# Polygenic risk and hazard scores for Alzheimer's disease prediction

Ganna Leonenko, Rebecca Sims, Maryam Shoai, Aura Frizzati, Paola Bossù, Gianfranco Spalletta, Nick C Fox, Julie Williams, John Hardy, Valentina Escott-Price, et al.

<figure><img src="image_1.png" /></figure>

► To cite this version:

Ganna Leonenko, Rebecca Sims, Maryam Shoai, Aura Frizzati, Paola Bossù, et al. Polygenic risk and hazard scores for Alzheimer's disease prediction. Annals of Clinical and Translational Neurology, 2019, 6 (3), pp.456-465. 10.1002/acn3.716. hal-04444983

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# Polygenic risk and hazard scores for Alzheimer's disease prediction

Ganna Leonenko, Rebecca Sims, Maryam Shoai, Aura Frizzati, Paola Bossù, Gianfranco Spalletta, Nick C Fox, Julie Williams, John Hardy, Valentina Escott-Price, et al.

<figure><img src="image_1.png" /></figure>

► To cite this version:

Ganna Leonenko, Rebecca Sims, Maryam Shoai, Aura Frizzati, Paola Bossù, et al. Polygenic risk and hazard scores for Alzheimer's disease prediction. Annals of Clinical and Translational Neurology, 2019, 6 (3), pp.456-465. 10.1002/acn.3.716. hal-04444983

HAL Id: hal-04444983

https://hal.sorbonne-universite.fr/hal-04444983v1

Submitted on 7 Feb 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
RESEARCH ARTICLE

# Polygenic risk and hazard scores for Alzheimer's disease prediction

Ganna Leonenko<fnref n="1" /> ID, Rebecca Sims<fnref n="1" />, Maryam Shoai<fnref n="2" />, Aura Frizzati<fnref n="1" />, Paola Bossù<fnref n="3" />,
Gianfranco Spalletta<fnref n="3" />, Nick C. Fox<fnref n="2" />, Julie Williams<fnref n="1" />,<fnref n="4" />,⁵, for the GERAD consortiumª, John Hardy<fnref n="2" />,⁵,⁶
Valentina Escott-Price<fnref n="1" />,<fnref n="4" />,⁵,⁶

**Correspondence**

Valentina Escott-Price, Division of
Psychological Medicine and Clinical
Neurosciences, Hadyn Ellis Building, Cardiff
University, Maindy Road, Cardiff, CF24 4HQ.
Tel: +(44)29 2068 8429; Fax: +(44)29 2068
7068; E-mail: escottpricev@cardiff.ac.uk

**Funding Information**

This work was supported by JPND 505472
Medical Research Council MR/L010305/1;
MR/L023784/2; UKDR/data023.

Received: 10 August 2018; Revised: 5
December 2018; Accepted: 5 December
2018

*Annals of Clinical and Translational*
*Neurology 2019; 6(3): 456–465*

doi: 10.1002/acn3.716

ªStudy Group members are listed in the
Acknowledgments section, and their
affiliations and contributions are provided in
a separate file (File S1).

ᵇJoint contribution.

**Abstract**

**Objective:** Genome-wide association studies (GWAS) have identified over 30 susceptibility loci associated with Alzheimer's disease (AD). Using AD GWAS data from the International Genomics of Alzheimer's Project (IGAP), Polygenic Risk Score (PRS) was successfully applied to predict life time risk of AD development. A recently introduced Polygenic Hazard Score (PHS) is able to quantify individuals with age-specific genetic risk for AD. The aim of this study was to quantify the age-specific genetic risk for AD with PRS and compare the results generated by PRS with those from PHS. **Methods:** Quantification of individual differences in age-specific genetic risk for AD identified by the PRS, was performed with Cox Regression on 9903 (2626 cases and 7277 controls) individuals from the Genetic and Environmental Risk in Alzheimer's Disease consortium (GERAD). Polygenic Hazard Scores were generated for the same individuals. The age-specific genetic risk for AD identified by the PRS was compared with that generated by the PHS. This was repeated using varying SNPs *P*-value thresholds for disease association. **Results:** Polygenic Risk Score significantly predicted the risk associated with age at AD onset when SNPs were preselected for association to AD at *P* ≤ 0.001. The strongest effect (*B* = 0.28, SE = 0.04, *P* = 2.5 × 10⁻¹²) was observed for PRS based upon genome-wide significant SNPs (*P* ≤ 5 × 10⁻⁸). The strength of association was weaker with less stringent SNP selection thresholds. **Interpretation:** Both PRS and PHS can be used to predict an age-specific risk for developing AD. The PHS approach uses SNP effect sizes derived with the Cox Proportional Hazard Regression model. When SNPs were selected based upon AD GWAS case/control *P* ≤ 10⁻<fnref n="3" />, we found no advantage of using SNP effects sizes calculated with the Cox Proportional Hazard Regression model in our study. When SNPs are selected for association with AD risk at *P* > 10⁻<fnref n="3" />, the age-specific risk prediction results are not significant for either PRS or PHS. However PHS could be more advantageous than PRS of age specific AD risk predictions when SNPs are prioritized for association with AD age at onset (i.e., powerful Cox Regression GWAS study).

