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PubMedDate not supplied

[Update on regression: softening relationships].

A frequently used methodology for the analysis of different kinds of health problems is based on regression models: lineal, logistic, etc.; these models depend on a set of parameters that must be estimated from the data. However, they present the drawback of being very rigid since, occasionally, they impose overly strict relations between the variables. Non-parametric regression methods present the advantage of not establishing a priori restrictions, allowing the data to indicates us the appropriate functional form. In this paper several modern non-parametric regression methods are presented that in addition to their usefulness per se can prone to be of invaluable help in the diagnostic process for parametric regression methods. The current availability of the necessary software should contribute to their increased use which, in turn, will probably lead to an improved understanding of the health problems under study.

Linear Models↗
PubMed2004

Evaluation of type I error rates when modeling ordered categorical data in NONMEM.

The development of non-linear mixed pharmacokinetic/pharmacodynamic models for continuous variables is usually guided by graphical assessment of goodness of fit and statistical significance criteria. The latter is usually the likelihood ratio test (LR). When the variable to be modeled is categorical, on the other hand, the available graphical methods are less informative and/or more complicated to use and the modeler needs to rely more heavily on statistical significance assessment in the model development. The aim of this study was to evaluate the type I error rates, obtained from using the LR test, for inclusion of a false parameter in a non-linear mixed effects model for ordered categorical data when modeling with NONMEM. Data with four ordinal categories were simulated from a logistic model. Two nested multinomial models were fitted to the data, the model used for simulation and a model containing one additional parameter. The difference in fit (objective function value) between models was calculated. Three types of models were explored; (i) a model without interindividual variability (IIV) where the addition of a parameter describing IIV was assessed, (ii) a model with IIV where the addition of a drug effect parameter (either categorical or continuous drug exposure measure) was evaluated, and (iii) a model including IIV and drug effect where the inclusion of a random effects parameter on the drug effect was assessed. Alterations were made to the simulation conditions, for example, varying the number of individuals and the size and distribution of the IIV, to explore potential influences on the type I error rate. The estimated type I error rate for inclusion of a false random effect parameter in model (i) and (iii) were, as expected, lower than the nominal. When the additional parameter was a fixed effects parameter describing drug effect (model(II)) the estimated type I error rates were in agreement with the nominal. None of the different simulation conditions tried changed this pattern. Thus, the LR test seems appropriate for judging the statistical significance of fixed effects parameters when modeling categorical data with NONMEM.

Clinical Trials as Topic↗
PubMedDate not supplied

A longitudinal study of the growth pattern of the maxillary sinus in the pig-tailed macaque (Macaca nemestrina).

The ontogeny of sexual dimorphism in maxillary sinus size in a nonhuman primate was studied longitudinally for a period of 8 years in 25 female and 25 male Macaca nemestrina via lateral cephalograms. The maxillary sinus was traced and its area digitized. The growth of female maxillary sinuses was described with a Gompertz model; the best fit to the male data was obtained by the logistic model. Growth curves and confidence intervals revealed that the sinuses grew in a similar fashion for 3-4 years in both sexes. After this, female sinuses achieved a plateau in their development while male sinuses continued to grow. Confidence intervals suggested that size dimorphism appeared at the age of 6.3 years. Lowess regression indicated growth spurts in both sexes. Females experienced an earlier and smaller spurt than males. Sexual dimorphism in maxillary sinus size seems to represent a combination of differences in velocity and length of growth. This study indicates that growth of the maxillary sinus follows closely the growth in body size. Nevertheless, due to the variation in sinus size in Macaca, it is questionable if body size is the main determinant of maxillary sinus size. It is suggested that Macaca, with its wide geographic range and different environments, is an especially appropriate genus to use to test hypotheses about the evolution of skull pneumatization in primates.

Animals↗
PubMed2006

Estimating receiver operating characteristic curves with covariates when there is no perfect reference test for diagnosis of Johne's disease.

