Statistical methods for ordered categorical data based on a constrained odds model

The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann-Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.

Description and process evaluation of pharmacists’ interventions in a pharmacist-led information technology-enabled multicentre cluster randomised controlled trial for reducing medication errors in general practice (PINCER trial)

Objective To undertake a process evaluation of pharmacists' recommendations arising in the context of a complex IT-enabled pharmacist-delivered randomised controlled trial (PINCER trial) to reduce the risk of hazardous medicines management in general practices. Methods PINCER pharmacists manually recorded patients’ demographics, details of interventions recommended, actions undertaken by practice staff and time taken to manage individual cases of hazardous medicines management. Data were coded and double entered into SPSS v15, and then summarised using percentages for categorical data (with 95% CI) and, as appropriate, means (SD) or medians (IQR) for continuous data. Key findings Pharmacists spent a median of 20 minutes (IQR 10, 30) reviewing medical records, recommending interventions and completing actions in each case of hazardous medicines management. Pharmacists judged 72% (95%CI 70, 74) (1463/2026) of cases of hazardous medicines management to be clinically relevant. Pharmacists recommended 2105 interventions in 74% (95%CI 73, 76) (1516/2038) of cases and 1685 actions were taken in 61% (95%CI 59, 63) (1246/2038) of cases; 66% (95%CI 64, 68) (1383/2105) of interventions recommended by pharmacists were completed and 5% (95%CI 4, 6) (104/2105) of recommendations were accepted by general practitioners (GPs), but not completed at the end of the pharmacists’ placement; the remaining recommendations were rejected or considered not relevant by GPs. Conclusions The outcome measures were used to target pharmacist activity in general practice towards patients at risk from hazardous medicines management. Recommendations from trained PINCER pharmacists were found to be broadly acceptable to GPs and led to ameliorative action in the majority of cases. It seems likely that the approach used by the PINCER pharmacists could be employed by other practice pharmacists following appropriate training.

Family-based association analysis with ordered categorical phenotypes, covariates and interactions

Genetic association analyses of family-based studies with ordered categorical phenotypes are often conducted using methods either for quantitative or for binary traits, which can lead to suboptimal analyses. Here we present an alternative likelihood-based method of analysis for single nucleotide polymorphism (SNP) genotypes and ordered categorical phenotypes in nuclear families of any size. Our approach, which extends our previous work for binary phenotypes, permits straightforward inclusion of covariate, gene-gene and gene-covariate interaction terms in the likelihood, incorporates a simple model for ascertainment and allows for family-specific effects in the hypothesis test. Additionally, our method produces interpretable parameter estimates and valid confidence intervals. We assess the proposed method using simulated data, and apply it to a polymorphism in the c-reactive protein (CRP) gene typed in families collected to investigate human systemic lupus erythematosus. By including sex interactions in the analysis, we show that the polymorphism is associated with anti-nuclear autoantibody (ANA) production in females, while there appears to be no effect in males.

Crossbred cow adoption and milk market participation in a multivariate count data framework

Cross-bred cow adoption is an important and potent policy variable precipitating subsistence household entry into emerging milk markets. This paper focuses on the problem of designing policies that encourage and sustain milkmarket expansion among a sample of subsistence households in the Ethiopian highlands. In this context it is desirable to measure households’ ‘proximity’ to market in terms of the level of deficiency of essential inputs. This problem is compounded by four factors. One is the existence of cross-bred cow numbers (count data) as an important, endogenous decision by the household; second is the lack of a multivariate generalization of the Poisson regression model; third is the censored nature of the milk sales data (sales from non-participating households are, essentially, censored at zero); and fourth is an important simultaneity that exists between the decision to adopt a cross-bred cow, the decision about how much milk to produce, the decision about how much milk to consume and the decision to market that milk which is produced but not consumed internally by the household. Routine application of Gibbs sampling and data augmentation overcome these problems in a relatively straightforward manner. We model the count data from two sites close to Addis Ababa in a latent, categorical-variable setting with known bin boundaries. The single-equation model is then extended to a multivariate system that accommodates the covariance between crossbred-cow adoption, milk-output, and milk-sales equations. The latent-variable procedure proves tractable in extension to the multivariate setting and provides important information for policy formation in emerging-market settings