**Introduction**

Alzheimer's disease (AD) is the most common form of
neurodegenerative disorder<fnref n="1" /> with over 47 million people

affected worldwide and a global economic impact esti-
mated at about US $818 billion.<fnref n="2" />

AD is highly heritable with an estimated 80% of the
liability explained by genetic factors.<fnref n="3" /> Risk for developing

<footnote n="1">¹MRC Centre for Neuropsychiatric Genetics and Genomics, Cardiff University, Cardiff, United Kingdom</footnote>

<footnote n="2">²Institute of Neurology, University College London, London, United Kingdom</footnote>

<footnote n="3">³Department of Clinical and Behavioral Neurology, Experimental Neuropsychobiology Laboratory, IRCCS Santa Lucia Foundation, Rome, Italy</footnote>

<footnote n="4">⁴UK Dementia Research Institute, Cardiff University, Cardiff, United Kingdom</footnote>
RESEARCH ARTICLE

# Polygenic risk and hazard scores for Alzheimer's disease prediction

Ganna Leonenko<fnref n="1" /> ID, Rebecca Sims<fnref n="1" />, Maryam Shoai<fnref n="2" />, Aura Frizzati<fnref n="1" />, Paola Bossù<fnref n="3" />,
Gianfranco Spalletta<fnref n="3" />, Nick C. Fox<fnref n="2" />, Julie Williams<fnref n="1" />,<fnref n="4" />,⁵, for the GERAD consortiumª, John Hardy<fnref n="2" />,⁵,⁶
Valentina Escott-Price<fnref n="1" />,<fnref n="4" />,⁵,⁶

**Correspondence**

Valentina Escott-Price, Division of
Psychological Medicine and Clinical
Neurosciences, Hadyn Ellis Building, Cardiff
University, Maindy Road, Cardiff, CF24 4HQ.
Tel: +(44)29 2068 8429; Fax: +(44)29 2068
7068; E-mail: escottpricev@cardiff.ac.uk

**Funding Information**

This work was supported by JPND 505472
Medical Research Council MR/L010305/1;
MR/L023784/2; UKDR/data023.

Received: 10 August 2018; Revised: 5
December 2018; Accepted: 5 December
2018

Annals of Clinical and Translational
Neurology 2019; 6(3): 456–465

doi: 10.1002/acn3.716

**Abstract**

**Objective:** Genome-wide association studies (GWAS) have identified over 30 susceptibility loci associated with Alzheimer's disease (AD). Using AD GWAS data from the International Genomics of Alzheimer's Project (IGAP), Polygenic Risk Score (PRS) was successfully applied to predict life time risk of AD development. A recently introduced Polygenic Hazard Score (PHS) is able to quantify individuals with age-specific genetic risk for AD. The aim of this study was to quantify the age-specific genetic risk for AD with PRS and compare the results generated by PRS with those from PHS. **Methods:** Quantification of individual differences in age-specific genetic risk for AD identified by the PRS, was performed with Cox Regression on 9903 (2626 cases and 7277 controls) individuals from the Genetic and Environmental Risk in Alzheimer's Disease consortium (GERAD). Polygenic Hazard Scores were generated for the same individuals. The age-specific genetic risk for AD identified by the PRS was compared with that generated by the PHS. This was repeated using varying SNPs *P*-value thresholds for disease association. **Results:** Polygenic Risk Score significantly predicted the risk associated with age at AD onset when SNPs were preselected for association to AD at *P* ≤ 0.001. The strongest effect (*B* = 0.28, SE = 0.04, *P* = 2.5 × 10⁻¹²) was observed for PRS based upon genome-wide significant SNPs (*P* ≤ 5 × 10⁻⁸). The strength of association was weaker with less stringent SNP selection thresholds. **Interpretation:** Both PRS and PHS can be used to predict an age-specific risk for developing AD. The PHS approach uses SNP effect sizes derived with the Cox Proportional Hazard Regression model. When SNPs were selected based upon AD GWAS case/control *P* ≤ 10⁻<fnref n="3" />, we found no advantage of using SNP effects sizes calculated with the Cox Proportional Hazard Regression model in our study. When SNPs are selected for association with AD risk at *P* > 10⁻<fnref n="3" />, the age-specific risk prediction results are not significant for either PRS or PHS. However PHS could be more advantageous than PRS of age specific AD risk predictions when SNPs are prioritized for association with AD age at onset (i.e., powerful Cox Regression GWAS study).