Paratuberculosis (Johne's disease) is a significant animal health problem. Evaluation of diagnostic tests for Johne's disease has been difficult due to lack of a gold standard test. In recent years, there has been interest in receiver operating characteristic (ROC) curve estimation without any gold standard test. Typically, either Bayesian or maximum likelihood methods are proposed. Although these methods overcome the lack of a gold standard test in ROC curve estimation, little work has been done to incorporate covariates in the analysis. In this paper, we propose a method for estimation of ROC curves based on statistical models to adjust for covariate effects when the true disease states of test animals are unknown. The covariates may be correlated with the disease process or with the diagnostic testing procedure, or both. We propose a 2-part Bayesian model: first, a logistic regression model for disease prevalence is used to fit the covariates; second, a linear model is used to fit the covariates to the distribution of test scores. We used Markov chain Monte Carlo methods to compute the posterior estimates of the sensitivities and specificities that provide the groundwork for inference concerning the diagnostic procedure's accuracy. We applied the methodology to milk ELISA scores from several dairy-cow herds for the diagnostic testing of paratuberculosis. We found that both milk yield and its interaction with age had significant effects on the disease process whereas only milk yield was significant on the testing procedure.

Animals↗
PubMed2005

Assessment of exposure to wheat flour and the shape of its relationship with specific sensitization.

OBJECTIVES: Dust and wheat-allergen exposure were assessed among bakers, flour millers, and bakery-ingredient producers, and the risk for sensitization was studied. METHODS: About 520 inhalable dust and wheat-allergen measurements were made among 270 Dutch workers. Data on sensitization to wheat and common allergens (atopy) were also available. Exposure was estimated according to the sector of industry, job title, and tasks. The shape of the relationship between sensitization and exposure was studied using a two-stage modeling approach: semi-parametric generalized additive modeling and, consequently, a simple description of the relationship using a parametric logistic model. To reduce the effect of exposure measurement errors (attenuation), a combination of the actual measured exposure and variance-weighted estimates of exposure was used. Results The effect of exposure to both inhalable dust and wheat allergens on sensitization was described best by a linear relationship in three industries and a quadratic relationship in one industry. The relation for the whole study population was best described as quadratic, and the probability of sensitization increased with exposure up to -2.7 mg/m3 for inhalable dust and approximately 25.7 microg EQ/m3 for wheat allergens. The risk decreased at higher exposures (P = 0.0121 and P = 0.0731 for dust and wheat, respectively). Atopy and sector of industry modified the sensitization risk significantly in all the analyses. Using a variant-weighted estimator to calculate exposures corrected for the bias and resulted in almost the same point risk estimators. Conclusions Exposure-response relationships for allergens may be nonlinear and differ between industries. A threshold is not indicated on which to base occupational exposure standards; alternatively, other approaches, such as benchmarking, seem warranted.

Allergens↗
PubMed1993

Obstetric correlates of neonatal retinal hemorrhage.

OBJECTIVE: To determine whether maternal or fetal factors, other than vacuum-assisted delivery, play a role in neonatal retinal hemorrhage, and whether correlates are similar in retinal hemorrhage after spontaneous vaginal delivery. METHODS: A cross-section of assisted deliveries at an urban hospital (n = 156) over 7 months were compared with contemporaneous spontaneous vaginal deliveries (n = 122). A subset of assisted deliveries (n = 87) was prospectively randomized to forceps or vacuum-assisted delivery by sealed envelope. Maternal and neonatal biometric data were collected, and Apgar scores, umbilical artery blood gas analysis, and neonatal ophthalmologic evaluations were performed. RESULTS: Moderate to severe retinal hemorrhage was found in 18% of spontaneous, 13% of forceps, 28% of vacuum-assisted, and 50% of sequential vacuum and forceps-assisted deliveries. Fetal distress (P < .008), vacuum-assisted delivery (P < .02), decreased birth weight for gestation (P < .004), umbilical artery pH less than 7.20 (P < .004), and second stage of labor less than 30 minutes (P < .05) were most closely associated with increased degrees of retinal hemorrhage. Maternal parity, preeclampsia, length of labor, and head circumference were not correlated with retinal hemorrhage. Vacuum-assisted delivery among low birth weight infants (P < .0001), short second stage of labor (P < .006), fetal acidosis (P < .045), and sequential use of vacuum and forceps for assisted delivery (P < .005) formed a logistic model that correctly predicted 81% of moderate to severe retinal hemorrhage cases. Logistic analysis of the randomized assisted deliveries gave similar results. CONCLUSIONS: Maternal and fetal factors other than vacuum-assisted delivery are significant correlates of moderate to severe retinal hemorrhage. Vacuum-assisted delivery among small for gestational age infants is closely correlated with moderate to severe retinal hemorrhage.

