The modeling and analysis of networks and network data has
seen an explosion of interest in recent years and represents an exciting direction
for potential growth in statistics. Despite the already substantial amount
of work done in this area to date by researchers from various disciplines,
however, there remain many questions of a decidedly foundational nature—
natural analogues of standard questions already posed and addressed in more
classical areas of statistics—that have yet to even be posed, much less addressed.
Here we raise and consider one such question in connection with
network modeling. Specifically, we ask, “Given an observed network, what
is the sample size?” Using simple, illustrative examples from the class of
exponential random graph models, we show that the answer to this question
can very much depend on basic properties of the networks expected under
the model, as the number of vertices nV in the network grows. In particular,
adopting the (asymptotic) scaling of the variance of the maximum likelihood
parameter estimates as a notion of effective sample size (neff), we show that
when modeling the overall propensity to have ties and the propensity to reciprocate
ties, whether the networks are sparse or not under the model (i.e.,
having a constant or an increasing number of ties per vertex, respectively) is
sufficient to yield an order of magnitude difference in neff, from O(nV ) to
O(n2
V ). In addition, we report simulation study results that suggest similar
properties for models for triadic (friend-of-a-friend) effects. We then explore
some practical implications of this result, using both simulation and data on
food-sharing from Lamalera, Indonesia.

/pdf/on-the-question-of-effective-sample-size-in-network-modeling-1vde0fm5h5.pdf

On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry.

Asthma is a complex disease with striking disparities across racial and ethnic groups. Despite its relatively high burden, representation of individuals of African ancestry in asthma genome-wide association studies (GWAS) has been inadequate, and true associations in these underrepresented minority groups have been inconclusive. We report the results of a genome-wide meta-analysis from the Consortium on Asthma among African Ancestry Populations (CAAPA; 7009 asthma cases, 7645 controls). We find strong evidence for association at four previously reported asthma loci whose discovery was driven largely by non-African populations, including the chromosome 17q12-q21 locus and the chr12q13 region, a novel (and not previously replicated) asthma locus recently identified by the Trans-National Asthma Genetic Consortium (TAGC). An additional seven loci reported by TAGC show marginal evidence for association in CAAPA. We also identify two novel loci (8p23 and 8q24) that may be specific to asthma risk in African ancestry populations.

/pdf/association-study-in-african-admixed-populations-across-the-5e3welfz46.pdf

Association study in African-admixed populations across the Americas recapitulates asthma risk loci in non-African populations.

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this area to date by researchers from various disciplines, however, there remain many questions of a decidedly foundational nature - natural analogues of standard questions already posed and addressed in more classical areas of statistics - that have yet to even be posed, much less addressed. Here we raise and consider one such question in connection with network modeling. Specifically, we ask, "Given an observed network, what is the sample size?" Using simple, illustrative examples from the class of exponential random graph models, we show that the answer to this question can very much depend on basic properties of the networks expected under the model, as the number of vertices $n_V$ in the network grows. In particular, adopting the (asymptotic) scaling of the variance of the maximum likelihood parameter estimates as a notion of effective sample size ($n_{\mathrm{eff}}$), we show that when modeling the overall propensity to have ties and the propensity to reciprocate ties, whether the networks are sparse or not under the model (i.e., having a constant or an increasing number of ties per vertex, respectively) is sufficient to yield an order of magnitude difference in $n_{\mathrm{eff}}$, from $O(n_V)$ to $O(n^2_V)$. In addition, we report simulation study results that suggest similar properties for models for triadic (friend-of-a-friend) effects. We then explore some practical implications of this result, using both simulation and data on food-sharing from Lamalera, Indonesia.

On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry

Type 2 diabetes (T2D) disproportionally affects African Americans (AfA) but, to date, genetic variants identified from genome-wide association studies (GWAS) are primarily from European and Asian populations. We examined the single nucleotide polymorphism (SNP) and locus transferability of 40 reported T2D loci in six AfA GWAS consisting of 2,806 T2D case subjects with or without end-stage renal disease and 4,265 control subjects from the Candidate Gene Association Resource Plus Study. Our results revealed that seven index SNPs at the TCF7L2, KLF14, KCNQ1, ADCY5, CDKAL1, JAZF1, and GCKR loci were significantly associated with T2D (P < 0.05). The strongest association was observed at TCF7L2 rs7903146 (odds ratio [OR] 1.30; P = 6.86 × 10−8). Locus-wide analysis demonstrated significant associations (Pemp < 0.05) at regional best SNPs in the TCF7L2, KLF14, and HMGA2 loci as well as suggestive signals in KCNQ1 after correction for the effective number of SNPs at each locus. Of these loci, the regional best SNPs were in differential linkage disequilibrium (LD) with the index and adjacent SNPs. Our findings suggest that some loci discovered in prior reports affect T2D susceptibility in AfA with similar effect sizes. The reduced and differential LD pattern in AfA compared with European and Asian populations may facilitate fine mapping of causal variants at loci shared across populations.

