A two-stage model for multiple time series data of counts

We propose a two-stage model for time series data of counts from multiple locations. This method fits first-stage model(s) using the technique of iteratively weighted filtered least squares (IWFLS) to obtain location-specific intercepts and slopes, with possible lagged effects via polynomial distributed lag modeling. These slopes and/or intercepts are then taken to a second-stage mixed-effects meta-regression model in order to stabilize results from various locations. The representation of the models from the stages into a combined mixed-effects model, issues of inference and choices of the parameters in modeling the lag structure are discussed. We illustrate this proposed model via detailed analysis on the effect of air pollution on school absenteeism based on data from the Southern California Children's Health Study.     

Genome-wide linkage analysis of systolic blood pressure slope using the Genetic Analysis Workshop 13 data sets

Systolic blood pressure (SBP) is an age-dependent complex trait for which both environmental and genetic factors may play a role in explaining variability among individuals. We performed a genome-wide scan of the rate of change in SBP over time on the Framingham Heart Study data and one randomly selected replicate of the simulated data from the Genetic Analysis Workshop 13. We used a variance-component model to carry out linkage analysis and a Markov chain Monte Carlo-based multiple imputation approach to recover missing information. Furthermore, we adopted two selection strategies along with the multiple imputation to deal with subjects taking antihypertensive treatment. The simulated data were used to compare these two strategies, to explore the effectiveness of the multiple imputation in recovering varying degrees of missing information, and its impact on linkage analysis results. For the Framingham data, the marker with the highest LOD score for SBP slope was found on chromosome 7. Interestingly, we found that SBP slopes were not heritable in males but were for females; the marker with the highest LOD score was found on chromosome 18. Using the simulated data, we found that handling treated subjects using the multiple imputation improved the linkage results. We conclude that multiple imputation is a promising approach in recovering missing information in longitudinal genetic studies and hence in improving subsequent linkage analyses.     

Longitudinal variance components models for systolic blood pressure, fitted using Gibbs sampling

This paper describes an analysis of systolic blood pressure (SBP) in the Genetic Analysis Workshop 13 (GAW13) simulated data. The main aim was to assess evidence for both general and specific genetic effects on the baseline blood pressure and on the rate of change (slope) of blood pressure with time. Generalized linear mixed models were fitted using Gibbs sampling in WinBUGS, and the additive polygenic random effects estimated using these models were then used as continuous phenotypes in a variance components linkage analysis. The first-stage analysis provided evidence for general genetic effects on both the baseline and slope of blood pressure, and the linkage analysis found evidence of several genes, again for both baseline and slope.     

Multiple imputation methods for handling incomplete longitudinal and clustered data where the target analysis is a linear mixed effects model

Multiple imputation (MI) is increasingly popular for handling multivariate missing data. Two general approaches are available in standard computer packages: MI based on the posterior distribution of incomplete variables under a multivariate (joint) model, and fully conditional specification (FCS), which imputes missing values using univariate conditional distributions for each incomplete variable given all the others, cycling iteratively through the univariate imputation models. In the context of longitudinal or clustered data, it is not clear whether these approaches result in consistent estimates of regression coefficient and variance component parameters when the analysis model of interest is a linear mixed effects model (LMM) that includes both random intercepts and slopes with either covariates or both covariates and outcome contain missing information. In the current paper, we compared the performance of seven different MI methods for handling missing values in longitudinal and clustered data in the context of fitting LMMs with both random intercepts and slopes. We study the theoretical compatibility between specific imputation models fitted under each of these approaches and the LMM, and also conduct simulation studies in both the longitudinal and clustered data settings. Simulations were motivated by analyses of the association between body mass index (BMI) and quality of life (QoL) in the Longitudinal Study of Australian Children (LSAC). Our findings showed that the relative performance of MI methods vary according to whether the incomplete covariate has fixed or random effects and whether there is missingnesss in the outcome variable. We showed that compatible imputation and analysis models resulted in consistent estimation of both regression parameters and variance components via simulation. We illustrate our findings with the analysis of LSAC data.     

