On directors’ compensation: a multilevel analysis of Spanish listed companies

This study analyzes the determinants of the annual compensation of directors belonging to the boards of the Spanish companies that constitute the IBEX 35 stock index. We investigate the importance of observed and unobserved heterogeneity in explaining director compensation. Based on a three-level mixed effect model, our analysis includes time-invariant random effects at company and manager level as determinants of director pay. We find that company effects explain 30% of the variation in director pay, while company and director effects taken together explain 77% of that variation. Our findings suggest that the characteristics of the company, in terms of activity sector, size and financial performance, and the professional attributes of the director (especially the role within the board), influence the compensation received. In addition, some directors and companies show random effects (either positive or negative) that significantly separate them from the expected compensation estimated from the fixed part of the model.

Meta-analysis of health state utility values measured by EuroQol 5-dimensions (EQ5D) questionnaire in Chinese women with breast cancer

Background To synthesise EQ5D health state utility values in Chinese women with breast cancer for parameterising a cost utility model. Methods Eligible studies had to report health state utility values measured by EQ-5D in Chinese women diagnosed with breast cancer. Risk of bias was assessed using the Newcastle Ottawa Scale (NOS). Data from single arm studies was pooled using meta-analysis of single proportions to provide overall point estimates and 95% confidence intervals for fixed and random effects models using the inverse variance and Der Simonian-Laird methods respectively. Heterogeneity was evaluated using the I2 statistic and sensitivity analysis and meta-regression were conducted. Results Five papers were included, when all studies were combined (n = 4,100) the mean utility (95% confidence interval) for random effects model was 0.83 (0.78, 0.89); for TNM 0-1 0.85 (0.75, 0.95); for TNM II 0.85 (0.78, 0.93); for TNM III 0.83 (0.77, 0.90) and for TNM IV 0.73 (0.63, 0.82).The utility of patients in State P (first year after primary breast cancer) 0.84 (0.80, 0.88); in State R (first year after recurrence) 0.73 (0.69, 0.76), in State S (second and following years after primary breast cancer or recurrence) 0.88 (0.83, 0.92); and in State M (metastatic disease) 0.78 (0.74, 0.82). Mean utility for duration since diagnosis 13 to 36 months was 0.88 (0.80, 0.96, I2 =95%); for 37 to 60 months 0.89 (0.82, 0.96, I2 =90%); for more than 60 months 0.86 (0.76, 0.96, I2 =90%). Mean utility for chemotherapy was 0.86 (0.79, 0.92, I2 =97%); for radiotherapy 0.83 (0.69, 0.96, I2 =97%); surgery 0.80 (0.69, 0.91, I2 =98%); concurrent chemo-radiation 0.70 (0.60, 0.81, I2 =86%) and endocrine therapy 0.90 (0.83, 0.97, I2 =91%). Conclusion: This study synthesises the evidence for health state utility values for Chinese women with breast cancer which is useful to inform cost utility models.

Improving the Interpretation of Random Effects Regression Results

Mummolo and Peterson improve the use and interpretation of fixed-effects models by pointing out that unit intercepts fundamentally reduce the amount of variation of variables in fixed-effects models. Along a similar vein, we make two claims in the context of random effects models. First, we show that potentially large reductions in variation, in this case caused by quasi-demeaning, also occur in models using random effects. Second, in many instances, what authors claim to be a random effects model is actually a pooled model after the quasi-demeaning process, affecting how we should interpret the model. A literature review of random effects models in top journals suggests that both points are currently not well understood. To better help users interested in improving their interpretation of random effects models, we provide Stata and R programs to easily obtain post-estimation quasi-demeaned variables.

Accuracy and Precision of Fixed and Random Effects in Meta-Analyses of Randomized Control Trials for Continuous Outcomes

Meta-analyses of treatment effects in randomized control trials are often faced with the problem of missing information required to calculate effect sizes and their sampling variances. Particularly, correlations between pre- and posttest scores are frequently not available. As an ad-hoc solution, researchers impute a constant value for the missing correlation. As an alternative, we propose adopting a multivariate meta-regression approach that models independent group effect sizes and accounts for the dependency structure using robust variance estimation or three-level modeling. A comprehensive simulation study mimicking realistic conditions of meta-analyses in clinical and educational psychology suggested that the prevalent imputation approach works well for estimating the pooled effect but severely distorts the between-study heterogeneity. In contrast, the robust meta-regression approach resulted in largely unbiased fixed and random effects. Based on these results recommendations for meta-analytic practice and future meta-analytic developments are provided.

On estimating a constrained bivariate random effects model for meta-analysis of test accuracy studies

Tailored meta-analysis uses setting-specific knowledge for the test positive rate and disease prevalence to constrain the possible values for a test's sensitivity and specificity. The constrained region is used to select those studies relevant to the setting for meta-analysis using an unconstrained bivariate random effects model (BRM). However, sometimes there may be no studies to aggregate, or the summary estimate may lie outside the plausible or “applicable” region. Potentially these shortcomings may be overcome by incorporating the constraints in the BRM to produce a constrained model. Using a penalised likelihood approach we developed an optimisation algorithm based on co-ordinate ascent and Newton-Raphson iteration to fit a constrained bivariate random effects model (CBRM) for meta-analysis. Using numerical examples based on simulation studies and real datasets we compared its performance with the BRM in terms of bias, mean squared error and coverage probability. We also determined the ‘closeness’ of the estimates to their true values using the Euclidian and Mahalanobis distances. The CBRM produced estimates which in the majority of cases had lower absolute mean bias and greater coverage probability than the BRM. The estimated sensitivities and specificity for the CBRM were, in general, closer to the true values than the BRM. For the two real datasets, the CBRM produced estimates which were in the applicable region in contrast to the BRM. When combining setting-specific data with test accuracy meta-analysis, a constrained model is more likely to yield a plausible estimate for the sensitivity and specificity in the practice setting than an unconstrained model.