Adult↗
PubMed2000

A semiparametric approach to analysing dose-response data.

In the analysis of a quantal dose-response experiment with grouped data, the most commonly used parametric procedure is logistic regression, commonly referred to as 'logit analysis'. The adequacy of the fit by the logistic regression curve is tested using the chi-square lack-of-fit test. If the lack-of-fit test is not significant, then the logistic model is assumed to be adequate and estimation of effective doses and confidence intervals on the effective doses can be made. When the tolerance distribution of the dose-response data is not known and cannot be assumed by the user, one can use non-parametric methods, such as kernel regression or local linear regression, to estimate the dose-response curve, effective doses and confidence intervals. This research proposes another alternative based on semi-parametric regression to analysing quantal dose-response data called model-robust quantal regression (MRQR). MRQR linearly combines the parametric and non-parametric predictions with the use of a mixing parameter. MRQR uses logistic regression as the parametric portion of the model and local linear regression as the non-parametric portion of the model. Our research has shown that the MRQR procedure can improve the fit of the dose-response curve by producing narrower confidence intervals for predictions while providing improved precision of estimates of the effective doses with respect to either logistic or local linear regression results.

Dose-Response Relationship, Drug↗
PubMed2005

Multilevel generalized linear models for modelling age-related gender difference in violent behaviour and associated factors in the general household population.

It is preferable to use longitudinal data when studying patterns of violence and antisocial behaviour over the lifespan together with the associated risk factors in the general population. From the statistical modelling perspective, random samples of cross-sectional data, representative of the population, can be a reliable alternative. Sampling, weighting, and possible geographical clustering of the behaviour must be considered in the analysis together with correct choice of model as a function of age, although cohort effects and age effects are not separated from the analysis. This paper demonstrates the use of multilevel generalized linear models in the British National Survey of Psychiatric Morbidity in 2000. A multilevel logistic model as a special case of a generalized linear model with individual weightings was adapted for a dichotomous measure of violence and extended to Poisson and negative binomial outcomes. Three types of age function, discrete age effects, continuous age effects, and piecewise polynomial function of age intervals were evaluated for goodness of fit, and for their practical advantages and disadvantages. Models were developed for possible risk factors in relation to specific age groups of interest.

Adolescent↗
PubMedDate not supplied

Chagas disease in north-west Argentina: risk of domestic reinfestation by Triatoma infestans after a single community-wide application of deltamethrin.

The risk of domestic reinfestation by Triatoma infestans after a single community-wide application of delta-methrin (2.5% suspension concentrate at 25 mg active ingredient/m2) was studied in Amamá, north-west Argentina, where no insecticide spraying had been done by official control services. The percentage of infested houses fell from 88% before spraying in 1985 to nil during the 6 months after spraying, and thereafter increased from 5% in 1986 to 96% before a second treatment in 1992, fitting closely to a logistic model (r2 = 0.997). Significant risk factors associated with domestic reinfestation determined from stepwise logistic regression and one-factor analysis were the density of T. infestans in bedrooms just before spraying and the surface structure of indoor walls. Peak densities of bugs in 1988-1989 significantly differed between levels of both risk factors. Our study suggests the existence of stable determinants of infestation linked to the household which, in the absence of effective control measures, would also determine the speed of house recolonization and the ensuing bug densities. Plastering of mud walls before application of insecticides to all domestic and peridomestic structures is supported by the study.

Animals↗
PubMed1994

The probability of a successful treatment of infertility by in-vitro fertilization.

