Additive mixed effect model for clustered failure time data

We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and includes a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.     

A new serially correlated gamma-frailty process for longitudinal count data

We describe a new multivariate gamma distribution and discuss its implication in a Poisson-correlated gamma-frailty model. This model is introduced to account for between-subjects correlation occurring in longitudinal count data. For likelihood-based inference involving distributions in which high-dimensional dependencies are present, it may be useful to approximate likelihoods based on the univariate or bivariate marginal distributions. The merit of composite likelihood is to reduce the computational complexity of the full likelihood. A 2-stage composite-likelihood procedure is developed for estimating the model parameters. The suggested method is applied to a meta-analysis study for survival curves.     

Resolution of genetic and cultural inheritance in twin families by path analysis: application to HDL-cholesterol.

A path model and associated statistical method for the analysis of data on twin families are introduced and applied to high density lipoprotein cholesterol (HDL-c) observations in the Swedish Twin Family Study. The proposed path model incorporates both genetic and environmental sources of familial resemblance, maternal environmental effects, intergenerational differences in heritabilities, marital resemblance due to either primary or secondary phenotypic homogamy, and twin residual environmental correlations. Application of the model to HDL-c levels resulted in parameter estimates consistent with those reported in earlier reviews and in the analysis of nuclear family and twin data. Genetic heritability was estimated as h2 = .363 +/- .243, cultural heritability as c2 = .187 +/- .082, and the proportion of phenotypic variance due to residual environmental effects as r2 = .450 +/- .207. Although the parameter estimates were comparable, the statistical tests of hypotheses were, relative to other designs, of low statistical power. It appears that environmental indices are necessary for powerful tests of hypotheses.     

Gene-environment interaction effects on behavioral variation and risk of complex disorders: the example of alcoholism and other psychiatric disorders.

There have been few replicated examples of genotype x environment interaction effects on behavioral variation or risk of psychiatric disorder. We review some of the factors that have made detection of genotype x environment interaction effects difficult, and show how genotype x shared environment interaction (GxSE) effects are commonly confounded with genetic parameters in data from twin pairs reared together. Historic data on twin pairs reared apart can in principle be used to estimate such GxSE effects, but have rarely been used for this purpose. We illustrate this using previously published data from the Swedish Adoption Twin Study of Aging (SATSA), which suggest that GxSE effects could account for as much as 25% of the total variance in risk of becoming a regular smoker. Since few separated twin pairs will be available for study in the future, we also consider methods for modifying variance components linkage analysis to allow for environmental interactions with linked loci.     

Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Twin studies have been adopted for decades to disentangle the relative genetic and environmental contributions for a wide range of traits. However, heritability estimation based on the classical twin models does not take into account dynamic behavior of the variance components over age. Varying variance of the genetic component over age can imply the existence of gene–environment (G × E) interactions that general genome-wide association studies (GWAS) fail to capture, which may lead to the inconsistency of heritability estimates between twin design and GWAS. Existing parametric G × E interaction models for twin studies are limited by assuming a linear or quadratic form of the variance curves with respect to a moderator that can, however, be overly restricted in reality. Here we propose spline-based approaches to explore the variance curves of the genetic and environmental components. We choose the additive genetic, common, and unique environmental variance components (ACE) model as the starting point. We treat the component variances as variance functions with respect to age modeled by B-splines or P-splines. We develop an empirical Bayes method to estimate the variance curves together with their confidence bands and provide an R package for public use. Our simulations demonstrate that the proposed methods accurately capture dynamic behavior of the component variances in terms of mean square errors with a data set of >10,000 twin pairs. Using the proposed methods as an alternative and major extension to the classical twin models, our analyses with a large-scale Finnish twin data set (19,510 MZ twins and 27,312 DZ same-sex twins) discover that the variances of the A, C, and E components for body mass index (BMI) change substantially across life span in different patterns and the heritability of BMI drops to ∼50% after middle age. The results further indicate that the decline of heritability is due to increasing unique environmental variance, which provides more insights into age-specific heritability of BMI and evidence of G × E interactions. These findings highlight the fundamental importance and implication of the proposed models in facilitating twin studies to investigate the heritability specific to age and other modifying factors.     

