Design and analysis for three level hierarchical structures with count response

In numerous intervention studies and education field trials, random assignment to treatment occurs in clusters rather than at the level of observation. This departure of random assignment of units may be due to logistics, political feasibility, or ecological validity. Data within the same cluster or grouping are often correlated. Application of traditional regression techniques, which assume independence between observations, to clustered data produce consistent parameter estimates. However such estimators are often inefficient as compared to methods which incorporate the clustered nature of the data into the estimation procedure (Neuhaus 1993).1 Multilevel models, also known as random effects or random components models, can be used to account for the clustering of data by estimating higher level, or group, as well as lower level, or individual variation. Designing a study, in which the unit of observation is nested within higher level groupings, requires the determination of sample sizes at each level. This study investigates the design and analysis of various sampling strategies for a 3-level repeated measures design on the parameter estimates when the outcome variable of interest follows a Poisson distribution. ^ Results study suggest that second order PQL estimation produces the least biased estimates in the 3-level multilevel Poisson model followed by first order PQL and then second and first order MQL. The MQL estimates of both fixed and random parameters are generally satisfactory when the level 2 and level 3 variation is less than 0.10. However, as the higher level error variance increases, the MQL estimates become increasingly biased. If convergence of the estimation algorithm is not obtained by PQL procedure and higher level error variance is large, the estimates may be significantly biased. In this case bias correction techniques such as bootstrapping should be considered as an alternative procedure. For larger sample sizes, those structures with 20 or more units sampled at levels with normally distributed random errors produced more stable estimates with less sampling variance than structures with an increased number of level 1 units. For small sample sizes, sampling fewer units at the level with Poisson variation produces less sampling variation, however this criterion is no longer important when sample sizes are large. ^ 1Neuhaus J (1993). “Estimation efficiency and Tests of Covariate Effects with Clustered Binary Data”. Biometrics , 49, 989–996^

NETWORK TOPOLOGY IN HUMAN PROTEIN INTERACTION DATA PREDICTS FUNCTIONAL ASSOCIATION

High-throughput assays, such as yeast two-hybrid system, have generated a huge amount of protein-protein interaction (PPI) data in the past decade. This tremendously increases the need for developing reliable methods to systematically and automatically suggest protein functions and relationships between them. With the available PPI data, it is now possible to study the functions and relationships in the context of a large-scale network. To data, several network-based schemes have been provided to effectively annotate protein functions on a large scale. However, due to those inherent noises in high-throughput data generation, new methods and algorithms should be developed to increase the reliability of functional annotations. Previous work in a yeast PPI network (Samanta and Liang, 2003) has shown that the local connection topology, particularly for two proteins sharing an unusually large number of neighbors, can predict functional associations between proteins, and hence suggest their functions. One advantage of the work is that their algorithm is not sensitive to noises (false positives) in high-throughput PPI data. In this study, we improved their prediction scheme by developing a new algorithm and new methods which we applied on a human PPI network to make a genome-wide functional inference. We used the new algorithm to measure and reduce the influence of hub proteins on detecting functionally associated proteins. We used the annotations of the Gene Ontology (GO) and the Kyoto Encyclopedia of Genes and Genomes (KEGG) as independent and unbiased benchmarks to evaluate our algorithms and methods within the human PPI network. We showed that, compared with the previous work from Samanta and Liang, our algorithm and methods developed in this study improved the overall quality of functional inferences for human proteins. By applying the algorithms to the human PPI network, we obtained 4,233 significant functional associations among 1,754 proteins. Further comparisons of their KEGG and GO annotations allowed us to assign 466 KEGG pathway annotations to 274 proteins and 123 GO annotations to 114 proteins with estimated false discovery rates of <21% for KEGG and <30% for GO. We clustered 1,729 proteins by their functional associations and made pathway analysis to identify several subclusters that are highly enriched in certain signaling pathways. Particularly, we performed a detailed analysis on a subcluster enriched in the transforming growth factor β signaling pathway (P<10-50) which is important in cell proliferation and tumorigenesis. Analysis of another four subclusters also suggested potential new players in six signaling pathways worthy of further experimental investigations. Our study gives clear insight into the common neighbor-based prediction scheme and provides a reliable method for large-scale functional annotations in this post-genomic era.

A simulation study using the hybrid statistic and the meta-analysis t-test for data with matched and unmatched subjects in the interim analysis of clinical trials

An interim analysis is usually applied in later phase II or phase III trials to find convincing evidence of a significant treatment difference that may lead to trial termination at an earlier point than planned at the beginning. This can result in the saving of patient resources and shortening of drug development and approval time. In addition, ethics and economics are also the reasons to stop a trial earlier. In clinical trials of eyes, ears, knees, arms, kidneys, lungs, and other clustered treatments, data may include distribution-free random variables with matched and unmatched subjects in one study. It is important to properly include both subjects in the interim and the final analyses so that the maximum efficiency of statistical and clinical inferences can be obtained at different stages of the trials. So far, no publication has applied a statistical method for distribution-free data with matched and unmatched subjects in the interim analysis of clinical trials. In this simulation study, the hybrid statistic was used to estimate the empirical powers and the empirical type I errors among the simulated datasets with different sample sizes, different effect sizes, different correlation coefficients for matched pairs, and different data distributions, respectively, in the interim and final analysis with 4 different group sequential methods. Empirical powers and empirical type I errors were also compared to those estimated by using the meta-analysis t-test among the same simulated datasets. Results from this simulation study show that, compared to the meta-analysis t-test commonly used for data with normally distributed observations, the hybrid statistic has a greater power for data observed from normally, log-normally, and multinomially distributed random variables with matched and unmatched subjects and with outliers. Powers rose with the increase in sample size, effect size, and correlation coefficient for the matched pairs. In addition, lower type I errors were observed estimated by using the hybrid statistic, which indicates that this test is also conservative for data with outliers in the interim analysis of clinical trials.^