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PubMed1990

A family study of panic disorder: reanalysis using a regressive logistic model that incorporates a sibship environment.

Previous analysis of affection status in parents and siblings of 117 probands with panic disorder by a log-linear model for binary pedigree data found a common concordance across biological first-degree relatives and no spouse association [Hopper JL, Judd FK, Derrick PL, Burrows GD: Genet Epidemiol 4:33-41, 1987]. In this paper the data were reanalyzed using a regressive logistic model that modelled both vertical transmission and a shared sibship environment. Ascertainment correction was made by a) an "ascertainment assumption-free" procedure, following Ewens and Shute [Theor Pop Biol 30:388-412, 1986] and compared with b) complete ascertainment and c) single ascertainment. Under every scheme there was evidence for vertical transmission from parents to offspring. Inclusion of a sibship environment gave an improved fit, suggesting that vertical transmission alone may not be sufficient to explain the familial aggregation observed in these families. The effects of an affected parent, of the postulated environmental factor (present for all siblings if it was present for one sibling), and of the prevalence of the rare environmental factor were estimated and found to be roughly similar under the different schemes. Model predictions of lifetime prevalence were consistent with other population-based studies. Under the same assumption-free method, standard errors approximately doubled and computation time increased compared with the other ascertainment schemes that made specific, although not necessarily correct, assumptions. The regressive logistic model used less computation time and gave greater insight into the pattern of familial aggregation than did the previous modelling.

Adult↗
PubMed1990

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases.

The paper presents an extension of the regressive logistic models proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. This goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the kth interval (k = 1...K) given not affected before represents the hazard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotypes of ancestors, and other covariates which can be time dependent. The probability that a given person either becomes affected within the kth interval (i.e., interval k includes age of onset of the person) or remains unaffected by the end of the kth interval (i.e., interval k includes age at examination of the person) are derived from the general results of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenais, Am J Hum Genet 42:256-266, 1988], i.e., the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new model to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment.

Adolescent↗
PubMed1995

Logistic transmission modeling of simulated data.

A nonparametric method for linkage analysis has been developed and applied to the Problem 1 data set of the Genetic Analysis Workshop 9. Basically, the univariate matched pair strategy of the transmission disequilibrium test has been adapted to multivariate modeling using the conditional logistic function. After setting the critical value for significance at p < or = 0.0001, models at only D5G23 and D1G31 appear to be significant (p < 10(-7)). Logistic transmission modeling is a powerful method for establishing linkage by disequilibrium.

Alleles↗
PubMed1993

A comparison of the logistic regression and the Cox proportional hazard models in retrospective studies on the prognosis of patients with gastric cancer.

To define the independent prognostic factors reducing survival time for gastric cancer, we compared the logistic regression and the Cox proportional hazard models applied to patients who underwent curative gastrectomy. All patients were evaluated after being followed for long fixed periods. Of 1,019, 269 (26.4%) died of tumor recurrence within a 5-year period and 36 (3.5%) died over 5 years after the original surgery. With regard to survival time, multivariate analyses using the Cox proportional hazard model in a stepwise manner adjusted for the sex, age, and 10 other factors, suggested that size of tumor (P < 0.01, relative risk [rr] = 1.0962), degree of gastric wall invasion (P < 0.01, rr < 1.3520), and status of lymph node metastasis (P < 0.01, rr = 1.6572) were the most independent prognostic factors. As well as, using the stepwise logistic regression model, size of tumor, (P < 0.01, odds ratio [or] = 1.115), degree of gastric wall invasion (P < 0.01, or = 1.428), and status of lymph node metastasis (P < 0.01, or = 2.182) were also the most independent risk factors for recurrence within 5 years after surgery. Although regression coefficients are not all the same, these three factors proved significant in both multivariate analyses. This equation for risk factors for prognosis is approached when searching for an appropriate method of retrospective studies using multivariate analyses.

Female↗
PubMed2003

Transition models for change-point estimation in logistic regression.

Although a wide variety of change-point models are available for continuous outcomes, few models are available for dichotomous outcomes. This paper introduces transition methods for logistic regression models in which the dose-response relationship follows two different straight lines, which may intersect or may present a jump at an unknown change-point. In these models, the logit includes a differentiable transition function that provides parametric control of the sharpness of the transition at the change-point, allowing for abrupt changes or more gradual transitions between the two different linear trends, as well as for estimation of the location of the change-point. Linear-linear logistic models are particular cases of the proposed transition models. We present a modified iteratively reweighted least squares algorithm to estimate model parameters, and we provide inference procedures including a test for the existence of the change-point. These transition models are explored in a simulation study, and they are used to evaluate the existence of a change-point in the association between plasma glucose after an oral glucose tolerance test and mortality using data from the Mortality Follow-up of the Second National Health and Nutrition Examination Survey.

Adult↗
PubMed2005

Extending logistic regression to model diffuse interactions.

