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PubMed2005

Linear parameter haplotype models with stratification.

OBJECTIVES: The question of interest is estimating the relationship between haplotypes and an outcome measure, based upon unphased genotypes. The outcome of interest might be predicting the presence of disease in a logistic model, predicting a numeric drug response in a linear model, or predicting survival time in a parametric survival model with censoring. Explanatory variables may include phased haplotype design variables, environmental variables, or interactions between them. METHODS: We extend existing generalized linear haplotype models to parametric survival outcomes. To improve the stability of model variance estimates, a profile likelihood solution is proposed. An adjustment for population stratification is also considered. Here we investigate data sampled from known 'strata' (e.g., gender or ethnicity) that influence haplotype prior probabilities and thus the regression model weights. Differing linear model variance estimates, and the effect of stratification and departures from Hardy-Weinberg Equilibrium (HWE) on parameter estimates, are compared and contrasted via simulation. RESULTS: From simulations, we observed an improvement in statistical power when using a solution to profile likelihood equations. We also saw that stratification had little impact on estimates. Haplotypes that are not in HWE had a negative impact on power to test hypotheses. Finally, profile likelihood solutions for haplotypes deviating from HWE had improved power and confidence interval coverage of regression model coefficients.

Carcinoma, Squamous Cell↗

PubMed1990

Analysis of poultry fertility data.

Single Comb White Leghorn (SCWL) hens were inseminated intravaginally with spermatozoa from either SCWL or subfertile Delaware roosters in three replicate fertility trials. Overall fertility was analyzed with a log odds model following logit transformation. Duration of fertility was analyzed by iterative least squares. Hens inseminated with spermatozoa from SCWL males laid a higher proportion of fertilized eggs over a longer interval than those inseminated with spermatozoa from affected Delawares. Log-odds and logistic models may have advantages over the more traditional methods of evaluation. This is particularly true in regard to the distribution and normalization of error variances via the logit transformation and removal of nonadditivity via logistic regression.

Analysis of Variance↗

PubMed2002

Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects.

Modelling of censored survival data is almost always done by Cox proportional-hazards regression. However, use of parametric models for such data may have some advantages. For example, non-proportional hazards, a potential difficulty with Cox models, may sometimes be handled in a simple way, and visualization of the hazard function is much easier. Extensions of the Weibull and log-logistic models are proposed in which natural cubic splines are used to smooth the baseline log cumulative hazard and log cumulative odds of failure functions. Further extensions to allow non-proportional effects of some or all of the covariates are introduced. A hypothesis test of the appropriateness of the scale chosen for covariate effects (such as of treatment) is proposed. The new models are applied to two data sets in cancer. The results throw interesting light on the behaviour of both the hazard function and the hazard ratio over time. The tools described here may be a step towards providing greater insight into the natural history of the disease and into possible underlying causes of clinical events. We illustrate these aspects by using the two examples in cancer.

Antineoplastic Agents↗

PubMed1973

Global models of growth and competition.

Very precise data on the dynamics of a competitive system of two species of Drosophila have been obtained. By a curvilinear regression approach, analytical models of competition have been fitted. By statistical and biological criteria of simplicity, reality, generality, and accuracy, the best of these models has been chosen. This model represents an extension of the Lotka-Volterra model of competition; it adds a fourth parameter that controls the degree of nonlinearity in intraspecific growth regulation. It represents a similar extension of the logistic model of population growth.

Animals↗

PubMed2006

Predicting plutonium decorporation efficacy after intravenous administration of DTPA formulations: Study of pharmacokinetic-pharmacodynamic relationships in rats.

PURPOSE: The objectives of this study were: 1) to assess the relationship between plutonium decorporation (increased excretion and reduced retention in main organs of deposition) induced by intravenous liposome formulations of the chelating agent diethylene triamine pentaacetic acid (DTPA) and its pharmacokinetics, and 2) to model the renal excretion of plutonium after treatment with liposome-encapsulated DTPA in order to predict its efficacy and to optimise treatment schedules. MATERIALS AND METHODS: Pharmacokinetic parameters from plasma or urinary data (days 0-16 sample collections) were modelled versus decorporation efficacy, and best correlations were selected for their goodness of fit. RESULTS: The plutonium decorporation enhancement by DTPA liposomal formulations was well described by logistic models and the best correlation was observed with the area under the DTPA concentration curve of each formulation. The plutonium urinary excretion rates decreased mono-exponentially as a function of time after a single dose and the proposed model allowed a simple determination of the elimination half-life of the Pu-DTPA complex, a reasonably good approximation of the long-term efficacy of the treatments from truncated urinary data. CONCLUSIONS: Both liposomal formulations of chelating agents and pharmacokinetic approaches to plutonium decorporation should be helpful in optimising treatment protocols.