**Introduction**

Alzheimer's disease (AD) is the most common form of
neurodegenerative disorder<fnref n="1" /> with over 47 million people

affected worldwide and a global economic impact esti-
mated at about US $818 billion.<fnref n="2" />

AD is highly heritable with an estimated 80% of the
liability explained by genetic factors.<fnref n="3" /> Risk for developing

<footnote n="1">¹MRC Centre for Neuropsychiatric Genetics and Genomics, Cardiff University, Cardiff, United Kingdom</footnote>

<footnote n="2">²Institute of Neurology, University College London, London, United Kingdom</footnote>

<footnote n="3">³Department of Clinical and Behavioral Neurology, Experimental Neuropsychobiology Laboratory, IRCCS Santa Lucia Foundation, Rome, Italy</footnote>

<footnote n="4">⁴UK Dementia Research Institute, Cardiff University, Cardiff, United Kingdom</footnote>

<footnote>ªStudy Group members are listed in the Acknowledgments section, and their affiliations and contributions are provided in a separate file (File S1).</footnote>

<footnote>ᵇJoint contribution.</footnote>
AD involves multiple genetic and environmental compo-
nents, with *APOE* genotype⁴ having the strongest genetic
effect.⁵ In the last 20 years numerous relevant susceptibil-
ity loci, genes, and pathways have been identified that will
improve understanding of this complex disease and iden-
tify potential therapeutic targets. The largest Genome-
Wide association study (GWAS) identified more than 20
loci⁶ associated with late (after the age of 65 years) onset
AD (LOAD). The analysis was extended to biological
pathways with enrichment in immune response, regula-
tion of endocytosis, cholesterol response, and protea-
some-ubiquitin activity pathways.⁷

The development and validation of AD prediction algo-
rithms is a very important step towards therapeutic strate-
gies for AD prevention and intervention. A polygenic risk
score (PRS) approach has demonstrated 75–84% prediction
accuracy of AD risk with *APOE*, the polygenic score, sex and
age as predictors.⁸,⁹ PRS is constructed as a weighted sum of
allele counts, where the weights are the B-coefficients of
SNP association with the disease obtained with the Logistic
Regression (LR) analysis. Recent development of a polygenic
hazard score (PHS) approach goes beyond AD risk predic-
tion and provides prediction of individual age-specific risk
for developing AD.²² Prior to PHS analyses, Desikan et al.¹⁰
selected SNPs based on their association with AD at
$P \le 10^{-5}$ in the publicly available IGAP dataset. Then they
constructed PHS in a similar way to PRS, with the exception
that PHS uses log(HR) as SNP risk allele weighs, instead of
log(OR). Both, log(HR)s and the best PHS model were
identified by running step-wise Cox regression, yielding 31
SNPs in addition to *APOE ε2* and ε4 alleles (see Desikan
et al.¹⁰).

LR and Cox Proportional Hazard Regression (Cox
regression) analyses are widely used in epidemiological
studies depending upon the question of interest and avail-
able information. LR is used to measure the relationship
between a binary variable (e.g., case/control) and predic-
tor variables, while Cox regression investigates the associ-
ation between the time-to-event ("survival time") of
patients together with other predictor variables. Cox
regression¹¹ is one of the most-widely applied methods in
medical studies when investigating time-dependent
explanatory variable. Similar to odds ratio (OR) in LR,
Cox regression estimates the hazard ratio (HR) that is a
measure between the probability of events in a "case"
group compared to the probability of events in a "con-
trol" group. The advantage of Cox regression over LR is
that the former estimates an instantaneous risk for devel-
oping AD, based on genotype and age, while the latter
ignores "survival time" and censoring information.