Comparison of Haseman-Elston regression analyses using single, summary, and longitudinal measures of systolic blood pressure

To compare different strategies for linkage analyses of longitudinal quantitative trait measures, we applied the "revisited" Haseman-Elston (RHE) regression model (the cross product of centered sib-pair trait values is regressed on expected identical-by-descent allele sharing) to cross-sectional, summary, and repeated measurements of systolic blood pressure (SBP) values in replicate 34, randomly selected from the Genetic Analysis Workshop 13 simulated data. RHE linkage scans were performed without knowledge of the generating model using the following phenotypes derived from untreated SBP measurements: the first, the last, the mean, the ratio of the change between the first and last over time, and the estimated linear regression slope coefficient. Estimates of allele sharing in sibling pairs were obtained from the complete genotype data of Cohorts 1 and 2, but linkage analyses were restricted to the five visits of Cohort 2 siblings. Evidence for linkage was suggestive (p < 0.001) at markers neighboring SBP genes Gb35, Gs10, and Gs12, but weaker signals (p < 0.01) were obtained at markers mapping close to Gb34 and Gs11. Linkage to baseline genes Gb34 and Gb35 was best detected using the first SBP measurement, whereas linkage to slope genes Gs10-12 was best detected using the last or mean SBP value. At markers on chromosomes 13 and 21 displaying strongest linkage signals, marginal RHE-type models including repeated SBP measures were fit to test for overall and time-dependent genetic effects. These analyses assumed independent sib pairs and employed generalized estimating equations (GEE) with a first-order autoregressive working correlation structure to adjust for serial correlation present among repeated observations from the same sibling pair.     

Reducing the exome search space for Mendelian diseases using genetic linkage analysis of exome genotypes

Many exome sequencing studies of Mendelian disorders fail to optimally exploit family information. Classical genetic linkage analysis is an effective method for eliminating a large fraction of the candidate causal variants discovered, even in small families that lack a unique linkage peak. We demonstrate that accurate genetic linkage mapping can be performed using SNP genotypes extracted from exome data, removing the need for separate array-based genotyping. We provide software to facilitate such analyses.     

Heterogeneity of genetic control of blood pressure in ethnically different populations.

We review the literature on statistical genetic analyses of blood pressure in samples from various ethnic backgrounds using different statistical methods and packages. We then provide the results of a complex segregation analysis performed on familial data on systolic and diastolic blood pressure in 2 ethnically different populations, Chuvashans and Turkmenians. Two types of major gene models were tested in the segregation analysis: Model type 1 tests for a Mendelian mode of transmission and estimates genotype-specific averages regardless of age and sex effect, and model type 2 estimates age and sex effects on each of 3 genotypes within the putative major genotype. In both total samples, by both types of segregation analysis, familial aggregation of both systolic and diastolic blood pressure was inconsistent with the Mendelian mode of inheritance. In the next step of analysis the pedigrees in both samples were sorted into 2 groups on the basis of 2 likelihoods as obtained under Mendelian and nontransmission models for each entire sample. This procedure resulted in the appearance of 2 subsamples (large and small) in each ethnic sample. The segregation analysis that was carried out then on the larger subsample provided consistent evidence to support the major gene effect on systolic and diastolic blood pressure in 2 ethnic groups. Interestingly, model type 2 showed that in both ethnically different large subsamples, for each sex the genotype predisposing to a larger mean value of systolic (or diastolic) blood pressure also displayed the highest rate of blood pressure increase with age. We discuss in detail possible sources of heterogeneity in familial transmission of blood pressure observed in our 2 samples, and we suggest a method to improve the analysis of heterogeneity for trait inheritance.     

Estimation of segregation and linkage parameters in simulated data. I. Segregation analyses with different ascertainment schemes.

