Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Organisational justice and smoking: the Finnish Public Sector Study

Study Objective: To examine the extent to which justice of decision-making procedures and interpersonal relations is associated with smoking. Setting: Ten municipalities and 21 hospitals in Finland. Design and Participants: Cross-sectional data derived from the Finnish Public Sector Study were analysed with logistic regression analysis models with generalized estimating equations. Analyses of smoking status were based on 34 021 employees. Separate models for heavy smoking (>20 cigarettes per day) were calculated for 6295 current smokers. Main results: After adjustment for age, education, socio-economic position, marital status, job contract, and negative affectivity, smokers who reported low procedural justice were about 1.4 times more likely to smoke >20 cigarettes per day compared with their counterparts with high justice. In a similar way, after adjustments, low justice in interpersonal treatment was significantly associated with an elevated prevalence of heavy smoking (odds ratio (OR) = 1.35, 95% CI = 1.03 to 1.77 for men and OR = 1.41, 95% CI = 1.09 to 1.83 for women). Further adjustment for job strain and effort-reward imbalance had little effect on these results. There were no associations between justice components and smoking status or ex-smoking. Conclusions: The extent to which employees are treated with justice in the workplace seems to be associated with smoking intensity independently of established stressors at work.

Can we improve the statistical analysis of stroke trials? Statistical re-analysis of functional outcomes in stroke trials

Background: Most large acute stroke trials have been neutral. Functional outcome is usually analysed using a yes or no answer, e.g. death or dependency vs. independence. We assessed which statistical approaches are most efficient in analysing outcomes from stroke trials. Methods: Individual patient data from acute, rehabilitation and stroke unit trials studying the effects of interventions which alter functional outcome were assessed. Outcomes included modified Rankin Scale, Barthel Index, and ‘3 questions’. Data were analysed using a variety of approaches which compare two treatment groups. The results for each statistical test for each trial were then compared. Results: Data from 55 datasets were obtained (47 trials, 54,173 patients). The test results differed substantially so that approaches which use the ordered nature of functional outcome data (ordinal logistic regression, t-test, robust ranks test, bootstrapping the difference in mean rank) were more efficient statistically than those which collapse the data into 2 groups (chi square) (ANOVA p<0.001). The findings were consistent across different types and sizes of trial and for the different measures of functional outcome. Conclusions: When analysing functional outcome from stroke trials, statistical tests which use the original ordered data are more efficient and more likely to yield reliable results. Suitable approaches included ordinal logistic regression, t-test, and robust ranks test.

Can we improve the statistical analysis of stroke trials? Statistical reanalysis of functional outcomes in stroke trials

Background and Purpose—Most large acute stroke trials have been neutral. Functional outcome is usually analyzed using a yes or no answer, eg, death or dependency versus independence. We assessed which statistical approaches are most efficient in analyzing outcomes from stroke trials. Methods—Individual patient data from acute, rehabilitation and stroke unit trials studying the effects of interventions which alter functional outcome were assessed. Outcomes included modified Rankin Scale, Barthel Index, and “3 questions”. Data were analyzed using a variety of approaches which compare 2 treatment groups. The results for each statistical test for each trial were then compared. Results—Data from 55 datasets were obtained (47 trials, 54 173 patients). The test results differed substantially so that approaches which use the ordered nature of functional outcome data (ordinal logistic regression, t test, robust ranks test, bootstrapping the difference in mean rank) were more efficient statistically than those which collapse the data into 2 groups (2; ANOVA, P0.001). The findings were consistent across different types and sizes of trial and for the different measures of functional outcome. Conclusions—When analyzing functional outcome from stroke trials, statistical tests which use the original ordered data are more efficient and more likely to yield reliable results. Suitable approaches included ordinal logistic regression, test, and robust ranks test.