The objective of this study was to define several estimates of the success rate of in-vitro fertilization and embryo transfer treatment in relation to treatment outcome. The data were collected in a retrospective study of 591 patients treated during 3 years in one Belgian university hospital. Several models used for evaluating the treatment of infertility were fitted to the data (logistic model, binomial model, double binomial model, exponential model, the Speirs model. The number of oocytes retrieved and the proportion of fertilized oocytes at the first attempt can be used as prognostic factors. According to these factors, the success rate after five attempts varies from 28 to 88%.

Belgium↗
PubMed2005

Building prediction models for coronary heart disease by synthesizing multiple longitudinal research findings.

BACKGROUND: No methodology is currently available to allow the combining of individual risk factor information derived from different longitudinal studies for a chronic disease in a multivariate fashion. This paper introduces such a methodology, named Synthesis Analysis, which is essentially a multivariate meta-analytic technique. DESIGN: The construction and validation of statistical models using available data sets. METHODS AND RESULTS: Two analyses are presented. (1) With the same data, Synthesis Analysis produced a similar prediction model to the conventional regression approach when using the same risk variables. Synthesis Analysis produced better prediction models when additional risk variables were added. (2) A four-variable empirical logistic model for death from coronary heart disease was developed with data from the Framingham Heart Study. A synthesized prediction model with five new variables added to this empirical model was developed using Synthesis Analysis and literature information. This model was then compared with the four-variable empirical model using the first National Health and Nutrition Examination Survey (NHANES I) Epidemiologic Follow-up Study data set. The synthesized model had significantly improved predictive power (chi = 43.8, P<0.00001). CONCLUSIONS: Synthesis Analysis provides a new means of developing complex disease predictive models from the medical literature.

Coronary Disease↗
PubMed2005

Individualized predictions of disease progression following radiation therapy for prostate cancer.

PURPOSE: Following treatment for localized prostate cancer, men are monitored with serial prostate-specific antigen (PSA) measurements. Refining the predictive value of post-treatment PSA determinations may add to clinical management, and we have developed a model that predicts future PSA values and the time to future clinical recurrence for individual patients. PATIENTS AND METHODS: Data from 934 patients treated between 1987 and 2000 were used to develop a comprehensive statistical model to fit the clinical recurrence events and patterns of PSA data. A logistic model was used for the probability of cure, mixed models were used for serial PSA measurements, and a proportional hazards model was used for recurrences. Data available through February 2001 were fit to the model, and data collected between February 2001 and September 2003 were used for validation. RESULTS: T-stage, baseline PSA, and radiotherapy dosage are all associated with probability of cure. The risk of clinical recurrence in those not cured is strongly affected by the slope of PSA values. We show how the model can be used for individual monitoring of disease progression. For each patient the model predicts, based on baseline characteristics and all post-treatment PSA values, the probability of future clinical recurrences and future PSA values. The model accurately predicts risk of recurrence and future PSA values in the validation data set. CONCLUSION: This predictive information on future PSA values and the risk of clinical relapse for each individual patient, which can be updated with each additional PSA value, may prove useful to patients and physicians in determining post-treatment salvage strategies.

Adult↗
PubMed2005

Factors affecting cure and somatic cell count after pirlimycin treatment of subclinical mastitis in lactating cows.

