Gender difference in child mortality.
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Use and abuse of variance models in regression.
In (nonlinear) regression with heteroscedastic errors, introduction of a variance model can be useful to obtain good estimators of the regression parameter. For example, the variance model can be used to obtain the optimal weights in weighted least squares. Methodology of this kind is often used in the analysis of assay data in clinical chemistry, pharmacokinetics, and toxicology. In a series of papers in the pharmacological literature, Sheiner and Beal and others advocate the extended least squares (ELS) methodology that combines regression and variance model into a single objective function based on normal-theory maximum likelihood. The inadequacy of this method is folklore in the (mathematical) statistical literature. In this article it is pointed out that this methodology may lead to inconsistent estimators in practically relevant situations. A review is given of other methods that may be preferable to ELS.
Analysis of Variance↗
Optimal design for dose response using beta distributed responses.
Whenever a response is naturally confined to a finite interval (such as a visual analog scale for pain severity), the beta distribution provides a simple and flexible probability distribution to model such a response. The parameters of the distribution can then be related to covariates, such as dose, in a clinical trial through the generation of a beta regression model. In this article, we explore locally optimal designs for this class of regression models, focusing mainly on minimization of the generalized variance of maximum likelihood estimators (D-optimality). Optimal designs and sensitivity to misspecification of model parameters are examined using a candidate points searching algorithm. Although formally the model assumes that the response is continuous, it provides a parsimonious approximation for ordinal data when there is a relatively large number of categories. The resulting estimators and optimal designs are simpler and may offer more ease in interpretation than those derived from models for ordered categorical outcomes. The proposed methods are applied to data from a clinical trial.
Clinical Trials as Topic↗
Use of a vaccine strain of measles virus genetically engineered to produce carcinoembryonic antigen as a novel therapeutic agent against glioblastoma multiforme.
Despite the most aggressive medical and surgical treatments, glioblastoma multiforme remains incurable with a median survival of <1 year. We investigated the antitumor potential of a novel viral agent, an attenuated strain of measles virus (MV), derived from the Edmonston vaccine lineage, genetically engineered to produce carcinoembryonic antigen (CEA). CEA production as the virus replicates can serve as a marker of viral gene expression. Infection of a variety of glioblastoma cell lines including U87, U118, and U251 at MOIs 0.1, 1, and 10 resulted in significant cytopathic effect consisting of excessive syncycial formation and massive cell death at 72-96 h from infection. terminal deoxynucleotidyltransferase-mediated nick end labeling assays demonstrated the mechanism of cell death to be predominantly apoptotic. The efficacy of this approach in vivo was examined in BALB/c nude mice by using both s.c. and intracranial orthotopic U87 tumor models. In the s.c. U87 model, mice with established xenografts were treated with a total dose of 8 x 10(7) plaque forming units of MV-CEA, administered i.v. Mice treated with UV light inactivated MV, and untreated mice with established U87 tumors were used as controls. There was statistically significant regression of s.c. tumors (P < 0.001) and prolongation of survival (P = 0.007) in MV-CEA treated animals compared with the two control groups. In the intracranial orthotopic U87 model, there was significant regression of intracranial U87 tumors treated with intratumoral administration of MV-CEA at a total dose of 1.8 x 10(6) plaque forming units as assessed by magnetic resonance image (P = 0.002), and statistically significant prolongation of survival as compared with mice that received UV-inactivated virus and untreated mice (P = 0.02). Histological examination of brains of MV-CEA-treated animals revealed complete regression of the tumor with the presence of a residual glial scar and reactive changes, mainly presence of hemosiderin-laden macrophages. In addition, CEA levels in the peripheral blood in both the s.c. and orthotopic models increased before tumor regression, indicating viral gene expression, and returned to normal when the tumors regressed. Ifnar(ko) CD46 Ge transgenic mice, susceptible to MV infection, were used to assess central nervous system toxicity of MV-CEA. Intracranial administration of MV-CEA into the caudate nucleus of Ifnar(ko) CD46 Ge did not result in clinical neurotoxicity. Pathologic examination demonstrated limited microglial infiltration surrounding the injection site. In summary, MV-CEA has potent antitumor activity against gliomas in vitro, as well as in both s.c. and orthotopic U87 animal models. Monitoring CEA levels in the serum can serve as a low-risk method of detecting viral gene expression during treatment, and could allow dose optimization and individualization of treatment.