Animals↗

PubMed2004

Spatial patterns of infant mortality in Mali: the effect of malaria endemicity.

A spatial analysis was carried out to identify factors related to geographic differences in infant mortality risk in Mali by linking data from two spatially structured databases: the Demographic and Health Surveys of 1995-1996 and the Mapping Malaria Risk in Africa database for Mali. Socioeconomic factors measured directly at the individual level and site-specific malaria prevalence predicted for the Demographic and Health Surveys' locations by a spatial model fitted to the Mapping Malaria Risk in Africa database were examined as possible risk factors. The analysis was carried out by fitting a Bayesian hierarchical geostatistical logistic model to infant mortality risk, by Markov chain Monte Carlo simulation. It confirmed that mother's education, birth order and interval, infant's sex, residence, and mother's age at infant's birth had a strong impact on infant mortality risk in Mali. The residual spatial pattern of infant mortality showed a clear relation to well-known foci of malaria transmission, especially the inland delta of the Niger River. No effect of estimated parasite prevalence could be demonstrated. Possible explanations include confounding by unmeasured covariates and sparsity of the source malaria data. Spatial statistical models of malaria prevalence are useful for indicating approximate levels of endemicity over wide areas and, hence, for guiding intervention strategies. However, at points very remote from those sampled, it is important to consider prediction error.

Adult↗

PubMed1987

Comparison of three nonlinear regression models for describing broiler growth curves.

Three general growth models (Logistics, Gompertz and Saturation Kinetics) were compared for describing growth of broilers. Accuracy of fit, case of use and interpretation of data were used to compare the models. Data from a broiler feed restriction study was used to illustrate the parameter differences between the models. All three models accurately described the growth of the birds from the different experimental treatments based on coefficients of determination greater than or equal to .966. The Saturation Kinetics model proved to be the least accurate based on examination of residual values but still had a high association to the actual data. Linear regression applied to short intervals of the growth curve also proved to be an accurate means of interpreting growth rates.

Animals↗

PubMed1984

Data analytic methods for matched case-control studies.

The recent introduction of complex multivariate statistical models in matched case-control studies is a mixed blessing. Their use can lead to a better understanding of the way in which many variables contribute to the risk of disease. On the other hand, these powerful methods can obscure salient features in the data that might have been detected by other, less sophisticated methods. This shortcoming is due to a lack of support methodology for the routine use of these models. Satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model. Goodness of fit must be examined if inferences are to be trusted. This paper is concerned with the analysis of matched case-control studies with logistic models. Analogies of these models to linear regression models are emphasized. In particular, basic concepts such as analysis of variance, multiple correlation coefficient, one-degree-of-freedom tests, and residual analysis are discussed. The fairly new field of regression diagnostics is also introduced. All procedures are illustrated on a study of bladder cancer in males.

Analysis of Variance↗

PubMed1989

An integrated logistic formula for prediction of complications from radiosurgery.

An integrated logistic model for predicting the probability of complications when small volumes of tissue receive an inhomogeneous radiation dose is described. This model can be used with either an exponential or linear quadratic correction for dose per fraction and time. Both the exponential and linear quadratic versions of this integrated logistic formula provide reasonable estimates of the tolerance of brain to radiosurgical dose distributions where there are small volumes of brain receiving high radiation doses and larger volumes receiving lower doses. This makes it possible to predict the probability of complications from stereotactic radiosurgery, as well as combinations of fractionated large volume irradiation with a radiosurgical boost. Complication probabilities predicted for single fraction radiosurgery with the Leksell Gamma Unit using 4, 8, 14, and 18 mm diameter collimators as well as for whole brain irradiation combined with a radiosurgical boost are presented. The exponential and linear quadratic versions of the integrated logistic formula provide useful methods of calculating the probability of complications from radiosurgical treatment.

Adult↗

PubMed2001

The effect of ignoring item interactions on the estimated discrimination parameters in item response theory.

Most item response theory models assume conditional independence, and it is known that interactions between items affect the estimated item discrimination. In this article, this effect is further investigated from a theoretical perspective and by means of simulation studies. To this end, a parametric model for item interactions is introduced. Next, it is shown that ignoring a positive interaction results in an overestimation of the discrimination parameter in the two-parameter logistic model (2PLM), whereas ignoring a negative interaction leads to an underestimation of the parameter. Furthermore, it is demonstrated that in some cases the item characteristic curves of the 2PLM and of an item involved in an interaction are quite similar, indicating that the 2PLM can provide a good fit to data with interactions.

Humans↗

PubMed1976

Multivariate prediction of coronary heart disease in the Western Collaborative Group Study compared to the findings of the Framingham study.