There have been several studies conducted to compare
Logistic and Cox regression models.¹²⁻¹⁵ Earlier studies
have shown that if the time-to-event data are available,

Cox proportional hazards models have more statistical
power to detect risk factors than LR models,¹⁶ since it
accounts for the time until events occur. However, the
two models yield similar estimates of regression coeffi-
cients in studies with short follow-up (5 years or less)
time and high survival rate. In addition, although these
two regression models have different purposes, it has been
shown that the risk factors with strong effect size will be
significant in both models and present similar regression
coefficient estimates.¹⁴,¹⁷

The aim of this study was to quantify the age-specific
genetic risk for AD with PRS and compare the results
with PHS. Previously, 31 SNPs in addition to *APOE ε2*
and *ε4* alleles were identified¹⁰ that were used in deriving
PHS and then predicting the age-specific individual risk.
There are two components in the PHS/PRS analyses, (1)
how the individual score is generated, that is, how the
SNPs were selected and their effect sizes are derived, and
(2) what aspect of the disease is predicted by this score
(age at onset or overall risk).

First, we compared the effect sizes of SNP association
to AD derived in the same dataset using two different
models (1) Logistic regression and (2) Cox regression. To
explore the second component, we compared the accuracy
in quantification of individual differences in age-specific
genetic risk for AD using PRS, that is, when the SNP
effect sizes are derived by LR, and PHS when the effect
sizes are derived by Cox regression.

Tan et al.¹⁸ in their editorial claim that PHS has advan-
tage over PRS to help inform disease management decisions
for at-risk individuals in the clinic. Our study shows that
PHS, as constructed in Desikan et al.¹⁰ gives very similar
results to PRS when tested in the Genetic and Environmen-
tal Risk for Alzheimer’s disease (GERAD) dataset.

**Materials and Methods**

Data

Generation of PRS (and similar PHS) requires two inde-
pendent datasets: a discovery sample, where the summary
statistics are sufficient, and a validation samples, which is
independent of the discovery sample and contains geno-
types for each individual.¹⁹ We compared individual SNP
hazard ratio (HR)¹⁰ with odds ratios (OR) reported by
the International genomics of Alzheimer’s project (IGAP)
GWAS.⁶ The original IGAP summary statistics was
derived using a meta-analysis of four GWAS datasets,
namely European Alzheimer ‘s disease Initiative (EADI),
Cohorts for Heart and Aging Research in Genomic
Epidemiology (CHARGE), Alzheimer’s Disease Genetics
Consortium (ADGC) and Genetic and Environmental
Risk for Alzheimer’s disease (GERAD) consortia.
AD involves multiple genetic and environmental compo-
nents, with *APOE* genotype⁴ having the strongest genetic
effect.⁵ In the last 20 years numerous relevant susceptibil-
ity loci, genes, and pathways have been identified that will
improve understanding of this complex disease and iden-
tify potential therapeutic targets. The largest Genome-
Wide association study (GWAS) identified more than 20
loci⁶ associated with late (after the age of 65 years) onset
AD (LOAD). The analysis was extended to biological
pathways with enrichment in immune response, regula-
tion of endocytosis, cholesterol response, and protea-
some-ubiquitin activity pathways.⁷

The development and validation of AD prediction algo-
rithms is a very important step towards therapeutic strate-
gies for AD prevention and intervention. A polygenic risk
score (PRS) approach has demonstrated 75–84% prediction
accuracy of AD risk with *APOE*, the polygenic score, sex and
age as predictors.⁸,⁹ PRS is constructed as a weighted sum of
allele counts, where the weights are the B-coefficients of
SNP association with the disease obtained with the Logistic
Regression (LR) analysis. Recent development of a polygenic
hazard score (PHS) approach goes beyond AD risk predic-
tion and provides prediction of individual age-specific risk
for developing AD.²² Prior to PHS analyses, Desikan et al.¹⁰
selected SNPs based on their association with AD at
$P \le 10^{-5}$ in the publicly available IGAP dataset. Then they
constructed PHS in a similar way to PRS, with the exception
that PHS uses log(HR) as SNP risk allele weighs, instead of
log(OR). Both, log(HR)s and the best PHS model were
identified by running step-wise Cox regression, yielding 31
SNPs in addition to *APOE ε2* and ε4 alleles (see Desikan
et al.¹⁰).