The heritability of mortality due to heart diseases: a correlated frailty model applied to Danish twins.

Data of the Danish Twin Registry on monozygotic and dizygotic twins are used to analyse genetic and environmental influences on susceptibility to heart diseases for males and females, respectively. The sample includes 7955 like-sexed twin pairs born between 1870 and 1930. Follow-up was from 1 January 1943 to 31 December 1993 which results in truncation (twin pairs were included in the study if both individuals were still alive at the beginning of the follow-up) and censoring (nearly 40% of the study population was still alive at the end of the follow-up). We use the correlated gamma-frailty model for the genetic analysis of frailty to account for this censoring and truncation. During the follow-up 9370 deaths occurred, 3393 deaths were due to heart diseases in general, including 2476 deaths due to coronary heart disease (CHD). Proportions of variance of frailty attributable to genetic and environmental factors were analyzed using the structural equation model approach. Different standard biometric models are fitted to the data to evaluate the magnitude and nature of genetic and environmental factors on mortality. Using the best fitting model heritability of frailty (liability to death) was found to be 0.55 (0.07) and 0.53 (0.11) with respect to heart diseases and CHD, respectively, for males and 0.52 (0.10) and 0.58 (0.14) for females in a parametric analysis. A semi-parametric analysis shows very similar results. These analyses may indicate the existence of a strong genetic influence on individual frailty associated with mortality caused by heart diseases and CHD in both, males and females. The nature of genetic influences on frailty with respect to heart diseases and CHD is probably additive. No evidence for dominance and shared environment was found.     

Using bivariate models to understand between- and within-cluster regression coefficients, with application to twin data

In the regression analysis of clustered data it is important to allow for the possibility of distinct between- and within-cluster exposure effects on the outcome measure, represented, respectively, by regression coefficients for the cluster mean and the deviation of the individual-level exposure value from this mean. In twin data, the within-pair regression effect represents association conditional on exposures shared within pairs, including any common genetic or environmental influences on the outcome measure. It has therefore been proposed that a comparison of the within-pair regression effects between monozygous (MZ) and dizygous (DZ) twins can be used to examine whether the association between exposure and outcome has a genetic origin. We address this issue by proposing a bivariate model for exposure and outcome measurements in twin-pair data. The between- and within-pair regression coefficients are shown to be weighted averages of ratios of the exposure and outcome variances and covariances, from which it is straightforward to determine the conditions under which the within-pair regression effect in MZ pairs will be different from that in DZ pairs. In particular, we show that a correlation structure in twin pairs for exposure and outcome that appears to be due to genetic factors will not necessarily be reflected in distinct MZ and DZ values for the within-pair regression coefficients. We illustrate these results in a study of female twin pairs from Australia and North America relating mammographic breast density to weight and body mass index.     

A joint mixed effects dispersion model for menstrual cycle length and time-to-pregnancy

Menstrual cycle patterns are often used as indicators of female fecundity and are associated with hormonally dependent diseases such as breast cancer. A question of considerable interest is in identifying menstrual cycle patterns, and their association with fecundity. A source of data for addressing this question is prospective pregnancy studies that collect detailed information on reproductive aged women. However, methodological challenges exist in ascertaining the association between these two processes as the number of longitudinally measured menstrual cycles is relatively small and informatively censored by time to pregnancy (TTP), as well as the cycle length distribution being highly skewed. We propose a joint modeling approach with a mixed effects dispersion model for the menstrual cycle lengths and a discrete survival model for TTP to address this question. This allows us to assess the effect of important characteristics of menstrual cycle that are associated with fecundity. We are also able to assess the effect of fecundity predictors such as age at menarche, age, and parity on both these processes. An advantage of the proposed approach is the prediction of the TTP, thus allowing us to study the efficacy of menstrual cycle characteristics in predicting fecundity. We analyze two prospective pregnancy studies to illustrate our proposed method by building a model based on the Oxford Conception Study, and predicting for the New York State Angler Cohort Prospective Pregnancy Study. Our analysis has relevant findings for assessing fecundity.     