We report the results of a simulation study designed to assess the capability of segregation analysis to detect Mendelian transmission and to estimate genetic model parameters for complex qualitative traits, characterized by heritability in the range 0.20-0.45 and low heterozygote penetrance. The pedigree analysis package, PAP, was used to perform the analyses. For all data sets, models of no transmission could be rejected. In most cases, models of Mendelian transmission could not be rejected; however, several samples approached significance levels. When Mendelian transmission was assumed, reasonably good parameter estimates were obtained, although heterozygote penetrances were often overestimated. Different sampling schemes were imposed on the simulated data in order to examine the extent of information loss with the reduction in sample size. One of these strategies (a sequential sampling scheme) appears to have resulted in critical loss of information in some cases.     

On the use of the classical tests for detecting linkage.

Some drawbacks of the classical Mather's linkage text XL2 are considered, and the simple contingency analysis is suggested as an alternative method. The former test is conditional on Mendelian segregation at both loci, whereas the simple contingency test is not. Furthermore, the contingency test and the test for Mendelian segregation at each locus are orthogonal when performed using the G statistic. Simulation results show that, when the XL2 is used, the actual type I error probability (alpha a) can be dramatically perturbed. As expected, no alpha a perturbation is observed when the G contingency test is used. On the other hand, when segregation is Mendelian at both loci, the power of the XL2 method is larger than that of the contingency G test when sample size is small and strong marginal distortion is observed. Because strong marginal distortion may suggest that segregation may be non-Mendelian, the XL2 is in general discouraged in favor of the simple contingency analysis.     

Modeling segregation distortion for viability selection I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F₂ population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.     

Graphical aids to interpretation of Scatchard plots and dose-response curves

General expressions are derived for the limiting slopes and intercepts of graphical representations of experimental binding data in either the Scatchard or the “dose-response” co-ordinate systems. We apply a previously formulated general model that includes heterogeneity and/or cooperativity of receptor affinity. One must establish or assume a physical chemical mechanism in order to fully interpret these limiting slopes and intercepts. However, they do provide satisfactory initial estimates for the binding parameters, for use in a non-linear least squares curve fitting approach using an exact model.     

Genome-wide linkage scan for genes affecting longitudinal trends in systolic blood pressure

Only one genome scan to date has attempted to make use of the longitudinal data available in the Framingham Heart Study, and this attempt yielded evidence of linkage to a gene for mean systolic blood pressure. We show how the additional information available in these longitudinal data can be utilized to examine linkages for not only mean systolic blood pressure (SBP), but also for its trend with age and its variability. Prior to linkage analysis, individuals treated for hypertension were adjusted to account for right-censoring of SBP. Regressions on age were fitted to obtain orthogonal measures of slope, curvature, and residual variance of SBP that were then used as dependent variables in the model-free linkage program SIBPAL. We included mean age, gender, and cohort as covariates in the analysis. To improve power, sibling pairs were weighted for informativity using weights derived from both the marker and trait. The most significant results from our analyses were found on chromosomes 12, 15, and 17 for mean SBP, and chromosome 20 for both SBP slope and curvature.     

A Two-Way Analysis of Covariance Model for Classification of Stability Data

This paper proposes a procedure for testing and classifying data with multiple factors. A two-way analysis of covariance is used to classify the differences among the batches as well as another factor such as package type and/or product strength. In the test procedure, slopes and intercepts of the main effects are tested using a combination of simultaneous and sequential F-tests. Based on the test procedure results, the data are classified into one of four different groups. For each group, shelf life can be calculated accordingly. We examine if the procedure produces satisfactory control of the probability of a Type I error and the power of detecting the difference of degradation rates and intercepts for different nominal levels. The method is evaluated with a Monte Carlo simulation study. The proposed procedure is compared with the current FDA procedure using real data.     

A single-gene explanation for the probability of having idiopathic talipes equinovarus.