In an observational study focussed on association between a health outcome and numerous explanatory variables, the question of interactions can be problematic. Commonly, logistic regression of the outcome on the explanatory variables might be employed. Such modelling often includes an attempt to select some pairwise product interaction terms, from amongst the many such possible pairs. For several reasons, however, this can be unsatisfying. Here we consider a different approach based on a parsimonious extension of a logistic regression model without interaction terms. This extension permits an overall synergism or antagonism in how the explanatory variables combine to associate with the outcome, without any attempt to identify specific variables which give rise to interactive behaviour. We call this diffuse interaction. We elucidate some simple properties of the diffuse interaction model, and give an example of its application to epidemiological data. We also consider asymptotic behaviour in a restricted case of the model, to gain some insight into how well this kind of interaction can be detected from data.

Analysis of Variance↗
PubMed2006

Adaptation of multiple logistic regression to a multiple inverse sampling design: application to the Isfahan healthy heart program.

In observational and experimental studies in the health sciences involving human populations, it is sometimes considered desirable to recruit subjects according to designs that specify a predetermined number of subjects in each of several mutually exclusive classes (generally but not necessarily demographic in nature). This type of adaptive sampling design, now generally referred to as multiple inverse sampling (MIS), has received recent attention, and estimation methods are now available for several sequential MIS sampling designs. In this class of designs, subjects are sampled randomly and sequentially, usually one at a time, until all classes have the pre-specified number of subjects. In this paper, we extend MIS for finite population sampling to estimation of the parameters in multiple logistic regression under MIS. Using estimated logistic regression parameters and cost components obtained from the Isfahan Healthy Heart Program (IHHP), we report findings from a simulation experiment in which it appears that, at fixed cost, MIS at the last stage of sampling compares favourably to simple random sampling. The IHHP is a large community intervention study for prevention of cardiovascular disease being conducted in Isfahan, Iran and two other cities in Iran. The IHHP identified subjects through a multistage sample survey in which MIS was used at the final stage of sampling. MIS is one of several methods of adaptive sampling that are generating considerable interest and show promise of being useful in a wide variety of applications.

Age Factors↗
PubMed2006

Proportional odds logistic regression--effective means of dealing with limited uncertainty in dichotomizing clinical outcomes.

Classifying a measurable clinical outcome as a dichotomous variable often involves difficulty with borderline cases that could fairly be assigned either of the two binary class memberships. In such situations the indicated class membership is often highly subjective and subject to, for instance, a measurement error. In other situations the intermediate level of a three-level ordinal factor may sometimes be explicitly reserved for cases which could likely belong to either of the two binary classes. Such indefinite readings are often eliminated from the statistical analysis. In this article we review conceptual and methodological aspects of employing proportional odds logistic regression for a three level ordinal factor as a suitable alternative to ordinary logistic regression when dealing with limited uncertainty in classifying clinical outcome as a binary variable.

Atherosclerosis↗
PubMed2006

A comparative investigation of methods for logistic regression with separated or nearly separated data.

In logistic regression analysis of small or sparse data sets, results obtained by classical maximum likelihood methods cannot be generally trusted. In such analyses it may even happen that the likelihood meets the convergence criteria while at least one parameter estimate diverges to +/-infinity. This situation has been termed 'separation', and it typically occurs whenever no events are observed in one of the two groups defined by a dichotomous covariate. More generally, separation is caused by a linear combination of continuous or dichotomous covariates that perfectly separates events from non-events. Separation implies infinite or zero maximum likelihood estimates of odds ratios, which are usually considered unrealistic. I provide some examples of separation and near-separation in clinical data sets and discuss some options to analyse such data, including exact logistic regression analysis and a penalized likelihood approach. Both methods supply finite point estimates in case of separation. Profile penalized likelihood confidence intervals for parameters show excellent behaviour in terms of coverage probability and provide higher power than exact confidence intervals. General advantages of the penalized likelihood approach are discussed.

Amniotic Fluid↗
PubMed2007

Sample size determination for logistic regression revisited.

There is no consensus on the approach to compute the power and sample size with logistic regression. Some authors use the likelihood ratio test; some use the test on proportions; some suggest various approximations to handle the multivariate case. We advocate the use of the Wald test since the Z-score is routinely used for statistical significance testing of regression coefficients. The null-variance formula became popular from early studies, which contradicts modern software, which utilizes the method of maximum likelihood estimation (MLE), when the variance of the MLE is estimated at the MLE, not at the null. We derive general Wald-based power and sample size formulas for logistic regression and then apply them to binary exposure and confounder to obtain a closed-form expression. These formulas are applied to minimize the total sample size in a case-control study to achieve a given power by optimizing the ratio of controls to cases. Approximately, the optimal number of controls to cases is equal to the square root of the alternative odds ratio. Our sample size and power calculations can be carried out online at www.dartmouth.edu/ approximately eugened.

Clinical Trials as Topic↗
PubMed1989

The ordered logistic regression model in psychiatry: rising prevalence of dementia in old people's homes.

Ordered logistic regression is an extension of binary logistic regression, and is particularly well suited to the analysis of many psychiatric scores. Its use is demonstrated in a pair of linked cross-sectional surveys of dementia in residents of old people's homes, first to model the association of dementia with demographic characteristics, and then to explore possible reasons for a rise in the prevalence of dementia in the homes over a four-year period.

