A note on implementation of decaying product correlation structures for quasi-least squares.

This note implements an unstructured decaying product matrix via the quasi-least squares approach for estimation of the correlation parameters in the framework of generalized estimating equations. The structure we consider is fairly general without requiring the large number of parameters that are involved in a fully unstructured matrix. It is straightforward to show that the quasi-least squares estimators of the correlation parameters yield feasible values for the unstructured decaying product structure. Furthermore, subject to conditions that are easily checked, the quasi-least squares estimators are valid for longitudinal Bernoulli data. We demonstrate implementation of the structure in a longitudinal clinical trial with both a continuous and binary outcome variable.

Genetic and pharmacologic inhibition of complement impairs endothelial cell function and ablates ovarian cancer neovascularization.

Complement activation plays a critical role in controlling inflammatory responses. To assess the role of complement during ovarian cancer progression, we crossed two strains of mice with genetic complement deficiencies with transgenic mice that develop epithelial ovarian cancer (TgMISIIR-TAg). TgMISIIR-TAg mice fully or partially deficient for complement factor 3 (C3) (Tg(+)C3(KO) and Tg(+)C3(HET), respectively) or fully deficient for complement factor C5a receptor (C5aR) (Tg(+)C5aR(KO)) develop either no ovarian tumors or tumors that were small and poorly vascularized compared to wild-type littermates (Tg(+)C3(WT), Tg(+)C5aR(WT)). The percentage of tumor infiltrating immune cells in Tg(+)C3(HET) tumors compared to Tg(+)C3(WT) controls was either similar (macrophages, B cells, myeloid-derived suppressor cells), elevated (effector T cells), or decreased (regulatory T cells). Regardless of these ratios, cytokine production by immune cells taken from Tg(+)C3(HET) tumors was reduced on stimulation compared to Tg(+)C3(WT) controls. Interestingly, CD31(+) endothelial cell (EC) function in angiogenesis was significantly impaired in both C3(KO) and C5aR(KO) mice. Further, using the C5aR antagonist PMX53, tube formation of ECs was shown to be C5a-dependent, possibly through interactions with the VEGF(165) but not VEGF(121) isoform. Finally, the mouse VEGF(164) transcript was underexpressed in C3(KO) livers compare to C3(WT) livers. Thus, we conclude that complement inhibition blocks tumor outgrowth by altering EC function and VEGF(165) expression.

The analysis of binary longitudinal data with time-dependent covariates.

We consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time. The goal of our analysis was to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject. However, additional care must be taken to adjust for the association between the repeated measurements on each subject. We propose a new maximum likelihood method for covariates that may be fixed or time varying. We also implement and make comparisons with two other approaches: generalized estimating equations, which may be more robust to misspecification of the true correlation structure, and alternating logistic regression, which models association via odds ratios that are subject to less restrictive constraints than are correlations. The proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters if the correlation on consecutive measurements on a subject is correctly specified. Simulations demonstrate that our approach can yield improved efficiency in estimation of the regression parameter; for equally spaced and complete data, the gains in efficiency were greatest for the parameter associated with a time-by-group interaction term and for stronger values of the correlation. For unequally spaced data and with dropout according to a missing-at-random mechanism, MARK1ML with correctly specified consecutive correlations yielded substantial improvements in terms of both bias and efficiency. We present an analysis to demonstrate application of the methods we consider. We also offer an R function for easy implementation of our approach.