It has been hypothesized that the pathogenesis of idiopathic talipes equinovarus (ITEV, or clubfoot) is explained by genetic regulation of development and growth. The objective of the present study was to determine whether a single Mendelian gene explains the probability of having ITEV in a sample of 143 Caucasian pedigrees from Iowa. These pedigrees were ascertained through probands with ITEV. Complex segregation analyses were undertaken using a regressive logistic model. The results of these analyses strongly rejected the hypotheses that the probability of having ITEV in these pedigrees was explained by a non-Mendelian pattern of transmission with residual sibling correlation, a nontransmitted (environmental) factor with residual sibling correlation, or residual sibling correlation alone. These results were consistent with the hypothesis that the probability of having ITEV was explained by the Mendelian segregation of a single gene with two alleles plus the effects of some unmeasured factor(s) shared among siblings. The segregation of alleles at this single Mendelian gene indicated that the disease allele A was incompletely dominant to the nondisease allele B. The disease allele A, associated with ITEV affection, was estimated to occur in the population of inference with a frequency of .007. After adjusting for sex-specific population incidences of ITEV, the conditional probability (penetrance) of ITEV affection given the AA, AB, and BB genotypes was computed to be 1.0, .039, and .0006, respectively. Individual pedigrees in this sample that most strongly supported the single Mendelian gene hypothesis were identified. These pedigrees are candidates for genetic linkage analyses or DNA association studies.     

Further evidence for the increased power of LOD scores compared with nonparametric methods.

In genetic analysis of diseases in which the underlying model is unknown, "model free" methods-such as affected sib pair (ASP) tests-are often preferred over LOD-score methods, although LOD-score methods under the correct or even approximately correct model are more powerful than ASP tests. However, there might be circumstances in which nonparametric methods will outperform LOD-score methods. Recently, Dizier et al. reported that, in some complex two-locus (2L) models, LOD-score methods with segregation analysis-derived parameters had less power to detect linkage than ASP tests. We investigated whether these particular models, in fact, represent a situation that ASP tests are more powerful than LOD scores. We simulated data according to the parameters specified by Dizier et al. and analyzed the data by using a (a) single locus (SL) LOD-score analysis performed twice, under a simple dominant and a recessive mode of inheritance (MOI), (b) ASP methods, and (c) nonparametric linkage (NPL) analysis. We show that SL analysis performed twice and corrected for the type I-error increase due to multiple testing yields almost as much linkage information as does an analysis under the correct 2L model and is more powerful than either the ASP method or the NPL method. We demonstrate that, even for complex genetic models, the most important condition for linkage analysis is that the assumed MOI at the disease locus being tested is approximately correct, not that the inheritance of the disease per se is correctly specified. In the analysis by Dizier et al., segregation analysis led to estimates of dominance parameters that were grossly misspecified for the locus tested in those models in which ASP tests appeared to be more powerful than LOD-score analyses.     

A multistage testing strategy for detection of quantitative trait Loci affecting disease resistance in Atlantic salmon

A multistage testing strategy to detect QTL for resistance to infectious salmon anemia (ISA) in Atlantic salmon is proposed. First, genotyping of amplified fragment length polymorphisms (AFLP) and a transmission disequilibrium test (TDT) were carried out using dead offspring from a disease resistance challenge test. Second, AFLP genotyping among survivors followed by a Mendelian segregation test was performed. Third, within-family survival analyses using all offspring were developed and applied to significant TDT markers with Mendelian inheritance. Maximum-likelihood methodology was developed for TDT with dominant markers to exploit linkage disequilibrium within families. The strategy was tested with two full-sib families of Atlantic salmon sired by the same male and consisting of 79 offspring in total. All dead offspring from the two families were typed for 64 primer combinations, resulting in 340 scored markers. There were 26 significant results out of 401 TDTs using dead offspring. In the second stage, only 17 marker families showed Mendelian segregation and were tested in survival analysis. A permutation test was performed for all survival analyses to compute experimentwise P-values. Two markers, aaccac356 and agccta150, were significant at P < 0.05 when accounting for multiple testing in the survival analyses. The proposed strategy might be more powerful than current mapping strategies because it reduces the number of tests to be performed in the last testing stage.     