LR and Cox Proportional Hazard Regression (Cox
regression) analyses are widely used in epidemiological
studies depending upon the question of interest and avail-
able information. LR is used to measure the relationship
between a binary variable (e.g., case/control) and predic-
tor variables, while Cox regression investigates the associ-
ation between the time-to-event ("survival time") of
patients together with other predictor variables. Cox
regression¹¹ is one of the most-widely applied methods in
medical studies when investigating time-dependent
explanatory variable. Similar to odds ratio (OR) in LR,
Cox regression estimates the hazard ratio (HR) that is a
measure between the probability of events in a "case"
group compared to the probability of events in a "con-
trol" group. The advantage of Cox regression over LR is
that the former estimates an instantaneous risk for devel-
oping AD, based on genotype and age, while the latter
ignores "survival time" and censoring information.

There have been several studies conducted to compare
Logistic and Cox regression models.¹²⁻¹⁵ Earlier studies
have shown that if the time-to-event data are available,

Cox proportional hazards models have more statistical
power to detect risk factors than LR models,¹⁶ since it
accounts for the time until events occur. However, the
two models yield similar estimates of regression coeffi-
cients in studies with short follow-up (5 years or less)
time and high survival rate. In addition, although these
two regression models have different purposes, it has been
shown that the risk factors with strong effect size will be
significant in both models and present similar regression
coefficient estimates.¹⁴,¹⁷

The aim of this study was to quantify the age-specific
genetic risk for AD with PRS and compare the results
with PHS. Previously, 31 SNPs in addition to *APOE ε2*
and *ε4* alleles were identified¹⁰ that were used in deriving
PHS and then predicting the age-specific individual risk.
There are two components in the PHS/PRS analyses, (1)
how the individual score is generated, that is, how the
SNPs were selected and their effect sizes are derived, and
(2) what aspect of the disease is predicted by this score
(age at onset or overall risk).

First, we compared the effect sizes of SNP association
to AD derived in the same dataset using two different
models (1) Logistic regression and (2) Cox regression. To
explore the second component, we compared the accuracy
in quantification of individual differences in age-specific
genetic risk for AD using PRS, that is, when the SNP
effect sizes are derived by LR, and PHS when the effect
sizes are derived by Cox regression.

Tan et al.¹⁸ in their editorial claim that PHS has advan-
tage over PRS to help inform disease management decisions
for at-risk individuals in the clinic. Our study shows that
PHS, as constructed in Desikan et al.¹⁰ gives very similar
results to PRS when tested in the Genetic and Environmen-
tal Risk for Alzheimer’s disease (GERAD) dataset.

**Materials and Methods**

Data

Generation of PRS (and similar PHS) requires two inde-
pendent datasets: a discovery sample, where the summary
statistics are sufficient, and a validation samples, which is
independent of the discovery sample and contains geno-
types for each individual.¹⁹ We compared individual SNP
hazard ratio (HR)¹⁰ with odds ratios (OR) reported by
the International genomics of Alzheimer’s project (IGAP)
GWAS.⁶ The original IGAP summary statistics was
derived using a meta-analysis of four GWAS datasets,
namely European Alzheimer ‘s disease Initiative (EADI),
Cohorts for Heart and Aging Research in Genomic
Epidemiology (CHARGE), Alzheimer’s Disease Genetics
Consortium (ADGC) and Genetic and Environmental
Risk for Alzheimer’s disease (GERAD) consortia.
In this study, since individual genotypes of the GERAD sample were available to us, we used GERAD data as the test set. For PRS calculation we used SNP's log(OR) from the meta-analysis of three consortia (EADI, CHARGE and ADGC), excluding GERAD, hereby referred to as IGAP\_noGERAD. Note that individual SNP effects (B = log (OR)) of IGAP\_noGEARD dataset were adjusted for age. To generate polygenic hazard scores in the GERAD sample, we used hazards ratio estimates for the 31 SNPs reported in ADGC data.¹⁰ To test other SNPs, we split the GERAD data and estimated hazards ratios in 75% of the data and generated and tested individual scores in the remaining 25% of the data.

