A lean additive frailty model: With an application to clustering of melanoma in Norwegian families

Additive frailty models are used to model correlated survival data. However, the complexity of the models increases with cluster size to the extent that practical usage becomes increasingly challenging. We present a modification of the additive genetic gamma frailty (AGGF) model, the lean AGGF (L-AGGF) model, which alleviates some of these challenges by using a leaner additive decomposition of the frailty. The performances of the models were compared and evaluated in a simulation study. The L-AGGF model was used to analyze population-wide data on clustering of melanoma in 2 391 125 two-generational Norwegian families, 1960-2015. Using this model, we could analyze the complete data set, while the original model limited the analysis to a restricted data set (with cluster sizes≤ 7 $$ \le 7 $$ ). We found a substantial clustering of melanoma in Norwegian families and large heterogeneity in melanoma risk across the population, where 52% of the frailty was attributed to the 10% of the population at highest unobserved risk. Due to the improved scalability, the L-AGGF model enables a wider range of analyses of population-wide data compared to the AGGF model. Moreover, the methods outlined here make it possible to perform these analyses in a computationally efficient manner.

Efficient and accurate frailty model approach for genome-wide survival association analysis in large-scale biobanks

With decades of electronic health records linked to genetic data, large biobanks provide unprecedented opportunities for systematically understanding the genetics of the natural history of complex diseases. Genome-wide survival association analysis can identify genetic variants associated with ages of onset, disease progression and lifespan. We propose an efficient and accurate frailty model approach for genome-wide survival association analysis of censored time-to-event (TTE) phenotypes by accounting for both population structure and relatedness. Our method utilizes state-of-the-art optimization strategies to reduce the computational cost. The saddlepoint approximation is used to allow for analysis of heavily censored phenotypes (>90%) and low frequency variants (down to minor allele count 20). We demonstrate the performance of our method through extensive simulation studies and analysis of five TTE phenotypes, including lifespan, with heavy censoring rates (90.9% to 99.8%) on ~400,000 UK Biobank participants with white British ancestry and ~180,000 individuals in FinnGen. We further analyzed 871 TTE phenotypes in the UK Biobank and presented the genome-wide scale phenome-wide association results with the PheWeb browser.

How Genes Modulate Patterns of Aging-Related Changes on the Way to 100: Biodemographic Models and Methods in Genetic Analyses of Longitudinal Data

BACKGROUND AND OBJECTIVE

To clarify mechanisms of genetic regulation of human aging and longevity traits, a number of genome-wide association studies (GWAS) of these traits have been performed. However, the results of these analyses did not meet expectations of the researchers. Most detected genetic associations have not reached a genome-wide level of statistical significance, and suffered from the lack of replication in the studies of independent populations. The reasons for slow progress in this research area include low efficiency of statistical methods used in data analyses, genetic heterogeneity of aging and longevity related traits, possibility of pleiotropic (e.g., age dependent) effects of genetic variants on such traits, underestimation of the effects of (i) mortality selection in genetically heterogeneous cohorts, (ii) external factors and differences in genetic backgrounds of individuals in the populations under study, the weakness of conceptual biological framework that does not fully account for above mentioned factors. One more limitation of conducted studies is that they did not fully realize the potential of longitudinal data that allow for evaluating how genetic influences on life span are mediated by physiological variables and other biomarkers during the life course. The objective of this paper is to address these issues.

DATA AND METHODS

We performed GWAS of human life span using different subsets of data from the original Framingham Heart Study cohort corresponding to different quality control (QC) procedures and used one subset of selected genetic variants for further analyses. We used simulation study to show that approach to combining data improves the quality of GWAS. We used FHS longitudinal data to compare average age trajectories of physiological variables in carriers and non-carriers of selected genetic variants. We used stochastic process model of human mortality and aging to investigate genetic influence on hidden biomarkers of aging and on dynamic interaction between aging and longevity. We investigated properties of genes related to selected variants and their roles in signaling and metabolic pathways.

RESULTS

We showed that the use of different QC procedures results in different sets of genetic variants associated with life span. We selected 24 genetic variants negatively associated with life span. We showed that the joint analyses of genetic data at the time of bio-specimen collection and follow up data substantially improved significance of associations of selected 24 SNPs with life span. We also showed that aging related changes in physiological variables and in hidden biomarkers of aging differ for the groups of carriers and non-carriers of selected variants.

CONCLUSIONS

. The results of these analyses demonstrated benefits of using biodemographic models and methods in genetic association studies of these traits. Our findings showed that the absence of a large number of genetic variants with deleterious effects may make substantial contribution to exceptional longevity. These effects are dynamically mediated by a number of physiological variables and hidden biomarkers of aging. The results of these research demonstrated benefits of using integrative statistical models of mortality risks in genetic studies of human aging and longevity.