Complex segregation analysis of obsessive-compulsive disorder in families with pediatric probands

OBJECTIVE: The purpose of this study was to assess the mode of inheritance for obsessive-compulsive disorder (OCD) in families ascertained through pediatric probands. METHODS: We ascertained 52 families (35 case and 17 control families) through probands between the ages of 10 and 17 years. Direct interviews were completed with 215 individuals. Family informant data were collected on another 450 individuals without direct interviews, forming two data sets with one contained within the other. Complex segregation analyses were performed using regressive models as programmed in REGTL in the S.A.G.E. package.All models used in the analyses included sex-specific age and type parameters. RESULTS: All models that excluded a residual effect of an affected parent were rejected. With that parameter included, the environmental and sporadic models were rejected in comparisons with the most general model in both data sets (all p < 0.005). With the direct interview data, the general codominant Mendelian model was not rejected when compared with the most general model (p = 0.140). We could not distinguish between any of the simple Mendelian models using either data set. However, the dominant Mendelian model provided a somewhat better fit than the other Mendelian models to the direct interview data. CONCLUSIONS: The results provide evidence for a major susceptibility locus in families with OCD when age at onset is incorporated into the model. Mendelian factors at most partially explained the familial aggregation of the phenotype, and residual familial effects were necessary to fit the data adequately. The results support the importance of linkage efforts by suggesting that a major locus is segregating within a proportion of families with OCD ascertained through pediatric probands.     

Genome-wide linkage analysis of longitudinal phenotypes using σ<Superscript>2</Superscript><Subscript>A</Subscript> random effects (SSARs) fitted by Gibbs sampling

The study of change in intermediate phenotypes over time is important in genetics. In this paper we explore a new approach to phenotype definition in the genetic analysis of longitudinal phenotypes. We utilized data from the longitudinal Framingham Heart Study Family Cohort to investigate the familial aggregation and evidence for linkage to change in systolic blood pressure (SBP) over time. We used Gibbs sampling to derive sigma-squared-A-random-effects (SSARs) for the longitudinal phenotype, and then used these as a new phenotype in subsequent genome-wide linkage analyses. Additive genetic effects (sigma2A.time) were estimated to account for approximately 9.2% of the variance in the rate of change of SBP with age, while additive genetic effects (sigma2A) were estimated to account for approximately 43.9% of the variance in SBP at the mean age. The linkage results suggested that one or more major loci regulating change in SBP over time may localize to chromosomes 2, 3, 4, 6, 10, 11, 17, and 19. The results also suggested that one or more major loci regulating level of SBP may localize to chromosomes 3, 8, and 14. Our results support a genetic component to both SBP and change in SBP with age, and are consistent with a complex, multifactorial susceptibility to the development of hypertension. The use of SSARs derived from quantitative traits as input to a conventional linkage analysis appears to be valuable in the linkage analysis of genetically complex traits. We have now demonstrated in this paper the use of SSARs in the context of longitudinal family data.     

Isolation, characterization, inheritance and linkage of microsatellite markers in Tetranychus kanzawai (Acari: Tetranychidae)

We isolated and characterized seven microsatellite markers in Tetranychus kanzawai (Acari: Tetranychidae). We also examined the conformity of the isolated markers to Mendelian laws and analyzed linkage among the microsatellite loci. All microsatellite markers fit expected 1:1 disomic segregation ratio and hence were inherited in a Mendelian manner. Significant pairwise linkage was detected in three pairs of microsatellite loci. These isolated microsatellite markers may become a powerful tool for the study of behavioral ecology, population genetics, and genome mapping of T. kanzawai.     

Evidence of a rare gene for low systolic blood pressure in the Framingham Heart Study

A major risk factor for coronary heart disease in both men and women is elevated systolic blood pressure (SBP). We performed segregation analysis on age, sex-adjusted, and transformed systolic blood pressure data on 1,141 families from the Framingham cohort-offspring study using the segregation analysis program POINTER. The results of hypothesis testing revealed: (1) these data are consistent with familial transmission; (2) there is evidence for the transmission of a rare, major gene for low SBP with a gene frequency of q = 0.02; and (3) most of the transmissible component to SBP can be attributed to the polygenic background with H = 0.31.