Summary
Overdispersion and structural zeros are two major manifestations of departure from the Poisson assumption when modeling count responses using Poisson loglinear regression. As noted in a large body of literature, ignoring such departures could yield bias and lead to wrong conclusions. Different approaches have been developed to tackle these two major problems. In this paper, we review available methods for dealing with overdispersion and structural zeros within a longitudinal data setting and propose a distribution-free modeling approach to address the limitations of these methods by utilizing a new class of functional response models (FRM). We illustrate our approach with both simulated and real study data.
The generalized estimating equations (GEEs) and generalized linear mixed-effects model (GLMM) are the two most popular paradigms to extend models for cross-sectional data to a longitudinal setting. Although the two approaches yield well-interpreted models for continuous outcomes, it is quite a different story when applied to binomial responses. We discuss major modeling differences between the GEE-and GLMMderived models by presenting new results regarding the model-driven differences. Our results show that GLMM induces some artifacts in the marginal models at assessment times, making it inappropriate when applied to such responses from real study data. The different interpretations of parameters resulting from the conceptual difference between the two modeling approaches also carry quite significant implications and ramifications with respect to data and power analyses. Although a special case involving a scale difference in parameters between GEE and GLMM has been noted in the literature, its implications in real data analysis has not been thoroughly addressed. Further, this special case has a very limited covariate structure and does not apply to most real studies, especially multi-center clinical trials. The new results presented fill a substantial gap in the literature regarding the model-driven differences between the two dueling paradigms.
174 Background: Diabetes mellitus (DM) is identified as a negative prognostic indicator in hepatocellular carcinoma (HCC), though the basis for this is unknown. Methods: We conducted a retrospective review of 279 advanced and 191 transplanted HCC patients diagnosed between 1998 and 2008. Logistic regression analyses were conducted to assess the effect of clinical DM on clinical outcomes including distant metastasis and vascular invasion. Results: Eighty- four of 191 (44%) transplanted patients had DM at time of transplantation and 97 of 279 (34%) nontransplanted patients had DM at the time of diagnosis. The presence of DM was associated with an older age at time of diagnosis and a higher prevalence of hepatitis C virus (HCV) and nonalcoholic steatohepatitis (NASH). Also 30% (30/97) of diabetics compared to only 9.3% (17/182) of nondiabetics (p<0.0001) among the cohort with advanced disease had distant metastasis at the time of initial diagnosis, and this difference remained significant when adjusting for CLIP stage, age, and etiologic risk factors in a multivariate logistic regression analysis (OR=8.3, p<0.0001). The association of DM with invasive disease was echoed among early stage transplanted HCC patients in whom histologically confirmed macrovascular invasion was higher among patients with DM compared to those without (20.5% vs. 9.5%, p=0.032). The association of DM with increased risk of macrovascular invasion remained significant in a multivariate logistic regression analysis when adjusting for tumor size, number of nodules, age, obesity and etiologic risk factors (OR=3.2, p=0.025). Conclusions: DM was associated with significantly higher incidence of histological macrovascular invasion in a large cohort of HCC patients receiving liver transplantation and a significantly higher rate of distant metastatic disease at diagnosis in a large cohort of HCC patients with advanced disease. No significant financial relationships to disclose.
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