesizes several important studies on firm failure in the field of finance and compares them with recent studies of hospital survival. The inescapable conclusion is that most models predicting hospital financial distress are restricted, flawed, or both. As result, one must question whether such applications effectively serve hospital managers or public policy makers.

Data Collection↗

PubMed1997

Assessment of total body water using bioelectrical impedance analysis in neonates receiving intensive care.

AIMS: To determine the most suitable anthropometric and impedance measures and current frequency for the application of bioelectrical impedance to neonates receiving intensive care; and to derive predictive models for the estimation of total body water. METHODS: Twenty eight babies (median gestational age 30.5 weeks, range 24-38; median birthweight 1.388 kg, range 0.690-3.510) were each studied once during the first week after birth. Total body water was first measured by the method of dilution of isotopic water (H218O). Bioelectrical measurements were made using the tetrapolar surface electrode method from four main distal limb positions (right hand-right foot; right hand-left foot; left hand-left foot; left hand-right foot), the left upper arm-left thigh position and the left scapula-right buttock position, and using six frequencies ((500, 250, 100, 50, 10 and 5 kHz). Regression models, to predict total body water, which were both independent and dependent of body weight on the day of study, were derived. RESULTS: Resistance readings at 50 kHz obtained from the distal limb positions performed best. There was no difference between the distal limb positions. There was no difference in the goodness of fit of the models when using each of three indices of conductor length, foot, spine and sternum. The model total body water (litres) (TBW) = 0.016 + 0.674 body-weight(kg)-0.038 wt2 + 3.84 foot length (cm)2/resistance (50 kHz in OHMS) performed best, accounting for 99.5% of the variation in TBW, with a 95% prediction interval of 165 ml. The model TBW = 0.144 + 15.518 foot length (cm)2/resistance (50 kHz in ohms) accounted for 96.4% of the variation and had a 95% prediction interval of 420 ml. CONCLUSIONS: Bioelectrical impedance analysis is a simple, non-invasive method of estimating total body water in neonates receiving intensive care. It can be applied to both the assessment of changes in body water and body composition.

Body Composition↗

PubMed2002

Sexual dimorphism in the energy content of weight change.

BACKGROUND: The energy content of weight change is assumed to be sex- and age-neutral at 3,500 kcal/pound or 32.2 MJ/kg. OBJECTIVES: As sexual dimorphism in body composition generally exists in mammals, the primary hypothesis advanced and tested was that the energy content of weight change differs between men and women. DESIGN: The energy content of 129 adult men and 287 women was measured by neutron activation analysis. Cross-sectional energy content prediction models were developed and then evaluated in two longitudinal samples: one that used the same methods in 26 obese women losing weight; and the other a compilation of 18 previously reported weight change-body composition studies. RESULTS: Multiple regression modeling identified weight, sex, age and height as total energy content predictor variables with significant sex x weight (P<0.001) and age x weight (P<0.001) interactions; total model r(2) and s.e.e. were 0.89 and 107.3 MJ, respectively. The model's predictive value was supported in both longitudinal evaluation samples. Model calculations using characteristics of representative adults gaining or losing weight suggested that the energy content of weight change in women (approximately 30.1-32.2 MJ/kg) is near to the classical value of 32.2 MJ/kg and that in men the value is substantially lower, approximately 21.8-23.8 MJ/kg. The predicted energy content of weight change increases by about 10% in older (age approximately 70 y) vs younger (approximately 35 y) men and women. CONCLUSIONS: Sexual dimorphism and age-dependency appears to exist in the estimated energy content of weight change and these observations have important clinical and research implications.

Adult↗