So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

https://jeffreydachmd.com/wp-content/uploads/2015/01/Molecular-targets-of-dietary-agents-prevention-cancer-aggarwal-2006.pdf

Molecular targets of dietary agents for prevention and therapy of cancer

Much work has been done to identify susceptibility genes in schizophrenia and bipolar disorder. Several well established linkages have emerged in schizophrenia. Strongly supported regions are 6p24–22, 1q21–22, and 13q32–34, while other promising regions include 8p21–22, 6q16–25, 22q11–12, 5q21–q33, 10p15–p11, and 1q42. Genomic regions of interest in bipolar disorder include 6q16–q22, 12q23–q24, and regions of 9p22–p21, 10q21–q22, 14q24–q32, 13q32–q34, 22q11–q22, and chromosome 18. Recently, specific genes or loci have been implicated in both disorders and, crucially, replicated. Current evidence supports NRG1, DTNBP1, DISC1, DAOA(G72), DAO, and RGS4 as schizophrenia susceptibility loci. For bipolar disorder the strongest evidence supports DAOA(G72) and BDNF. Increasing evidence suggests an overlap in genetic susceptibility across the traditional classification systems that dichotomised psychotic disorders into schizophrenia or bipolar disorder, most notably with association findings at DAOA(G72), DISC1, and NRG1. Future identification of psychosis susceptibility genes will have a major impact on our understanding of disease pathophysiology and will lead to changes in classification and the clinical practice of psychiatry.

https://jmg.bmj.com/content/jmedgenet/42/3/193.full.pdf

The genetics of schizophrenia and bipolar disorder: dissecting psychosis

Psychiatric genetics has been fraught with controversy owing to the irreproducibility of many claimed risk factors. There is now some cause for optimism thanks to larger sample sizes and the incorporation of intermediate traits, rare mutations and environmental risk components into the analyses.

Psychiatric genetics: progress amid controversy

Introduction Goals and outline Examples Survival Analysis Basic concepts in survival analysis Censoring and truncation Parametric models Estimation of survival and hazard functions Regression models Identifiability problems Univariate Frailty Models The concept of univariate frailty Discrete frailty model Gamma frailty model Log-normal frailty model Inverse Gaussian frailty model Positive stable frailty model PVF frailty model Compound Poisson frailty model Quadratic hazard frailty model Levy-type frailty models Log-t frailty model Univariate frailty cure models Missing covariates in proportional hazard models Shared Frailty Models Marginal versus frailty model The concept of shared frailty Shared gamma frailty model Shared log-normal frailty model Shared positive stable frailty model Shared compound Poisson/PVF frailty model Shared frailty models more general Dependence measures Limitations of the shared frailty model Correlated Frailty Models The concept of correlated frailty Correlated gamma frailty model Correlated log-normal frailty model MCMC methods for the correlated log-normal frailty model Correlated compound Poisson frailty model Correlated quadratic hazard frailty model Other correlated frailty models Bivariate frailty cure models Comparison of different estimation strategies Dependent competing risks in frailty models Copula Models Shared gamma frailty copula Correlated gamma frailty copula General correlated frailty copula Cross-ratio function Different Aspects of Frailty Modeling Dependence and interaction between frailty and observed covariates Cox model with general Gaussian random effects Nested frailty models Recurrent event time data Tests for heterogeneity Log-rank test in frailty models Time-dependent frailty models Identifiability of frailty models Applications of frailty models Software for frailty models Appendix References Index

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Frailty Models in Survival Analysis

The aim of this study was to investigate the role of genes and environment in susceptibility to breast cancer and to give an estimate of heritability in the propensity to develop the disease. To do this we applied an interdisciplinary approach, merging models developed in the field of demography and survival analysis - so-called frailty models - and models coming from quantitative genetics and epidemiology, namely genetic models. In our study, the inferential problem was solved in a Bayesian framework and the numerical work was carried out using MCMC methods. We used the special information coming from twin data, particularly breast cancer data, from the Swedish Twin Register. The application of a correlated log-normal frailty model leads to a very large estimate of the population heterogeneity (sigma = 6.7), and relatively small correlations between co-twins' frailties - around 0.3 for monozygotic and 0.1 for dizygotic twins. Comparing three different genetic models (an ACE, an AE and an ADE model), we furthermore concluded that genetic effects would explain globally almost 30% of the total variability of propensity to breast cancer. Environmental effects would be predominant in determining breast cancer susceptibility and these effects would be primarily individual-specific, that is, non-shared effects. Finally, a model which includes dominance genetic effects (ADE model) is preferred for genetic and statistical reasons.