This study investigated the associations of both bacteriological cure and quarter somatic cell count (SCC) after intramammary antibiotic treatment with treatment duration, cow characteristics, and pretreatment bacteriology and SCC. For the purpose of this paper, data from 2 treatment groups in each of 2 multi-location studies were selected. These studies were conducted to evaluate the efficacy of daily intramammary infusions with 50 mg of pirlimycin hydrochloride for the treatment of subclinical mastitis. Data from study 1 allowed for comparison of a group of cows that received pirlimycin intramammarily for 2 d with a group that received no treatment, and study 2 provided data for comparison of pirlimycin for 2 d with pirlimycin for 8 d. Quarter milk samples from cows with a high monthly SCC were tested for bacteriology and SCC. If one or more quarters had both a positive bacteriology and an SCC >/=300,000 cells/mL, the cow was enrolled and randomly allocated to a treatment group. Enrolled cows were monitored for clinical mastitis and other disease for 4 wk after treatment initiation. At 3 and 4 wk after treatment initiation, milk samples were taken from each enrolled quarter to determine the SCC and conduct a bacteriological culture. Bacteriological culture results were interpreted such that quarters where the same bacterial species was cultured before treatment and found in at least 1 of the 2 posttreatment samples were considered a failure. The analysis of SCC used a mixed linear model (SAS proc mixed) and the analysis of bacteriological cure used a mixed logistic model (SAS glimmix macro). Bacteriological cure rate was significantly higher for lower parity, lower number of colonies in the pretreatment culture, longer treatment duration, and for streptococci compared with Staphylococcus aureus. However, treatment regimen affected bacteriological cure differently in major than in minor pathogens and there was a significant interaction of treatment regimen with stage of lactation. Posttreatment SCC was significantly higher with increasing parity, in rear quarters, and with shorter duration of treatment. In the group of second and third parity animals, post-treatment SCC was more reduced in front quarters than in rear quarters. Also, the difference in posttreatment SCC between younger and older cows increased with higher pretreatment SCC. In conclusion, when predicting bacteriological cure following treatment of subclinical mastitis during lactation both treatment regimen and other risk factors need to be considered. The other risk factors may vary with treatment regimen. Posttreatment SCC was associated with treatment regimen, other risk factors, and interactions among the other risk factors; but these other risk factors did not vary significantly with treatment regimen.

Animals↗
PubMed2006

Cerebrovascular disease, APOE epsilon4 allele and cognitive decline in a cognitively normal population.

OBJECTIVES: To investigate whether cerebrovascular disease (CVD) and apolipoprotein E (APOE) epsilon4 allele were associated with cognitive decline and whether the relationship between CVD and cognitive decline varied by APOE epsilon4 status. METHODS: A total of 809 cognitively normal community-dwelling residents aged >75 years were followed to detect subjects with cognitive decline, defined as follow-up. Mini-mental state examination (MMSE) score was >10% decease of the baseline score. Logistic and multinomial logistic models were developed to estimate odds ratio (OR) and 95% confidence interval (CI) of cognitive decline related to a history of CVD and APOE epsilon4 by taking into account major potential confounders including baseline MMSE score. RESULTS: During the mean 3.5 years of follow-up, 190 subjects experienced cognitive decline. Multi-adjusted ORs (95% CIs) of overall cognitive decline were 2.27 (1.23-4.17) for CVD and 1.69 (1.13-2.54) for APOE epsilon4, but no interaction was detected. Multinomial logistic analysis led to the CVD-related ORs of 1.42 (0.75-2.67) for cognitive decline without progression to dementia and 3.41 (1.55-7.55) for the decline progressing to dementia; similar analysis from a separate model led to adjusted OR of 2.28 (0.88-5.87; p=0.09) for the decline progressing to Alzheimer's disease. The risk effects of CVD on cognitive decline with progression to dementias were statistically significant mainly among individuals without APOE epsilon4 allele. CONCLUSIONS: CVD is a major risk factor for cognitive decline associated with progression to dementia and Alzheimer's disease. There appears no interaction between CVD and APOE epsilon4 on cognitive decline in very old people.

Aged↗
PubMedDate not supplied

Fitting multistate transition models with autoregressive logistic regression: supervised exercise in intermittent claudication.

The purpose of this study was to develop a model that predicts the outcome of supervised exercise for intermittent claudication. The authors present an example of the use of autoregressive logistic regression for modeling observed longitudinal data. Data were collected from 329 participants in a six-month exercise program. The levels of the polytomous outcome variable correspond to states they defined in a Markov decision model comparing treatment strategies for intermittent claudication. Autoregressive logistic regression can be used to fit multistate transition models to observed longitudinal data with standard statistical software. The technique allows exploration of alternative assumptions about the dependence in the outcome series and provides transition probabilities for different covariate patterns. Of the alternatives examined, a Markov model including two preceding responses, time, age, ankle brachial index, and duration of disease best described the data.

Decision Support Techniques↗
PubMed2000

Outcome of nursing home-acquired pneumonia: derivation and application of a practical model to predict 30 day mortality.