Animals↗
Further results on covariate measurement errors in cohort studies with time to response data.
The impact of covariate measurement errors on the estimation of relative risk regression parameters is discussed. First the dependence of the induced relative risk process on the cumulative baseline failure rate function is noted. Next induced relative risk models under some specific failure time and measurement error models are described, including the much simplified models that are appropriate under a 'rare disease' assumption. The presentation then turns to the joint estimation of relative risk parameters of primary interest along with measurement error parameters. A partial likelihood product is proposed for such estimation and asymptotic properties are indicated. Guidance is also presented as to the appropriate size of a 'validation' sample relative to the full cohort size. Finally some more general considerations are presented as to the usefulness and interpretation of deattenuated regression coefficients.
Analysis of Variance↗
The application of K-function analysis to the geographical distribution of road traffic accident outcomes in Norfolk, England.
One method applicable to the examination of spatial point patterns of disease, the calculation of K-functions, is presented. The technique is used to determine the degree of clustering exhibited by the residuals from a spatially referenced logit model constructed to ascertain the factors influencing the likelihood of death in a road traffic accident. This was done to test if there was some systematic geographical factor influencing outcome not adequately controlled for in the model. K-functions are extremely versatile, overcoming many of the problems of incorporating the notion of scale associated with traditional methods of spatial autocorrelation. Recently software has become available which allows their calculation in an easy to use Geographical Information System style environment. This study illustrates the relevance of the method, not only to the analysis of data on mortality and morbidity, but also to the examination of the residuals from any spatial regression.
Accidents, Traffic↗
Acoustic reflex thresholds: variability and distribution effects.
Acoustic reflex thresholds (ARTs) at 500, 1000, and 2000 Hz from 1833 ears were subjected to multiple linear regression analyses using a stepwise inclusion model to determine the effects of hearing losses in the 500- to 4000-Hz range for each of the activators. Although statistically significant regression equations were developed, these accounted for only 1 to 47% of the variance of ART levels. In light of the wide variance of ARTs unexplainable directly from audiometric data, it was deemed more appropriate to consider the range of ARTs from the standpoint of the sampling distribution of ARTs as a function of hearing level. Deciles were calculated in the 10th through 90th percentile ranges. These data corroborate and expand upon previously reported material on the distributions of ARTs among ears with normal hearing and cochlear impairment.
Adolescent↗
Risk factors for lateral ankle sprain: a prospective study among military recruits.
In a prospective study of risk factors for lateral ankle sprain among 390 male Israeli infantry recruits, a 18% incidence of lateral ankle sprains was found in basic training. There was no statistically significant difference in the incidence of lateral ankle sprains between recruits who trained in modified basketball shoes or standard lightweight infantry boots. By multivariate stepwise logistic regression a statistically significant relationship was found between body weight x height (a magnitude which is proportional to the mass moment of inertia of the body around a horizontal axis through the ankle), a previous history of ankle sprain, and the incidence of lateral ankle sprains. Recruits who were taller and heavier and thus had larger mass moments of inertia (P = 0.004), and those with a prior history of ankle sprain (P = 0.01) had higher lateral ankle sprain morbidity in basic training.
Analysis of Variance↗
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↗
A regression-based method to identify differentially expressed genes in microarray time course studies and its application in an inducible Huntington's disease transgenic model.
Time-course studies with microarray technologies provide enormous potential for exploring underlying mechanisms of biological phenomena in many areas of biomedical research, but the large amount of gene expression data generated by such studies also presents great challenges to data analysis. Here we introduce a regression-based statistical modeling approach that identifies differentially expressed genes in microarray time-course studies. To illustrate this method, we applied it to data generated from an inducible Huntington's disease transgenic model. The regression method accounts for the induction process, incorporates relevant experimental information, and includes parameters that specifically address the research interest: the temporal differences in gene expression profiles between the mutant and control mice over the time course, in addition to heterogeneities that commonly exist in microarray data. Least-squares and estimating equation techniques were used to estimate parameters and variances, and inferences were made based on efficient and robust Z-statistics under a set of well-defined assumptions. A permutation test was also used to estimate the number of false-positives, providing an alternative measurement of statistical significance useful for investigators to make decisions on follow-up studies.