Rapid Sustainability Modeling for Raptors by Radiotagging and DNA-Fingerprinting

Abstract: Sustainable use of wildlife is crucial to ensuring persistence of natural resources. We used age-specific survival and breeding data to parameterize a demographic model for a harvested Kazakh saker falcon (Falco cherrug) population by radiotagging juveniles and estimating adult turnover with DNA-fingerprinting during 1993–1997. We gathered similar data during 1990–1998 to model populations of British buzzards (Buteo buteo), and during 1980–1998 to model populations of Swedish goshawks (Accipiter gentilis). Leg-bands and implanted microtransponders provided ways to test for bias and to estimate the harvest of sakers for falconry. Despite an estimated minimum first-year survival of only 23%, the observed productivity of 3.14 young per clutch would sustain a saker population (i.e., λ = 1) with a breeding rate (at laying) of only 0.63 for adults or with a residual juvenile yield of 37% if all adults breed. Higher first-year survival rates for goshawks and buzzards correlated with juvenile yields of up to 71%, but no more than half as many individuals if adults also were harvested. An annual population decline of 40% for sakers in southern Kazakhstan could be explained by observed productivity of only 0.71 young per clutch if there was also an estimated harvest of 55% of adults. This study shows that demographic models such as these can now be built rapidly if nestlings are fitted with reliable and safe radiotags and adult turnover is estimated from genetic analyses or other techniques.     

Use of monozygotic twins in search for breast cancer susceptibility loci.

We have used Swedish monozygotic twins concordant for breast cancer to study genetic changes associated with the development of breast cancer. Because loss of heterozygosity (LOH) at a specific genomic region may reflect the presence of a tumour suppressor gene, loss of the same allele in both of the twins concordant for breast cancer may pinpoint a tumour suppressor gene that confers a strong predisposition to breast cancer. DNA samples extracted from the matched tumour and normal tissues of nine twin pairs were analysed for allelic imbalance using a set of microsatellite markers on chromosomes 1, 13, 16 and 17, containing loci with known tumour suppressor genes. The two main regions, where more twin pairs than expected had lost the same allele, were located at 16qtel', including markers D16S393, D16S305 and D16S413, and at 17p13, distal to the p53 locus. Our results show that the monozygotic twin model can be used to suggest candidate regions of potential tumour suppressor genes, even with a limited number of twin pairs.     

Aetiology of teenage childbearing: reasons for familial effects.

The aims of the present study were to evaluate the contribution of the genetic and environmental factors to the risk of teenage childbearing, and to study whether life style, socio-economic conditions, and personality traits could explain possible familial effects. We linked two population-based registers: the Swedish Twin Register and the Swedish Medical Birth Register. The study covers female twin pairs born between 1953 and 1958, having their first infant before the age of 30 years (n = 1885). In order to separate familial effects from other environmental influences, and genetic effects from shared environmental effects, only complete twin pairs with known zygosity were included, in all 260 monozygotic and 370 dizygotic twin pairs. We used quantitative genetic analyses to evaluate the importance of genetic and environmental effects for liability to teenage childbearing. Logistic regression analyses were used to estimate the effects of life style, socio-economic situation, and personality on the probability of teenage childbearing, and to study whether psychosocial factors could explain possible familial effects. Fifty-nine percent (0-76%) of the variance in being a teenage mother was attributable to heritable factors; 0% (0-49%) was due to shared environmental factors; and 41% (23-67%) was explained by non-shared environmental factors. Thus, the data were consistent with the hypothesis that the familial aggregation of teenage childbearing is completely explained by genetic factors, although the alternative hypothesis that familial aggregation is entirely explained by shared environmental factors cannot be ruled out. Significant effects of smoking habits, housing conditions, and educational level were found in relation to liability to teenage childbearing. However, the familial effects on risk of teenage childbearing were not mediated through similarities in life style and socio-economic factors. When studying risk factors for teenage childbearing, it is recommended to include life style and socio-economic variables as well as information about family history of teenage childbearing. Twin Research (2000) 3, 23-27.     

Occupational Complexity and Risk of Parkinson's Disease

Background

The etiology of Parkinson''s disease (PD) remains unclear, and environmental risk-factors such as occupation have attracted interest.

Objective

The goal was to investigate occupational complexity in relation to PD.