The Western Collaborative Group Study (WCGS) is a prospective epidemiological study of 3,154 initially well men, aged 39059 years at intake in 1960-61, who were employed in ten participating companies in California. Clinical coronary heart disease (CHD) occurred in 257 men during a follow-up period of eight and one-half years. Coronary heart disease risk is predicted using the additive multiple logistic model with the risk factors: age, cholesterol, systolic blood pressure, hematocrit, ECG status, smoking at intake, and relative body weight. The predicted individual CHS risk levels, using the logistic results derived from the WCGS data, are highly correlated with predicted risk levels using a Framington study (FS) equation for these same risk factors with 12-year follow-up. The observed number of CHS events in the WCGS is not significantly different from the expected number of events derived from the FS logistic equation, after correction of length of follow-up. Multiple logistic analysis of the direct association between CHD incidence and behavior pattern gives an approximate relative risk of 1.9 (P = 0.0006) and 2.1 (P = 0.0015) for Type A compared to Type B men aged 39-49 and 50-59 years, respectively. It is estimated that removal of the excess risk associated with Type A behavior would correspond to a 31% (standard error = 6.6%) reduction of coronary heart disease incidence in the Western Collaborative Group Study population.

Adult↗

PubMed2004

Oleic acid from cooking oils is associated with lower insulin resistance in the general population (Pizarra study).

AIM: To evaluate the relation between type of dietary fatty acid and degree of insulin resistance. DESIGN: A cross-sectional study. METHODS: Anthropometrical data were measured in 538 subjects, aged 18-65 Years, selected randomly from the municipal census of Pizarra (Spain). An oral glucose tolerance test (OGTT) was given to all subjects and measurements were made of glycemia, insulinemia and the proportion of fatty acids in plasma phospholipids. Insulin resistance (IR) was estimated by homeostasis model assessment. Samples of cooking oil being used were obtained from the kitchens. The strength of association between variables was measured by calculating the odds ratio (OR) from logistic models, and the relationships were measured by linear correlation coefficients. RESULTS: Insulin resistance was significantly less in people who used olive oil compared with those who used sunflower oil or a mixture. Statistical significance remained in the group of people with normal OGTT after adjusting for obesity. In the whole sample, IR correlated negatively with the concentration of oleic acid (r=-0.11; P=0.02) and positively with that of linoleic acid (r=0.10; P=0.02) from the cooking oil. In subjects with normal OGTT, IR correlated negatively with oleic acid from cooking oil (r=-0.17; P=0.004) and from plasma phospholipids (r=-0.11; P=0.01) and positively with the concentration of linoleic acid in cooking oil (r=0.18; P=0.004) and plasma phospholipids (r=0.12; P=0.005). The risk (OR) of having raised IR was significantly lower in people who consumed olive oil, either alone (OR=0.50) or mixed (OR=0.52) compared with those who consumed only sunflower oil. CONCLUSION: There is an association between the intake of oleic acid, the composition of oleic acid in plasma phospholipids and peripheral insulin action.

Adolescent↗

PubMed2005

Maternal depressive symptoms and children's receipt of health care in the first 3 years of life.

BACKGROUND: Maternal depression is widely recognized to negatively influence mother-child interactions and children's behavior and development, but little is known about its relation to children's receipt of health care. OBJECTIVE: To determine if maternal depressive symptoms reported at 2 to 4 and 30 to 33 months postpartum are associated with children's receipt of acute and preventive health care services in the first 30 months. DESIGN: Cohort study of data collected prospectively as part of the National Evaluation of Healthy Steps for Young Children (HS). Data sources included medical records abstracted for the first 32 months, enrollment questionnaires, and parent interviews when children were 2 to 4 and 30 to 33 months old. Acute care use included hospitalizations and emergency department visits. Preventive care included well-child visits and vaccinations. Maternal depressive symptoms were assessed by using the Center for Epidemiologic Studies-Depression Scale. Generalized linear models (logistic regression for dichotomous outcomes and Poisson regression for count outcomes) were used to estimate the effect of maternal depressive symptoms on children's receipt of care. The models were adjusted for baseline demographic characteristics, child health status, participation in HS, and site of enrollment. RESULTS: Of the 5565 families enrolled in HS, 88% completed 2- to 4-month parent interviews, 67% completed 30- to 33-month parent interviews, and 96% had medical records abstracted. The percentages of mothers reporting depressive symptoms were 17.8% at 2 to 4 months, 15.5% at 30 to 33 months, and 6.4% at both. Children whose mothers had depressive symptoms at 2 to 4 months had increased use of acute care reported at 30 to 33 months including emergency department visits in the past year (odds ratio [OR]: 1.44; confidence interval [CI]: 1.17, 1.76). These children also had decreased receipt of preventive services including age-appropriate well-child visits (eg, at 12 months [OR: 0.80; CI: 0.67, 0.95]) and up-to-date vaccinations at 24 months for 4 doses of diphtheria, tetanus, pertussis, 3 doses of polio vaccine, and 1 dose of measles-mumps-rubella (OR: 0.79; CI: 0.68, 0.93). There was no association of maternal depressive symptoms at 30 to 33 months with children's preceding use of care. CONCLUSIONS: Maternal depressive symptoms in early infancy contribute to unfavorable patterns of health care seeking for children. Increased provider training for recognizing maternal depressive symptoms in office settings, more effective systems of referral, and development of partnerships between adult and pediatric providers could contribute to enhanced receipt of care among young children.