Age Factors↗
PubMed1990

Relation of pooled logistic regression to time dependent Cox regression analysis: the Framingham Heart Study.

A standard analysis of the Framingham Heart Study data is a generalized person-years approach in which risk factors or covariates are measured every two years with a follow-up between these measurement times to observe the occurrence of events such as cardiovascular disease. Observations over multiple intervals are pooled into a single sample and a logistic regression is employed to relate the risk factors to the occurrence of the event. We show that this pooled logistic regression is close to the time dependent covariate Cox regression analysis. Numerical examples covering a variety of sample sizes and proportions of events display the closeness of this relationship in situations typical of the Framingham Study. A proof of the relationship and the necessary conditions are given in the Appendix.

Adult↗
PubMed1991

Comparison of different maximum likelihood estimators in a small sample logistic regression with two independent binary variables.

In order to examine the bias of the estimate of the log odds ratio in a 2 x 2 contingency table, Walter computed the entire distribution of the estimated log odds ratio using various small sample sizes. This is equivalent to computing the distribution of the estimated parameter b1 in a logistic regression with one independent binary variable. In this paper, the distributions of the estimated parameters b1 and b2 for two independent binary variables are computed for some small sample logistic regressions using six different estimation methods based on maximum likelihood. These estimates are then compared to the true parameter values. The best estimation method depends on the frequency of the outcome of interest and on whether the bias or mean square error is considered more important.

Bias↗
PubMed1991

Validation techniques for logistic regression models.

This paper presents a comprehensive approach to the validation of logistic prediction models. It reviews measures of overall goodness-of-fit, and indices of calibration and refinement. Using a model-based approach developed by Cox, we adapt logistic regression diagnostic techniques for use in model validation. This allows identification of problematic predictor variables in the prediction model as well as influential observations in the validation data that adversely affect the fit of the model. In appropriate situations, recommendations are made for correction of models that provide poor fit.

Benzothiadiazines↗
PubMed1993

Generalized logistic models for low-dose response data.

We discuss a generalization of the logistic response function of the form Pr(y = 1/x) = [1 + exp(- theta - beta'x)]-alpha, where alpha > 0. This function coincides with the usual logistic response when the shape parameter alpha is equal to one. We describe the use of this model for analysing cancer rates in mice for low-dose exposure to a known carcinogen. When estimating the low-dose responses, the errors associated with extrapolation are reduced when a priori knowledge about the rates among unexposed individuals is incorporated into the fitting procedures.

2-Acetylaminofluorene↗
PubMed1995

Confidence interval estimates of an index of quality performance based on logistic regression models.

This paper considers an index of hospital quality performance defined as the ratio of the observed number deaths to the number predicted by a fitted logistic regression model. We study tests and confidence intervals under two different scenarios depending on the availability of an estimate of the covariance matrix of the coefficients from the fitted logistic regression model. We propose parametric as well as bootstrap-based confidence intervals. We apply the methods to an analysis of the performance of 27 intensive care units.

Aged↗
PubMedDate not supplied

Computational tools for exact conditional logistic regression.

Logistic regression analyses are often challenged by the inability of unconditional likelihood-based approximations to yield consistent, valid estimates and p-values for model parameters. This can be due to sparseness or separability in the data. Conditional logistic regression, though useful in such situations, can also be computationally unfeasible when the sample size or number of explanatory covariates is large. We review recent developments that allow efficient approximate conditional inference, including Monte Carlo sampling and saddlepoint approximations. We demonstrate through real examples that these methods enable the analysis of significantly larger and more complex data sets. We find in this investigation that for these moderately large data sets Monte Carlo seems a better alternative, as it provides unbiased estimates of the exact results and can be executed in less CPU time than can the single saddlepoint approximation. Moreover, the double saddlepoint approximation, while computationally the easiest to obtain, offers little practical advantage. It produces unreliable results and cannot be computed when a maximum likelihood solution does not exist.

Adolescent↗
PubMed2001

Logistic discrimination of mixtures of M. tuberculosis and non-specific tuberculin reactions.

Interpretation of the Mantoux test for tuberculous infection can be complicated by cross-reactions caused by infection with non-specific mycobacteria. Thus, the distribution of positive indurations is a mixture of two distributions. To estimate tuberculous infection prevalence, the marginal distribution of indurations needs to be separated into its component distributions. Observations from several populations with different mixes of the two types of infection are required. Homogeneity across populations of distributions of indurations for each type of infection is assumed. A logistic model is specified for the probability of having tuberculous infection conditional on the observed induration size. No other assumptions about the two distributions are made. Maximum likelihood is used to estimate the logistic function. Goodness-of-fit criteria are discussed. The method is applied to a series of tuberculin surveys carried out in (South) Korea. Estimated infection prevalence agrees reasonably well with several ad hoc criteria. The goodness-of-fit test rejects underlying assumptions of homogeneity. One reason appears to be a decline over time in induration sizes caused by tuberculous infection. However, not all reasons for this rejection are obvious. The proposed method of mixture analysis provides an additional tool for the interpretation of prevalence survey data where the diagnostic test lacks specificity as a result of cross-reactions.

Adolescent↗