Methods

We conducted a population-based cohort study based on the Swedish Twin Registry that included 28,778 twins born between 1886 and 1950. We identified 433 PD cases during the study period. Data on occupation were collected from either the 1970 or 1980 Swedish census, and occupational complexity was assessed via a job exposure matrix. Cox proportional hazard regression analyses with age as the underlying time scale were used to assess PD risk as a function of the three domains of occupational complexity: data, people, and things. Sex and smoking were included as covariates. Analyses stratified by twin pair were conducted to test for confounding by familial factors.

Results

High occupational complexity with data and people was associated with increased risk overall (Hazard Ratio [HR] = 1.07, 95% confidence interval [CI] 1.02–1.14, and HR = 1.10, 95% CI 1.01–1.21, respectively), and in men (HR = 1.08, 95% CI 1.01–1.16, and HR = 1.15, 95% CI 1.03–1.28, respectively). Complexity with things was not associated with risk of PD. When the analyses were stratified by twin pair, the HRs for occupational complexity with data and people were attenuated in men.

Conclusions

High complexity of work with data and people is related to increased risk of PD, particularly in men. The attenuation of risk observed in the twin pair-stratified analyses suggests that the association may partly be explained by familial factors, such as inherited traits contributing to occupational selection or other factors shared by twins.     

Longevity studies in GenomEUtwin.

Previous twin studies have indicated that approximately 25% of the variation in life span can be attributed to genetic factors and recent studies have also suggested a moderate clustering of extreme longevity within families. Here we discuss various definitions of extreme longevity and some analytical approaches with special attention to the challenges due to censored data. Lexis diagrams are provided for the Danish, Dutch, Finnish, Italian, Norwegian, and Swedish Twin registries hereby outlining possibilities for longevity studies within GenomEUtwin. We extend previous analyses of lifespan for the Danish 1870-1900 twin cohorts to include the new 1901-1910 cohorts, which are consistent with the previous findings. The size of the twin cohorts in GenomEUtwin and the existence of population-based, nationwide health and death registers make epidemiological studies of longevity very powerful. The combined GenomEUtwin sample will also allow detailed age-specific heritability analyses of lifespan. Finally, it will provide a resource for identifying unusual sibships (i.e., dizygotic twin pairs) where both survived to extreme ages, as a basis for discovering genetic variants of importance for extreme survival.     

A general approach for two-stage analysis of multilevel clustered non-Gaussian data

In this article, we propose a two-stage approach to modeling multilevel clustered non-Gaussian data with sufficiently large numbers of continuous measures per cluster. Such data are common in biological and medical studies utilizing monitoring or image-processing equipment. We consider a general class of hierarchical models that generalizes the model in the global two-stage (GTS) method for nonlinear mixed effects models by using any square-root-n-consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model, and by extending the stage 2 model to accommodate random effects from multiple levels of clustering. The second-stage model is a standard linear mixed effects model with normal random effects, but the cluster-specific distributions, conditional on random effects, can be non-Gaussian. This methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest. For estimation of the population parameters, we propose a conditional restricted maximum likelihood (CREML) approach and establish the asymptotic properties of the CREML estimators. The proposed general approach is illustrated using quartiles as cluster-specific parameters estimated in the first stage, and applied to the data example from a collagen fibril development study. We demonstrate using simulations that in samples with small numbers of independent clusters, the CREML estimators may perform better than conditional maximum likelihood estimators, which are a direct extension of the estimators from the GTS method.     

How heritable is individual susceptibility to death? The results of an analysis of survival data on Danish, Swedish and Finnish twins.

Molecular epidemiological studies confirm a substantial contribution of individual genes to variability in susceptibility to disease and death for humans. To evaluate the contribution of all genes to susceptibility and to estimate individual survival characteristics, survival data on related individuals (eg twins or other relatives) are needed. Correlated gamma-frailty models of bivariate survival are used in a joint analysis of survival data on more than 31,000 pairs of Danish, Swedish and Finnish male and female twins using the maximum likelihood method. Additive decomposition of frailty into genetic and environmental components is used to estimate heritability in frailty. The estimate of the standard deviation of frailty from the pooled data is about 1.5. The hypothesis that variance in frailty and correlations of frailty for twins are similar in the data from all three countries is accepted. The estimate of narrow-sense heritability in frailty is about 0.5. The age trajectories of individual hazards are evaluated for all three populations of twins and both sexes. The results of our analysis confirm the presence of genetic influences on individual frailty and longevity. They also suggest that the mechanism of these genetic influences may be similar for the three Scandinavian countries. Furthermore, results indicate that the increase in individual hazard with age is more rapid than predicted by traditional demographic life tables.     