How the effects of aging and stresses of life are integrated in mortality rates: insights for genetic studies of human health and longevity

Increasing proportions of elderly individuals in developed countries combined with substantial increases in related medical expenditures make the improvement of the health of the elderly a high priority today. If the process of aging by individuals is a major cause of age related health declines then postponing aging could be an efficient strategy for improving the health of the elderly. Implementing this strategy requires a better understanding of genetic and non-genetic connections among aging, health, and longevity. We review progress and problems in research areas whose development may contribute to analyses of such connections. These include genetic studies of human aging and longevity, the heterogeneity of populations with respect to their susceptibility to disease and death, forces that shape age patterns of human mortality, secular trends in mortality decline, and integrative mortality modeling using longitudinal data. The dynamic involvement of genetic factors in (i) morbidity/mortality risks, (ii) responses to stresses of life, (iii) multi-morbidities of many elderly individuals, (iv) trade-offs for diseases, (v) genetic heterogeneity, and (vi) other relevant aging-related health declines, underscores the need for a comprehensive, integrated approach to analyze the genetic connections for all of the above aspects of aging-related changes. The dynamic relationships among aging, health, and longevity traits would be better understood if one linked several research fields within one conceptual framework that allowed for efficient analyses of available longitudinal data using the wealth of available knowledge about aging, health, and longevity already accumulated in the research field.

A frailty model for (interval) censored family survival data, applied to the age at onset of non-physical problems

Family survival data can be used to estimate the degree of genetic and environmental contributions to the age at onset of a disease or of a specific event in life. The data can be modeled with a correlated frailty model in which the frailty variable accounts for the degree of kinship within the family. The heritability (degree of heredity) of the age at a specific event in life (or the onset of a disease) is usually defined as the proportion of variance of the survival age that is associated with genetic effects. If the survival age is (interval) censored, heritability as usually defined cannot be estimated. Instead, it is defined as the proportion of variance of the frailty associated with genetic effects. In this paper we describe a correlated frailty model to estimate the heritability and the degree of environmental effects on the age at which individuals contact a social worker for the first time and to test whether there is a difference between the survival functions of this age for twins and non-twins.

Reducing the effects of lead-time bias, length bias and over-detection in evaluating screening mammography: a censored bivariate data approach

Measuring the benefit of screening mammography is difficult due to lead-time bias, length bias and over-detection. We evaluated the benefit of screening mammography in reducing breast cancer mortality using observational data from the SEER-Medicare linked database. The conceptual model divided the disease duration into two phases: preclinical (T(0)) and symptomatic (T(1)) breast cancer. Censored information for the bivariate response vector ( T(0), T(1)) was observed and used to generate a likelihood function. However, the contribution to the likelihood function for some observations could not be calculated analytically, thus, censoring boundaries for these observations were modified. Inferences about the impact of screening mammography on breast cancer mortality were made based on maximum likelihood estimates derived from this likelihood function. Hazard ratios (95% confidence intervals) of 0.54 (0.48-0.61) and 0.33 (0.26- 0.42) for single and regular users (vs. non-users), respectively, demonstrated a protective effect of screening mammography among women 69 years and older. This method reduced the impact of lead-time bias, length bias and over-detection, which biased the estimated hazard ratios derived from standard survival models in favour of screening.

A relaxation of the gamma frailty (Burr) model

Frailty models are used in univariate data to account for individual heterogeneity. In the popular gamma frailty model the marginal hazard has the form of a Burr model. Although the Burr model is very useful and can offer insight on the data, it is far from perfect. The estimation of the covariate effects is linked to the baseline hazard and this makes the model coefficients hard to interpret. At the same time, the frailties are assumed constant over time, while biological reasoning in some cases may indicate that frailties may be time dependent. In this paper we present a relaxation of the Burr model which is based on loosening the link between the estimation of the covariate effects and the baseline hazard. This can be achieved by replacing the cumulative baseline hazard in the Burr model by a set of time functions, and the frailty variance by a vector of coefficients directly estimated from the data using a partial likelihood. We illustrate the similarities of the model with the Burr model and a further extension of the latter, a model with an autoregressive stochastic process for the frailty. We compare the models on simulated data sets with constant and time-dependent frailties and show how the relaxed Burr models performs on two different real data sets. We show that the relaxed Burr model serves as a good approximation to the Burr model when the frailty is constant, and furthermore it gives better results when the frailty is time dependent.