Statistical analysis of correlated binary data in ophthalmology: a weighted logistic regression approach

Analysis of neonatal clinical trials with twin births

Background

In neonatal trials of pre-term or low-birth-weight infants, twins may represent 10–20% of the study sample. Mixed-effects models and generalized estimating equations are common approaches for handling correlated continuous or binary data. However, the operating characteristics of these methods for mixes of correlated and independent data are not well established.

Methods

Simulation studies were conducted to compare mixed-effects models and generalized estimating equations to linear regression for continuous outcomes. Similarly, mixed-effects models and generalized estimating equations were compared to ordinary logistic regression for binary outcomes. The parameter of interest is the treatment effect in two-armed clinical trials. Data from the National Institute of Child Health & Human Development Neonatal Research Network are used for illustration.

Results

For continuous outcomes, while the coverage never fell below 0.93, and the type I error rate never exceeded 0.07 for any method, overall linear mixed-effects models performed well with respect to median bias, mean squared error, coverage, and median width. For binary outcomes, the coverage never fell below 0.90, and the type I error rate never exceeded 0.07 for any method. In these analyses, when randomization of twins was to the same treatment group or done independently, ordinary logistic regression performed best. When randomization of twins was to opposite treatment arms, a rare method of randomization in this setting, ordinary logistic regression still performed adequately. Overall, generalized linear mixed models showed the poorest coverage values.

Conclusion

For continuous outcomes, using linear mixed-effects models for analysis is preferred. For binary outcomes, in this setting where the amount of related data is small, but non-negligible, ordinary logistic regression is recommended.

A likelihood approach to estimating sensitivity and specificity for binocular data: application in ophthalmology

Binocular data typically arise in ophthalmology where pairs of eyes are evaluated, through some diagnostic procedure, for the presence of certain diseases or pathologies. Treating eyes as independent and adopting the usual approach in estimating the sensitivity and specificity of a diagnostic test ignores the correlation between eyes. This may consequently yield incorrect estimates, especially of the standard errors. The paper proposes a likelihood-based method of accounting for the correlations between eyes and estimating sensitivity and specificity using a model for binocular or paired binary outcomes. Estimation of model parameters via maximum likelihood is outlined and approximate tests are provided. The efficiency of the estimates is assessed in a simulation study. An extension of the methodology to the case of several diagnostic tests, or the same test measured on several occasions, which arises in multi-reader studies, is given. A further extension to the case of multiple diseases is outlined as well. Data from a study on diabetic retinopathy are analysed to illustrate the methodology.

A randomized, double-blind, controlled trial of the effects of ivermectin at normal and high doses, given annually or three-monthly, against Onchocerca volvulus: ophthalmological results

A three-year randomized, controlled, double-blind trial was conducted in Cameroon to determine whether ivermectin, given at three-monthly intervals and/or at high doses (800 microg/kg), had a greater effect on adult Onchocerca volvulus than standard doses (150 microg/kg annually). As several patients complained of transitory subjective visual problems after treatment, some of them being of an unexpected type, we organized two series of detailed ophthalmological examinations to evaluate whether they were associated with ocular lesions. Analysis showed that these complaints were significantly more frequent in the two groups treated with high doses of ivermectin than in the reference group. In the ophthalmological examinations, the only differences recorded between the groups were a lower prevalence and mean number of microfilariae in the anterior chamber in the groups treated three-monthly, and, at the first examination round, a higher prevalence of early lesions of the iris in the group treated at high doses annually. These findings do not allow us to explain the cause of the transitory ocular complaints, nor why they were more frequent in the groups treated at high doses. However, one may conclude that using doses of ivermectin higher than the standard one should be considered with caution.

The population requirement for cataract extraction: a cross-sectional study

PURPOSE

To examine the distribution in the population of indications for cataract extraction in order to relate demand for this procedure to the capacity for satisfying it.

METHODS

An age-stratified random population sample of 2783 individuals aged 55 years and over was taken from inner-city, urban and rural areas of Avon and Somerset. The requirement for cataract extraction was estimated on the basis of measures of vision-related quality of life, refracted visual acuity, and application of the Oxford Clinical Cataract Classification and Grading System. Data were also collected concerning suitability for surgery, including relative contraindications to surgery and whether participants considered their eyesight bad enough to merit surgery. Three sets of composite indications were defined.

RESULTS

Estimated prevalent requirements for cataract extraction for the three sets of composite criteria were: 29 per 1000 aged over 55 years (95% CI 20-41) for the most inclusive criterion; 17 per thousand (95% CI 10-27) for the intermediate criterion; and 7 per thousand (95% CI 3-14) for the most stringent criterion. These rates are equivalent to a national prevalent requirement for England of 384,000 for the most inclusive criterion. If the approximately 15% of individuals whose desire or fitness for surgery was questionable are removed from this estimate, the prevalent requirement, including the backlog from previous unsatisfied demand, becomes 325,000 individuals.

CONCLUSIONS

The findings suggest only a modest imbalance between supply and demand for cataract surgery. In particular there was a very small prevalence of untreated severe cataract, less than the annual health service surgical capacity, suggesting that the current National Health Service surgical capacity is adequate for cases of severe cataract.