Table 1.
Summary of evidence for age-varying genetic risk by disease.
Fig 1.
Schematic representation of methodology.
(A) Independent variants associated with a trait of interest are identified by analysis of the entire UK Biobank cohort using the TreeWAS methodology [40]. (B) Logistic regression is applied to estimate coefficients for variants on each trait using the training set. (C) Coefficients are used to compute individual genetic risk scores; the odds ratio associated with high GRS within each age group are estimated in the testing set. (D) An interval-censored proportional hazards model [44] is used to estimate the effect (and associated standard error) of each variant on the trait of interest within each of eight age intervals. (E) Bayesian clustering is used to estimate population age-profiles of risk, using either linear models or quadratic polynomials to encourage smoothness. (F-H) Permutation is used to test for age-homogeneity of effect size as well as to assess the evidence for multiple age profiles.
Fig 2.
Age-stratified odds-ratios for combined genetic risk scores.
(A-F) Age-stratified odds ratios in held-out testing data for genetic risk scores for six disorders where there is evidence for a single non-constant genetic risk profile, “Primary (essential) hypertension” (ICD-10 code I10), “pure hypercholesterolaemia” (E78.0); “Calculus of gallbladder without cholecystitis” (K80.2) and “Hypothyroidism, unspecified” (E03.9); “atherosclerotic heart disease of native coronary artery” (I25.1) and “other and unspecified malignant neoplasm of skin and unspecified parts of face” (C44.3). Results for all diseases are shown in S1 Fig. Odds ratios for the 80th (blue) and 90th percentiles of a combined genetic risk score within matched case-control samples (four controls for each case) are shown for each age interval; points indicate the average odds ratio of twenty five-fold cross-validation analyses with lines indicating the 95% confidence interval.
Fig 3.
Overview of simulation results.
(A) Power at P ≤ 0.05 to detect deviation from age-homogeneity as a function of slope in a model where effect sizes change linearly with age. The blue line indicates the point estimate when using a linear model to fit, the red line indicates the point estimate with a quadratic polynomial model and the grey shading indicates the 95% confidence interval. (B) Example showing the age-profile under which data are simulated (dashed blue line) and the inferred age profile (dashed red line) and 95% credible interval (red shading). (C) Power at P ≤ 0.05 to detect multiple age profiles in a simulation where 90% of variants have a time-invariant profile and 10% have an effect size that increases with age. The solid blue line indicates power when fitting a linear model and the solid red line indicates power when fitting a quadratic model. The dashed red line indicates the nominal significance threshold. Note the change in x-axis scale compared to Fig 2A. (D) Example showing inferred age-profiles for the two components (mean posterior and 95% credible interval). Additional simulation details are provided in the S1 Supplemental Methods and S2 Fig.
Fig 4.
Age-varying disease risk profiles.
(A-D) Inferred cluster profiles for four disorders where there is evidence for single non-constant profile; “Primary (essential) hypertension” (ICD-10 code I10; P = 0.0001), “pure hypercholesterolaemia” (E78.0; P = 0.0001), “Calculus of gallbladder without cholecystitis” (K80.2; P = 0.0236) and “Hypothyroidism, unspecified” (E03.9, P = 0.0329); (E-F) Inferred cluster profiles for two disorders where there is evidence for multiple non-constant profiles; “atherosclerotic heart disease of native coronary artery” (I25.1; P = 0.0001) and “other and unspecified malignant neoplasm of skin and unspecified parts of face” (C44.3; P = 0.0092). Curves for all diseases are shown in S4 Fig; Curves for all UK Biobank subjects regardless of ethnic background and for subjects from Black or South Asian ethnic background are shown in S6 Fig. The solid line indicates the posterior mean and the shaded area the 95% credible interval; Numbers in boxes indicate the number of variants in each cluster; All estimates are made with quadratic models for age-varying risk profiles.
Fig 5.
The impact of frailty on genetic risk profiles.
(A) Estimated age-profiles for genetic risk for I10 “essential (primary) hypertension” (left) and I25.1 “atherosclerotic heart disease of native coronary artery” (right) fitted under the univariable (purple) and multivariable (green) approaches. For I10, the solid line indicates the posterior mean and the shaded area the 95% credible interval; For I25.1, the solid and dashed lines indicate the means for the two clusters of variants. Comparisons for all diseases are shown in S10 Fig. (B) Estimated incidence by age for K80.2 “Calculus of gallbladder without cholecystitis” (left) and C44.3 “Other and unspecified malignant neoplasm of skin and unspecified parts of face” (right). The red solid line indicates the rate estimated from the UK Biobank (see S1 Supplemental Methods) and the dotted blue line indicates the fitted incidence curve from the parametric model. The P value indicates the Goodness-of-Fit test. Curves for all diseases are shown in S11 Fig. (C) Comparison of inferred genetic effect sizes (red curve) and those implied by the frailty parameters estimated from incidence rate within the UK Biobank (blue dashed curve).
Fig 6.
Models for a decreasing influence of genetic risk with age.
(A) A threshold model, in which each individual has a disease “liability” which evolves over age. Disease onset occurs when liability crosses a threshold. The upper panel shows example trajectories, where genetic risk alters only the liability baseline. The middle panel is a schematic representation of a simulation in which genetic risk affects developmental pathways at birth, while non-genetic risk accumulates over time. The lower panel shows an estimation of the effect size from a simulated dataset of UK Biobank sample size (see S1 Supplemental Methods). (B) Interactions between genetic and environmental risk factors can create a distribution of effect sizes for a specific genotype. The upper panel shows example trajectories, where the environment influences the slope of the trajectory. The middle panel shows illustrative examples of the liability distributions among individuals at different ages. Those individuals at highest risk (with both the risk allele and risk environment) enter disease earlier, diluting the apparent effect size at a later age. The lower panel shows simulation results under such a model using realistic parameters from UK Biobank (see S1 Supplemental Methods).