Animals↗
Assessment of agreement under nonstandard conditions using regression models for mean and variance.
The total deviation index of Lin and Lin et al. is an intuitive approach for the assessment of agreement between two methods of measurement. It assumes that the differences of the paired measurements are a random sample from a normal distribution and works essentially by constructing a probability content tolerance interval for this distribution. We generalize this approach to the case when differences may not have identical distributions -- a common scenario in applications. In particular, we use the regression approach to model the mean and the variance of differences as functions of observed values of the average of the paired measurements, and describe two methods based on asymptotic theory of maximum likelihood estimators for constructing a simultaneous probability content tolerance band. The first method uses bootstrap to approximate the critical point and the second method is an analytical approximation. Simulation shows that the first method works well for sample sizes as small as 30 and the second method is preferable for large sample sizes. We also extend the methodology for the case when the mean function is modeled using penalized splines via a mixed model representation. Two real data applications are presented.
Likelihood Functions↗
Conditions for choosing between drug-induced and surgical abortions.
In France, pregnant women with amenorrhoea of no more than 49 days intending to terminate pregnancy can choose between a surgical abortion via vacuum aspiration under local or general anesthesia and a drug method combining Mifepristone orally administered (RU 486 degrees), with a prostaglandin analogue. This prospective survey was conducted to study the conditions under which women choose their abortion method, and to evaluate the acceptability of each method after the abortion. The data gathered from 488 women were analyzed according to their initial decision, and then according to the method actually used. The majority (62%) chose RU 486. The women's choice was found to be linked to sociodemographic characteristics such as age, education, occupation, geographic origin, and certain attitudes towards pregnancy, as well as to the individual criteria of each method. The women who chose the drug protocol had most often already made their decision before going to the family planning center (68%), having been advised by their doctor (20%). They were slightly less satisfied with the abortion experience than they had expected: 12.4% were unsatisfied in the RU group and 3.6% in the aspiration group. They needed more rest and quiet afterwards (50%) than the other women. They were distinguished by their desire to verify the expulsion (63%). The length of pregnancy is therefore not the only criterion to be considered when recommending one or other of these methods: the women concerned have different requirements and should have several possibilities to choose from.
Abortion, Induced↗
Risk factors for hypertension: results from a cross-sectional survey.
A case-control study of hypertension was conducted, using as a sampling frame a cross-sectional survey of Canadian Federal civil servants. Three case groups were selected, based on prior knowledge of hypertensive status and measured blood pressure. A 3-to-1 matching scheme was employed. Data was analysed using a logistic regression model. Statistically significantly elevated odds ratios, in excess of 3.0, were noted for overweight or obese status. Other odds ratios associated with a significantly increased risk of hypertension were maternal and paternal history of hypertension and current cigarette smoking.
Adult↗
Prostate cancer: gadolinium-enhanced MR imaging at 3 weeks compared with needle biopsy at 6 months after cryoablation.
PURPOSE: To determine if nonenhancing tissue on gadolinium-enhanced magnetic resonance (MR) images obtained 3 weeks after cryoablation of the prostate helps reliably and accurately predict nonviable cryoablated tissue at 6-month biopsy. MATERIALS AND METHODS: Fifty-four consecutive patients with prostate cancer who underwent cryoablation were followed up prospectively. Fifty-one underwent gadolinium-enhanced MR imaging at 3 weeks (three had gadolinium allergy); 49, biopsy at 6 months (three refused and two had other primary malignancies); and all, prostate-specific antigen (PSA) tests at 6 weeks, 3 months, and every 3 months thereafter. MR images were evaluated and scored according to the degree of signal void and were correlated with the 6-month biopsy reports and, to a lesser degree, PSA levels. The biopsy reports were examined for the presence or absence of cancerous tissue, viable tissue, and nonviable tissue. A one-way analysis of variance was used for statistical and regression analyses. RESULTS: The correlation of MR imaging scores with PSA levels and MR imaging scores with biopsy findings resulted in P values of.337 and.780, respectively. A slight statistically significant trend existed for the relation of biopsy results with PSA levels, with a P value of.041, which was expected. CONCLUSION: Findings of postoperative gadolinium-enhanced MR imaging are not predictive of 6-month biopsy results or follow-up PSA levels.