Genetic susceptibility to prostate, breast, and colorectal cancer among Nordic twins

To investigate the role of genetics in the development of cancer, we developed a new approach to analyze data on prostate, breast, and colorectal cancer from the Swedish, Danish, and Finnish twin registries on monozygotic (MZ) and same-sex dizygotic (DZ) twins. In the spirit of a sensitivity analysis, we modeled genetic inheritance as either an autosomal recessive or dominant cancer susceptibility (CS) genotype that involves either a single gene, many genes with equal allele frequencies, or three genes with a ninefold range of allele frequencies. We also modeled the joint probability of cancer incidence among five age categories, conditional on the presence or absence of the CS genotype. The main assumptions are: (1) The joint distribution of unobserved environmental effects in a twin pair conditional on the presence or absence of the CS genotype is the same for MZ and DZ twins, (2) the probability of cancer conditional on the presence or absence of the CS genotype and the unobserved environmental effects (i.e., the gene-environment interaction) is the same for MZ and DZ twins, and (3) the probability of cancer is independent between twins with the CS genotype. Estimation was maximum likelihood via a search over allele frequency and two levels of EM algorithms. Models had acceptable or good fits. Variability was estimated using a bootstrap approach, but only 50 replications were feasible. The 94th percentile of bootstrap replications for the estimated fraction of cancers with the CS genotype ranged, over the various genetic models, from 0.16 to 0.45 for prostate cancer, 0.12 to 0.30 for breast cancer, and 0.08 to 0.27 for colorectal cancer. We conclude that genetic susceptibility makes only a small to moderate contribution to the incidence of prostate, breast, and colorectal cancer.     

Population HIV-1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials

In this paper, we introduce a novel application of hierarchical nonlinear mixed-effect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV-1 dynamics (HIV-1 RNA copies) after initiation of potent antiviral treatments and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixed-effect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV-1 RNA measurements and demonstrate the potential use of the models in clinical decision-making.     

Overdispersed fungus germination data: statistical analysis using R

ABSTRACT

Proportion data from dose-response experiments are often overdispersed, characterised by a larger variance than assumed by the standard binomial model. Here, we present different models proposed in the literature that incorporate overdispersion. We also discuss how to select the best model to describe the data and present, using R software, specific code used to fit and interpret binomial, quasi-binomial, beta-binomial, and binomial-normal models, as well as to assess goodness-of-fit. We illustrate applications of these generalized linear models and generalized linear mixed models with a case study from a biological control experiment, where different isolates of Isaria fumosorosea (Hypocreales: Cordycipitaceae) were used to assess which ones presented higher resistance to UV-B radiation. We show how to test for differences between isolates and also how to statistically group isolates presenting a similar behaviour.     

The cost of complexity in forecasts of population abundances is reduced but not eliminated by borrowing information across space using a hierarchical approach

Anticipating ecological changes is paramount if we are to manage biodiversity and the services they provide to humanity. When forecasting population abundances, studies have shown that simple statistical models often have better forecast performance than complex models. These studies have evaluated forecasts of models fitted separately to data from single sites (single-site approach). Here, we aim to contrast the forecast performance and forecast horizon between a single-site approach and a hierarchical multi-site approach where a single model is fitted to data from multiple-sites, and to investigate how they vary with model complexity. We used 5273 population time series on 84 species from the Swedish breeding bird survey program, and found that simple models on average had better forecast performance and forecast horizon than complex models for both the single- and the multi-site approach. However, the cost of complexity was considerably reduced under the multi-site approach, while the proportion of species for which complex models had better forecast performance than simple models was also much larger than under the single-site approach. This suggests that the multi-site approach is useful for inclusion of more detailed processes which may benefit forecasts for some species and which are of importance for managers. Still, our results are in line with some previous studies suggesting that it is surprisingly difficult to construct complex models that, on average, beat trivial baseline forecasts.