We derive an estimator of the asymptotic variance of both single and multiple imputation estimators. We assume a parametric imputation model but allow for non-and semiparametric analysis models. Our variance estimator, in contrast to the estimator proposed by Rubin (1987), is consistent even when the imputation and analysis models are misspecified and incompatible with one another. Some

We consider marginal generalized semiparametric partially linear models for clustered data. Lin and Carroll derived the semiparametric efficient score function for this problem in the multivariate Gaussian case, but they were unable to construct a semiparametric efficient estimator that actually achieved the semiparametric information bound. Here we propose such an estimator and generalize the work to marginal generalized partially linear models. We investigate asymptotic relative efficiencies of the estimators that ignore the within-cluster correlation structure either in nonparametric curve estimation or throughout. We evaluate the finite-sample performance of these estimators through simulations and illustrate it using a longitudinal CD4 cell count dataset. Both theoretical and numerical results indicate that properly taking into account the within-subject correlation among the responses can substantially improve efficiency.

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We have hypothesized that dietary modulation of intestinal non-coding RNA [microRNA (miRNA)] expression may contribute to the chemoprotective effects of nutritional bioactives (fish oil and pectin). To fully understand the effects of these agents on the expression of miRNAs, Sprague-Dawley rats were fed diets containing corn oil or fish oil with pectin or cellulose and injected with azoxymethane (AOM, a colon-specific carcinogen) or saline (control). Real-time polymerase chain reaction using miRNA-specific primers and Taq Man probes was carried out to quantify effects on miRNA expression in colonic mucosa. From 368 mature miRNAs assayed, at an early stage of cancer progression (10 week post AOM injection), let-7d, miR-15b, miR-107, miR-191 and miR-324-5p were significantly (P < 0.05) affected by diet x carcinogen interactions. Overall, fish oil fed animals exhibited the smallest number of differentially expressed miRNAs (AOM versus saline treatment). With respect to the tumor stage (34 week post AOM injection), 46 miRNAs were dysregulated in adenocarcinomas compared with normal mucosa from saline-injected animals. Of the 27 miRNAs expressed at higher (P < 0.05) levels in tumors, miR-34a, 132, 223 and 224 were overexpressed at >10-fold. In contrast, the expression levels of miR-192, 194, 215 and 375 were dramatically reduced (< or = 0.32-fold) in adenocarcinomas. These results demonstrate for the first time the utility of the rat AOM model and the novel role of fish oil in protecting the colon from carcinogen-induced miRNA dysregulation.