Association models for a multivariate binary response

A Logit Model for Bivariate Binary Responses

This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with 3p degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

ORTH: R and SAS software for regression models of correlated binary data based on orthogonalized residuals and alternating logistic regressions

This article describes a new software for modeling correlated binary data based on orthogonalized residuals, a recently developed estimating equations approach that includes, as a special case, alternating logistic regressions. The software is flexible with respect to fitting in that the user can choose estimating equations for association models based on alternating logistic regressions or orthogonalized residuals, the latter choice providing a non-diagonal working covariance matrix for second moment parameters providing potentially greater efficiency. Regression diagnostics based on this method are also implemented in the software. The mathematical background is briefly reviewed and the software is applied to medical data sets.

Association of Clinical Signs and Symptoms with Pneumococcal Acute Otitis Media by Serotype--Implications for Vaccine Effect

BACKGROUND

Clinical symptoms and signs in acute otitis media (AOM) may differ depending on the various pneumococcal serotypes causing the disease. Alteration in clinical presentation of AOM could be expected after wide-scale pneumococcal vaccinations if there were considerable differences between vaccine serotypes and nonvaccine serotypes.

METHODS

In this study, data from 831 children in the control arm of the Finnish Otitis Media Vaccine Trial were used. The children were followed up prospectively in 8 study clinics from 2 to 24 months of age. If AOM was diagnosed, myringotomy was done, and middle ear fluid was aspirated for bacterial culture. Clinical symptoms and signs of AOM were routinely recorded on structured case report forms.

RESULTS

Consistent with previous studies, 60% of pneumococcal episodes were caused by vaccine serotypes. There were no major differences between the clinical presentations of AOM due to different serotypes or serotype categories. However, earache was more often associated with AOM caused by vaccine and cross-reactive serotypes, compared with AOM caused by non-vaccine-related serotypes (42% vs. 29%; odds ratio, 1.66; 95% confidence interval, 1.02-2.70).

CONCLUSIONS

Introduction of the currently available pneumococcal conjugate vaccine is unlikely to result in a remarkable alteration in the clinical presentation of pneumococcal AOM in infants.

Joint Regression and Association Modeling of Longitudinal Ordinal Data

We propose models for longitudinal, or otherwise clustered, ordinal data. The association between subunit responses is characterized by dependence ratios (Ekholm, Smith, and McDonald, 1995, Biometrika 82, 847-854), which are extended from the binary to the multicategory case. The joint probabilities of the subunit responses are expressed as explicit functions of the marginal means and the dependence ratios of all orders, obtaining a computational advantage for likelihood-based inference. Equal emphasis is put on finding regression models for the univariate cumulative probabilities, and on deriving the dependence ratios from meaningful association-generating mechanisms. A data set on the effects of treatment with Fluvoxamine, which has been analyzed in parts before (Molenberghs, Kenward, and Lesaffre, 1997, Biometrika 84, 33-44), is analyzed in its entirety. Selection models are used for studying the sensitivity of the results to drop-out.

Estimating cumulative probabilities from incomplete longitudinal binary responses with application to HIV vaccine trials

When describing longitudinal binary response data, it may be desirable to estimate the cumulative probability of at least one positive response by some time point. For example, in phase I and II human immunodeficiency virus (HIV) vaccine trials, investigators are often interested in the probability of at least one vaccine-induced CD8+ cytotoxic T-lymphocyte (CTL) response to HIV proteins at different times over the course of the trial. In this setting, traditional estimates of the cumulative probabilities have been based on observed proportions. We show that if the missing data mechanism is ignorable, the traditional estimator of the cumulative success probabilities is biased and tends to underestimate a candidate vaccine's ability to induce CTL responses. As an alternative, we propose applying standard optimization techniques to obtain maximum likelihood estimates of the response profiles and, in turn, the cumulative probabilities of interest. Comparisons of the empirical and maximum likelihood estimates are investigated using data from simulations and HIV vaccine trials. We conclude that maximum likelihood offers a more accurate method of estimation, which is especially important in the HIV vaccine setting as cumulative CTL responses will likely be used as a key criterion for large scale efficacy trial qualification.

Combining regression and association modelling for longitudinal data on bacterial carriage

A longitudinal data set, from the Finnish Otitis Media (FinOM) Studies, reporting carriage or non-carriage of Streptococcus pneumoniae at 2, 3, 4, 5, 6, 9, 12, 15 and 18 months of age of 329 children living in Tampere, Finland, is analysed. A logistic regression model on five time varying explanatory variables is fitted. The temporal association between presence at different ages is measured by dependence ratios and the structure of these is shown to be well described by a model indicating that roughly 10 per cent of the children are not susceptible to the bacteria, while for those that are susceptible, carriage status at a future observation age is conditionally independent of past observed statuses, given the present status. The dependence ratios between carriage at adjacent observation ages decay exponentially with age. Maximum likelihood estimates are obtained for the parameters of the full model, which is the combination of the marginal logistic regression and the association models. The parameter estimates of the full model, strengthened by non-testable Markov assumptions, are used for assessing the median duration of carriage and the acquisition rate as functions of age.

Pneumococcal carriage in children during their first two years: important role of family exposure

BACKGROUND

Close family and day-care contacts have been identified as risk factors for pneumococcal (Pnc) carriage. This study addresses the risk of Pnc carriage by infants 2 to 24 months of age in terms of simultaneous carriage of pneumococcus by family members.

METHODS

Nasopharyngeal swabs were collected from 100 Finnish infants and their family members on 10 scheduled visits (when infant was 2, 3, 4, 5, 6, 9, 12, 15, 18 and 24 months of age). The 7 most common pneumococcal serogroups (4, 6, 9, 14, 18, 19, 23), also represented in the new heptavalent Pnc conjugate vaccine, were analyzed. Marginal logistic regression analyses were performed to assess the relative importance of different predictors for carriage.

RESULTS

The carriage of the studied Pnc serogroups increased with age, being highest at the age of 18 months (28%). Among children older than 6 months of age, the strongest predictor of carriage was simultaneous carriage of the same serogroup by another family member (odds ratio, 3.8; 95% confidence interval, 2.1 to 6.9). At the age of 6 months or younger, carriage was rare and was not significantly associated with a family carriage.

CONCLUSIONS

Young infants (< or =6 months old) were largely protected from pneumococcal carriage. After this age family transmission seemed very important despite the small family size. Contrary to some earlier studies communal day care was not associated with an increased risk of Pnc carriage. This could be partly because of the long parental leave in Finland and thus the late age of starting organized day care.