OBJECTIVES: To derive a prediction model of 30 day mortality for nursing home-acquired pneumonia (NHAP) based on factors that can be readily identified by nursing home staff at the time of diagnosis and to apply the model to management issues related to NHAP including clarifying the importance of prepneumonia functional status as a predictor of outcome of NHAP. DESIGN: This was a retrospective chart review of 378 episodes of NHAP treated in the nursing home or hospital during two periods: November 1997 to April 1998 and November 1998 to April 1999. SETTING: Eleven nursing homes in the greater Buffalo, NY region. PARTICIPANTS: Nursing home residents with radiographically proven pneumonia who had at least one of the following signs/symptoms: cough, fever, purulent sputum, respiratory rate > or =25 breaths/minute, localized auscultatory findings, or pleuritic pain. MEASUREMENTS: Status (alive or dead) of each resident at 30 days (30 day mortality) after diagnosis of NHAP was the dependent variable. Factors predicting 30 day mortality were identified by logistic regression analysis. A scoring system was developed based on the results of the logistic model. Each episode of NHAP in the derivation cohort was scored using the model and the cohort was stratified by the model score into six categories or risk for mortality (0-5). The predictability of the model in the derivation cohort was measured using receiver operator characteristics curve analysis. RESULTS: Of 378 episodes of NHAP, 74% were treated initially in the nursing home and 26% were hospitalized initially for treatment. The overall 30 day mortality was 21.4%; however, the mortality rate was significantly higher for those treated initially in the hospital (29.6% vs 16.6%; P = .012). Logistic regression analysis identified four predictors of 30 day mortality: (1) respiratory rate >30 breaths/minute (2 points), (2) pulse > 125 beats/minute (1 point), (3) altered mental status (1 point), and (4) a history of dementia (1 point). Applying the scoring system to each episode in the derivation cohort demonstrated increasing mortality with increasing score. The c statistic for the model in the derivation cohort was .74. Based on the severity of NHAP, model episodes treated initially in the hospital were more acutely ill than those who were treated initially in the nursing home, and episodes treated with a parenteral antibiotic in the nursing home were more acutely ill than those who were treated with an oral agent. Functional status was not a predictor of 30 day mortality although there was a trend of higher mortality in the most dependent group (P = .065). The severity of NHAP model was able to define low and high risk mortality groups within a functional status category. CONCLUSIONS: A severity of NHAP model was derived from a large cohort of episodes in multiple facilities. The model had reasonable discriminatory power in the derivation cohort. The model may aid clinicians in making treatment decisions in the nursing home setting and in making hospitalization decisions. Although prepneumonia functional status provides a reasonable estimate of NHAP severity and prognosis, the severity of NHAP model permitted further refinement of these estimates. The severity of NHAP model requires validation before it can be recommended for general use.

Activities of Daily Living↗
PubMed1997

A logistic-bivariate normal model for overdispersed two-state Markov processes.

We describe a logistic-bivariate normal mixture model for a two-state Markov chain in which each individual makes transitions between states according to a subject-specific transition probability matrix. The use of the bivariate normal mixing distribution facilitates inferences regarding the correlation of the random effects and hence provides insight as to the nature of the subject-to-subject variability in the transition probabilities. Tests regarding the correlation can be based on likelihood ratio, score, or Wald statistics. Estimates of the transition intensities of a latent continuous time conditionally Markov process may also be computed. We illustrate this methodology by application to a parasitic infection field study and contrast our findings with those previously published on this data set.

Biometry↗
PubMed1992

When does it pay to break the matches for analysis of a matched-pairs design?

Two methods of analysis are compared to estimate the treatment effect of a comparative study where each treated individual is matched with a single control at the design stage. The usual matched-pairs analysis accounts for the pairing directly in its model, whereas regression adjustment ignores the matching but instead models the pairing using a set of covariates. For a normal linear model, the estimated treatment effect from the matched-pairs analysis (paired t-test) is more efficient. For a Bernoulli logistic model, matched-pairs analysis performs better when the sample size is small, but is inferior to logistic regression for large sample sizes.

Clinical Trials as Topic↗