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The heritability of breast cancer: a Bayesian correlated frailty model applied to Swedish twins data.

Frailty models are becoming increasingly popular in multivariate survival analysis. Shared frailty models in particular are often used despite their limitations. To overcome their disadvantages numerous correlated frailty models were established during the last decade. In the present study, we examine bivariate correlated frailty models, and especially the behavior of the parameter estimates when using different estimation strategies. We consider three different bivariate frailty models: the gamma model and two versions of the log-normal model. The traditional maximum likelihood procedure of parameter estimation in the gamma case with an explicit available likelihood function is compared with maximum likelihood methods based on numerical integration and a Bayesian approach using MCMC methods with the help of a comprehensive simulation study. We detected a strong dependence between the two parameter estimates (variance and correlation of frailties) in the bivariate correlated frailty model and analyzed this dependence in detail.

A comparison of different bivariate correlated frailty models and estimation strategies

Three correlated frailty models are used to analyze bivariate timeto- event data by assuming gamma, log-normal and compound Poisson distributed frailty. All approaches allow to deal with right censored lifetime data and account for heterogeneity as well as for a non-susceptible (cure) fraction in the study population. In the gamma and compound Poisson model traditional ML estimation methods are used, whereas in the log-normal model MCMC methods are applied. Breast cancer incidence data of Swedish twin pairs illustrate the practical relevance of the models, which are used to estimate the size of the susceptible fraction and the correlation between the frailties of the twin partners. We discuss future directions of development of the methods and additional thoughts concerning their advantages and use.

/pdf/the-modelling-of-a-cure-fraction-in-bivariate-time-to-event-5bmkjibqbb.pdf

The Modelling of a Cure Fraction in Bivariate Time-to-Event Data

The aim of this study is to investigate the role of genetics and environment in susceptibility to breast cancer (frailty). An interdisciplinary approach was adopted, combining a correlated frailty-mixture model with genetic equations, allowing for decomposition of the frailty variance into genetic and environmental components. In addition, the possibility that a fraction of the population under study is 'immune' to the disease is evaluated, and changes in heritability estimates introducing a fraction of non-susceptible individuals are determined. The methodology is applied to breast cancer data from the Swedish Twin Registry, including information about all female monozygotic and dizygotic twin pairs born in Sweden between 1886 and 1967. The inferential problem is solved in a Bayesian framework and the numerical work is carried out using Markov chain Monte Carlo (MCMC) methods.

A correlated frailty model with long-term survivors for estimating the heritability of breast cancer.

Frailty models are becoming more and more popular in the area of multivariate survival analysis. In particular, shared frailty models are often used despite their limitations. To overcome the disadvantages of shared frailty models numerous correlated frailty models were established during the last decade. In the present study we examine correlated frailty models, especially the behavior of the parameter estimates when using different estimation strategies. Three different frailty models are considered: the gamma model and two versions of the log-normal model. The traditional maximum likelihood procedure of parameter estimation in the gamma case with an explicit available likelihood function is compared with maximum likelihood methods based on numerical integration and a Bayesian approach using MCMC methods with the help of a comprehensive simulation study. A strong dependence between the two parameter estimates (variance and correlation of frailties) in the multivariate correlated frailty model is detected and analyzed in detail.

/pdf/a-simulation-study-of-different-correlated-frailty-models-wnzgz8az1t.pdf

Isabella Locatelli

Papers

The heritability of breast cancer: a Bayesian correlated frailty model applied to Swedish twins data.

A comparison of different bivariate correlated frailty models and estimation strategies

The Modelling of a Cure Fraction in Bivariate Time-to-Event Data

A correlated frailty model with long-term survivors for estimating the heritability of breast cancer.

A simulation study of different correlated frailty models and estimation strategies