Overdispersion models for correlated multinomial data: Applications to blinding assessment

Abstract

4963 4964 LANDSMAN ET AL."marginalization," which, in turn, often entails the use of computationally intensive algorithms to integrate over the random effects. 3,4 For certain link functions and mixing distributions of random effects, as is the case with the multinomial overdispersion model (MOM) introduced in Section 2, the unconditional (on random effects) mean and variance of an outcome can be expressed analytically as functions of a global parameter and additional heterogeneity/overdispersion parameter(s). In such cases, the estimation of the unknown parameters of interest can be handled via generalized estimating equations (GEE). 5,6 In the marginal approach, the (unconditional) expectation of an outcome is modeled directly as a function of global parameters. Under mild regularity conditions and correct specification of the marginal mean model of an outcome, the GEE approach will lead to consistent estimators of a global parameter. The ("working") correlation matrix should be prespecified, and its choice may affect the efficiency of the resulting estimators, especially if the correlations between the individual outcomes within a cluster are strong. An "exchangeable" correlation structure is frequently used with clustered data. 7 In the absence of reliable information about the correlation structure, the identity matrix is assumed. In this case, the estimation of a global parameter is handled via independence estimating equations, a special case of GEE. Potential correlations among the observations within clusters should be taken into account when estimating the variances of the estimated global effects. The robust ("sandwich") variance estimator is used to obtain consistent estimators of the variances of the estimated global parameters. This approach is widely used in survey sampling to estimate standard errors from clustered data. 2 In this paper, we introduce MOM and study the performance of the GEE estimators for estimating global probabilities of outcomes from clustered multinomial data. Our study was motivated by two studies: (1) an RCT with multiple practitioners and (2) a meta-analysis of RCTs, 8 both aiming at evaluating the extent of blinding in the trials. 9,10 As will be described in the following sections, the data collected for blinding assessment can be viewed as a random sample from a multinomial distribution of order two (binomial), three (trinomial), or higher, and the target parameter can be presented as a linear combination of the global probabilities.The GEE method has been applied to estimating the regression coefficients from longitudinal data with nominal and ordinal outcomes. 7,11 Krewski and Zhu 12 and Zhu et al 13 estimated the regression parameters in dose-response models for clustered trinomial data arising from developmental toxicity studies. Robust variance estimators of the GEE estimators for global parameters have been shown to perform well in settings with a large number of clusters and a relatively small and equal number of observations within each cluster, as is typical in ...

Blinding, sham, and treatment effects in randomized controlled trials for back pain in 2000–2019: A review and meta-analytic approach

“…Fourth, when we excluded outliers in effect size (two acupunctures in primary and secondary outcomes, one procedure in primary outcome, and one PT/Chiro in secondary outcome), results were attenuated, while main findings were mostly unchanged; some results in Figure S3 and Table S3. When blinding index was computed with different statistical models 49 or data structures, main findings were similar, although 2 3 3 data yielded attenuation 27,30,49 (Table S4).…”

“…Moroz et al 23 reported blinding index of 0.34/−0.2 for verum/sham and the most common blinding scenario was that participants believed they received verum regardless of the treatment received in 54 acupuncture trials, namely, wishful thinking—similar to our subgroup analysis and the finding by Braithwaite et al in comparable treatments. In contrast, Freed et al, 24 Baethge et al, 25 and Landsman et al 49 showed that overall blinding in 40 psychiatric trials is summarized as Random–Random (blinding index of 0.14/0.0 in verum/sham), and reported positive correlation between effect size and correct guesses.…”

“…We summarized blinding index and effect size by treatment modality, blinding index in caterpillar plots, and computed the “pooled blinding index” with 95% confidence interval (CI) overall and by modality, via generalized estimating equations (GEE). 49…”

“…modality, year of publication, sample size, primary versus secondary outcome) as independent variables. For sensitivity analyses, we did the following: (1) Pearson in place of Spearman, (2) blinding index under different statistical models, 49 (3) blinding index from 2×2 and 2×3 formats separately, 49 (4) investigators’ blinding data instead for patients’ (10 outcomes from 5 trials, with primary and secondary outcomes combined), and (5) exclude outliers in effect sizes (i.e. > 2 for within or between).…”

“…We summarized blinding index and effect size by treatment modality, blinding index in caterpillar plots, and computed the ''pooled blinding index'' with 95% confidence interval (CI) overall and by modality, via generalized estimating equations (GEE). 49 We repeated the entire analyses for secondary outcomes. Multiple regression was fitted via GEE with effect size as a dependent variable and study characteristics (i.e.…”