/pdf/transferability-and-fine-mapping-of-type-2-diabetes-loci-in-5059edtbo5.pdf

Transferability and Fine Mapping of Type 2 Diabetes Loci in African Americans The Candidate Gene Association Resource Plus Study

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics Despite the already substantial amount of work done in this area to date by researchers from various disciplines, however, there remain many questions of a decidedly foundational nature --- natural analogues of standard questions already posed and addressed in more classical areas of statistics --- that have yet to even be posed, much less addressed Here we raise and consider one such question in connection with network modeling Specifically, we ask, "Given an observed network, what is the sample size?" Using simple, illustrative examples from the class of exponential random graph models, we show that the answer to this question can very much depend on basic properties of the networks expected under the model, as the number of vertices N in the network grows In particular, we show that whether the networks are sparse or not under our model (ie, having relatively few or many edges between vertices, respectively) is sufficient to change the asymptotic rates for maximum likelihood parameter estimation by an order of magnitude, from N^(1/2) to N We then explore some practical implications of this result, using both simulation and data on food-sharing from Lamalera, Indonesia

On the question of effective sample size in network modeling

Affected relatives are essential for pedigree linkage analysis, however, they cause a violation of the independent sample assumption in case-control association studies. To avoid the correlation between samples, a common practice is to take only one affected sample per pedigree in association analysis. Although several methods exist in handling correlated samples, they are still not widely used in part because these are not easily implemented, or because they are not widely known. We advocate the effective sample size method as a simple and accessible approach for case-control association analysis with correlated samples. This method modifies the chi-square test statistic, p-value, and 95% confidence interval of the odds-ratio by replacing the apparent number of allele or genotype counts with the effective ones in the standard formula, without the need for specialized computer programs. We present a simple formula for calculating effective sample size for many types of relative pairs and relative sets. For allele frequency estimation, the effective sample size method captures the variance inflation exactly. For genotype frequency, simulations showed that effective sample size provides a satisfactory approximation. A gene which is previously identified as a type 1 diabetes susceptibility locus, the interferon-induced helicase gene (IFIH1), is shown to be significantly associated with rheumatoid arthritis when the effective sample size method is applied. This significant association is not established if only one affected sib per pedigree were used in the association analysis. Relationship between the effective sample size method and other methods -- the generalized estimation equation, variance of eigenvalues for correlation matrices, and genomic controls -- are discussed.

/pdf/effective-sample-size-quick-estimation-of-the-effect-of-88gu81e489.pdf

Effective Sample Size: Quick Estimation of the Effect of Related Samples in Genetic Case-Control Association Analyses

Correlated samples have been frequently avoided in case-controlgenetic association studies in part because the methods for handling them are either noteasily implemented or not widely known. Weadvocate one method for case-control association analysis of correlatedsamples -- the effective sample size method -- as a simple andaccessible approach that does not require specialized computer programs.The effective sample size method captures the variance inflationof allele frequency estimation exactly, and can be used to modify thechi-square test statistic, p-value, and 95% confidence interval ofodds-ratio simply by replacing the apparent number of allele counts with theeffective ones. For genotype frequency estimation, although a singleeffective sample size is unable to completely characterize the variance inflation,an averaged one can satisfactorily approximate the simulated result.The effective sample size method is applied to the rheumatoid arthritissiblings data collected from the North American Rheumatoid Arthritis Consortium (NARAC)to establish a significant association with the interferon-inducedhelicasel gene (IFIH1) previously being identified as a type 1 diabetessusceptibility locus. Connections between the effective sample sizemethod and other methods, such as generalized estimation equation,variance of eigenvalues for correlation matrices, and genomic controls,are also discussed.

/pdf/effective-sample-size-quick-estimation-of-the-effect-of-3pnnz44f0a.pdf

Research Article: Effective sample size: Quick estimation of the effect of related samples in genetic case-control association analyses

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Effective Sample Size: Quick Estimation of the Effect of Related Samples in Genetic Case-Control Association Analyses

Effective Sample Size: Quick Estimation of the Effect of Related Samples in Genetic Case-Control Association Analyses

Research Article: Effective sample size: Quick estimation of the effect of related samples in genetic case-control association analyses