Aged↗
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↗
Characterizing the variability of system kernel and input estimates.
The identification of the input to, or kernels of, a system using nonparametric representations and least-squares estimation is becoming increasingly popular. Nonparametric representations avoid making a priori assumptions about the input or having detailed knowledge about the system, and only need to guarantee known general characteristics (for example, positivity), which are obtained through the imposition of constraints on the estimates. An often overlooked problem is how to characterize the variability of the estimates so obtained. This problem is caused by the presence of constraints--and/or the nonlinearities of the estimates, or the complexity of the (regression based) estimation algorithms used--which make standard methods of estimating variability incorrect. In this article we investigate the use of a resampling technique called the "bootstrap" to obtain the desired estimates of variability. We present real data analysis demonstrating the approach, and through simulations we test the performance of a novel bootstrap technique obtaining confidence bands for the estimated functions.
Algorithms↗
A non-parametric framework for estimating threshold limit values.
BACKGROUND: To estimate a threshold limit value for a compound known to have harmful health effects, an 'elbow' threshold model is usually applied. We are interested on non-parametric flexible alternatives. METHODS: We describe how a step function model fitted by isotonic regression can be used to estimate threshold limit values. This method returns a set of candidate locations, and we discuss two algorithms to select the threshold among them: the reduced isotonic regression and an algorithm considering the closed family of hypotheses. We assess the performance of these two alternative approaches under different scenarios in a simulation study. We illustrate the framework by analysing the data from a study conducted by the German Research Foundation aiming to set a threshold limit value in the exposure to total dust at workplace, as a causal agent for developing chronic bronchitis. RESULTS: In the paper we demonstrate the use and the properties of the proposed methodology along with the results from an application. The method appears to detect the threshold with satisfactory success. However, its performance can be compromised by the low power to reject the constant risk assumption when the true dose-response relationship is weak. CONCLUSION: The estimation of thresholds based on isotonic framework is conceptually simple and sufficiently powerful. Given that in threshold value estimation context there is not a gold standard method, the proposed model provides a useful non-parametric alternative to the standard approaches and can corroborate or challenge their findings.
Air Pollutants, Occupational↗
[Equilibrium and orthognathodontic surgery: correlations in a group of patients undergoing treatment].
BACKGROUND: The aim of this study was to evaluate the main parameters provided by the static stabilometric test (mean X, mean Y, mean velocity, length of tracing, standard deviation of velocity, ellipse area) in the follow-up of patients suffering from skeletal occlusive pathology undergoing orthognathodontic surgery to confirm the re-establishment of postural equilibrium. METHODS: Fifteen patients with skeletal dysgnathia were correlated with a group of 10 healthy subjects. The same parameters were analysed in the dysgnathic subjects at 6 and 12 months after surgical correction. The patients enrolled in this study underwent surgery at the Division of Maxillofacial surgery of Turin University. Student's "t"-test and multivariate statistical analysis (Cox regression) were used for the statistical analysis of results. RESULTS: A significant variability was noted in some of the main parameters analysed (mean X, mean Y, tracing length) between the two populations (healthy and dysgnathic) compared to visual signs (eyes opened-closed). The change in stabilometric values within the group of dysgnathic patients was highly significant 6 and 12 months after surgery, not only in terms of visual signs but also the cervical component (retroflexion of the head), above all the value of mean Y (p = 0.001). CONCLUSIONS: An analysis of these results shows that static stabilometry can be a valuable aid both during the preoperative evaluation and during the follow-up in patients undergoing jaw surgery since it can quantify the improvement of body balance.
Adolescent↗