Penetrance estimation of Alzheimer disease in SORL1 loss-of-function variant carriers using a family-based strategy and stratification by APOE genotypes

Abstract

Background: Alzheimer disease (AD) is a common complex disorder with a high genetic component. Loss-of-function (LoF) SORL1 variants are one of the strongest AD genetic risk factors. Estimating their age-related penetrance is essential before putative use for genetic counseling or preventive trials. However, relative rarity and co-occurrence with the main AD risk factor, APOE-ε4, make such estimations difficult.

Methods: We proposed to estimate the age-related penetrance of SORL1-LoF variants through a survival framework by estimating the conditional instantaneous risk combining (i) a baseline for non-carriers of SORL1-LoF variants, stratified by APOE-ε4, derived from the Rotterdam study (N = 12,255), and (ii) an age-dependent proportional hazard effect for SORL1-LoF variants estimated from 27 extended pedigrees (including 307 relatives ≥ 40 years old, 45 of them having genotyping information) recruited from the French reference center for young Alzheimer patients. We embedded this model into an expectation-maximization algorithm to accommodate for missing genotypes. To correct for ascertainment bias, proband phenotypes were omitted. Then, we assessed if our penetrance curves were concordant with age distributions of APOE-ε4-stratified SORL1-LoF variant carriers detected among sequencing data of 13,007 cases and 10,182 controls from European and American case-control study consortia.

Results: SORL1-LoF variants penetrance curves reached 100% (95% confidence interval [99-100%]) by age 70 among APOE-ε4ε4 carriers only, compared with 56% [40-72%] and 37% [26-51%] in ε4 heterozygous carriers and ε4 non-carriers, respectively. These estimates were fully consistent with observed age distributions of SORL1-LoF variant carriers in case-control study data.

Conclusions: We conclude that SORL1-LoF variants should be interpreted in light of APOE genotypes for future clinical applications.

Keywords: APOE; Alzheimer; Expectation-maximization algorithm; Lifetime risk; Missing genotypes; Pedigree; Penetrance; SORL1.

Fig. 1

Overview of the method for estimating the piecewise constant hazard model. λ(t | a, s) refers to the instantaneous risk to develop the disease depending on age t and genotype (a,s) ∊ APOE × SORL1. λ_nc(t | a) refers to the specific instantaneous risk associated with non-carriers of the SORL1 variant of interest stratified on APOE genotype and derived from the Rotterdam Study [25]. β(t) refers to the additional effect of the SORL1 variant. λ_nc(t | a) and β(t) are both piecewise constant over time. E/M-steps refer to expectation/maximization steps. w_i(a, s), individual weight updating at each E-step iteration referring to the posterior probability distribution of individual i for combined genotype (a,s); y, years; SORL1+, carrier of the variant of interest in SORL1 gene; SORL1 WT, wild type for SORL1 (non-carriers of the variant of interest); ?, unknown genotype. The red arrow indicates the proband

Fig. 2

Estimation of bias in our simulation study. Bias was estimated for each of the four constant parameters (in columns) of the piecewise constant β(t) referring to the additional effect of the SORL1 variant of interest through 4 scenarios of simulation (in rows). The results are provided for probands included and excluded from the analysis during the maximization step of the EM algorithm. For the baseline scenario, we generated 27 families mimicking what we observed in our dataset in terms of SORL1-LoF variant effect, ascertainment, and available genotypes. Then, the model was challenged through three additional scenarios: (i) Unbalanced phenotype information: if one of the parents was affected, we removed all the phenotypic information of the parental branch with the unaffected parent. (ii) Relatives’ genotypes 100% missing: we removed all information about relatives’ genotypes. (iii) Heterogeneous variant effect: instead of generating age at onset based on a constant variant effect, we generated age at onset based on a normal distribution of the variant effect with a variance equaling to 1. A bias greater than 0 indicates an overestimation and a bias lower than 0 indicates an underestimation of the risk associated with SORL1-LoF variants

Fig. 3

Number of affected and unaffected individuals according to their age and their SORL1 status after genotyping imputation. This graph was obtained for all individuals with AAO or censoring above 40 years. It represents the number of carriers (upper part) and non-carriers (lower part) of the SORL1-LoF variant according to their disease status and age intervals (AAO for probands and affected relatives and censoring for unaffected relatives). Transparency differentiates available genotypes (already known, including those of probands) from those estimated at the end of the algorithm

Fig. 4

Age-dependent penetrance for carriers and non-carriers of a SORL1 LoF variant. The penetrance is displayed with its 95% confidence interval according to the number of APOE-ε4 allele from 65 to 85 years of age. Curves for non-carriers and their confidence intervals were obtained from our estimation of λ_nc(t | a) based on the Rotterdam Study. Data from pedigrees were censored at 85 years. Confidence intervals for SORL1-LoF variant carriers were obtained from the 2.5th and 97.5th quantiles of 500 bootstrap iterations. Penetrance values at 65, 70, 75, 80, and 85 years of age for carriers of the SORL1-LoF variant are displayed below the figure