Adult↗

PubMed1981

Probability models in the analysis of radiation-related complications: utility and limitations.

In order to predict radiation-related enteric damage, 92 women were studied who had received identical radiation doses for cancer of the ovary from 1970 through 1977. A logistic model was used to predict the probability of complication as a function of number of laparotomies, hypertension, and thin physique. The utility and limitations of such probability models are presented.

Body Composition↗

PubMed1994

Polygenic control of susceptibility to murine systemic lupus erythematosus.

Susceptibility to glomerulonephritis (GN) and anti-dsDNA autoantibody production was analyzed in crosses with a newly developed systemic lupus erythematosus-susceptible inbred strain, NZM/Aeg2410. The mode of inheritance and the number and location of systemic lupus erythematosus-associated susceptibility loci were analyzed by interval mapping in a backcross with C57BL/6. Three chromosomal intervals containing strong recessive GN susceptibility alleles were identified on chromosomes 1, 4, and 7, each containing several potentially interesting candidate genes. Heterozygosity at H-2 was also found to correlate strongly with GN susceptibility, consistent with previous findings in the NZB/NZW parental strain model. Logistic regression analysis indicated that each of these susceptibility alleles independently accounted for a component of GN susceptibility, and that susceptibility was inherited as a threshold genetic liability in this model system.

Animals↗

PubMed1992

Prognostic factors of thyroid cancers in Ramathibodi Hospital.

The need to create different prognostic models for different populations is obvious after the findings that significant prognostic factors can change from one population to another. The purpose of this study is to fit a linear logistic model to a data set of Thai patients with thyroid cancers to find important prognostic factors and their effects on short-term mortality. Among the 89 cases selected, 20 died within 4 years after initial diagnosis and 69 survived more than 4 years. Age at diagnosis, sex, histological type and differentiation, microscopic vascular invasion, and extent of tumor spreading were included as independent variables. These variables were selected into the model by step-down selection procedure. Age at diagnosis was found to be the most significant prognostic factor followed by differentiation, vascular invasion and extent of spreading, respectively. However, vascular invasion appeared to exert the strongest impact on the prognosis with the risk of death increasing 62 fold for those showing microscopic evidence of this parameter. The odds ratios for the extent of spreading, age at diagnosis and differentiation were 7.5, 1.1 and 0.02, respectively.

Adult↗

PubMed2006

Age at which HIV infection can be detected in infants: place of the Yakovlev model.

The Yakovlev parametric cure rate model was used to study the age at which HIV-1 infection can be detected in nonbreast-fed infants and the independent predictors of transmission. Blood samples from 145 HIV-1-negative at birth infants born to HIV-1-positive untreated mothers were tested until 15 months. The age at actual detection and at potential detection providing daily tests was studied. The former was described using the Yakovlev model, and the cumulative probabilities of detection along time were calculated. Comparison of observed and predicted delays to positivity revealed the best representation of the age at which HIV becomes detectable among 8 Yakovlev models. Cumulative positive tests were as follows: 3 at 7 days, 10 at 15 days and 1 month, 17 at 3 months, and 18 at 15 months. The log-logistic model was the best-fitting one. The probability of onset of HIV-1 detectability was maximal at day 4. The mean and median age at which HIV becomes detectable were 12 and 6 days, respectively. Maternal CD4(+) cell count was associated with the risk of contamination [hazard ratio of low vs. high count 2.44; 95% (confidence interval): 1.15-6.67]. The model may explain HIV viremia dynamics and define the optimal antiretroviral regimens before randomized trial confirmation.

Age Factors↗

PubMed1994

Prediction of occult neck disease in laryngeal cancer by means of a logistic regression statistical model.

The ability to accurately predict the presence of subclinical metastatic neck disease in clinically N0 patients with primary epidermoid cancer of the larynx would be of great value in determining whether to perform an elective neck dissection. We describe a statistical approach to estimating the probability of occult neck disease given pretreatment clinical parameters. A retrospective study was performed involving 736 clinically N0 patients with primary laryngeal cancer who were treated surgically with primary resection and ipsilateral neck dissection. Nodal involvement was determined histologically after surgical lymphadenectomy. A logistic regression model was used to derive an equation that calculated the probability of occult neck metastasis based on pretreatment T stage, tumor location, and histologic grade. The model has a sensitivity of 74%, a specificity of 87%, and can be entered into a programmable calculator.

Adult↗