The GERAD dataset consists of 3177 cases and 7277 controls of Caucasian ancestry (see Table S1 for cohort statistical characteristics) and partly was published previously.²⁰ Haplotype Reference Consortium (HRC), version r1.1 2016, was used to impute GERAD genotype data on the Michigan Imputation Server,²¹ which to date, allows the most accurate imputation of genetic variants. Imputed genotype probabilities (also known as dosages) were converted to most probable genotype with a probability threshold of 0.9 and greater. SNPs were removed if their imputation INFO-score < 0.4, MAF < 0.1, missingness of genotypes ≥ 0.05 or HWE < 10⁻⁶. A total of 6,119,694 variants were retained. To correct for population

structure and genotyping differences, all our analyses were adjusted for gender and 3 principle components.²⁰

For the survival analysis model we used age at onset where available, and imputed age at onset for the remaining individuals. Imputed age at onset was estimated by subtracting 5 years from the age of the last assessment (as the mean difference between the age of the last assessment and age at onset was 4.7 years in our data). The age at onset has been imputed for 253 (8%) cases and for an additional 551 individuals had no age related information. Out of the remaining 9903 individuals (2626 cases and 7277 controls), APOE genotypes were available for 8415 individuals (2384 cases and 6031 controls) and these subjects were included in the analysis.

To validate the PHS approach in a sample which is independent of ADGC,¹⁰ we split our GERAD data into a discovery (75% or 1934 cases and 5493 controls) dataset, for estimation the HR, and validation (25% or 692 cases and 1784 controls) dataset, where we derived the PHS for each individual and tested for age-specific risk prediction.

In the GERAD sample 5570 controls were from the 1958 birth cohort (all included at age 45) (http://www.b58cgene.sgul.ac.uk), introducing differences in age distribution between cases and controls (Fig. 1). To avoid a potential bias due to these differences, we have repeated the analyses including only participants with age 55 and

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Histogram of age of AD cases and controls in the GERAD dataset.</figcaption></figure>
In this study, since individual genotypes of the GERAD sample were available to us, we used GERAD data as the test set. For PRS calculation we used SNP's log(OR) from the meta-analysis of three consortia (EADI, CHARGE and ADGC), excluding GERAD, hereby referred to as IGAP\_noGERAD. Note that individual SNP effects (B = log (OR)) of IGAP\_noGEARD dataset were adjusted for age. To generate polygenic hazard scores in the GERAD sample, we used hazards ratio estimates for the 31 SNPs reported in ADGC data.¹⁰ To test other SNPs, we split the GERAD data and estimated hazards ratios in 75% of the data and generated and tested individual scores in the remaining 25% of the data.

The GERAD dataset consists of 3177 cases and 7277 controls of Caucasian ancestry (see Table S1 for cohort statistical characteristics) and partly was published previously.²⁰ Haplotype Reference Consortium (HRC), version r1.1 2016, was used to impute GERAD genotype data on the Michigan Imputation Server,²¹ which to date, allows the most accurate imputation of genetic variants. Imputed genotype probabilities (also known as dosages) were converted to most probable genotype with a probability threshold of 0.9 and greater. SNPs were removed if their imputation INFO-score < 0.4, MAF < 0.1, missingness of genotypes ≥ 0.05 or HWE < 10⁻⁶. A total of 6,119,694 variants were retained. To correct for population

structure and genotyping differences, all our analyses were adjusted for gender and 3 principle components.²⁰

For the survival analysis model we used age at onset where available, and imputed age at onset for the remaining individuals. Imputed age at onset was estimated by subtracting 5 years from the age of the last assessment (as the mean difference between the age of the last assessment and age at onset was 4.7 years in our data). The age at onset has been imputed for 253 (8%) cases and for an additional 551 individuals had no age related information. Out of the remaining 9903 individuals (2626 cases and 7277 controls), APOE genotypes were available for 8415 individuals (2384 cases and 6031 controls) and these subjects were included in the analysis.

To validate the PHS approach in a sample which is independent of ADGC,¹⁰ we split our GERAD data into a discovery (75% or 1934 cases and 5493 controls) dataset, for estimation the HR, and validation (25% or 692 cases and 1784 controls) dataset, where we derived the PHS for each individual and tested for age-specific risk prediction.

In the GERAD sample 5570 controls were from the 1958 birth cohort (all included at age 45) (http://www.b58cgene.sgul.ac.uk), introducing differences in age distribution between cases and controls (Fig. 1). To avoid a potential bias due to these differences, we have repeated the analyses including only participants with age 55 and

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Histogram of age of AD cases and controls in the GERAD dataset.</figcaption></figure>
above, retaining 4100 individuals (2575 cases and 1525 controls).

## Statistical analysis

We calculated PHS for each subject in our GERAD sample using effect sizes as reported in the Desikan et al.¹⁰ (see fifth column of Table 1). The PRS were generated using IGAP_noGERAD effect sizes for the 25 SNPs reported (see seventh column of Table 1). To evaluate the contribution of the 25 SNPs over and above APOE ε2 and ε4 risk alleles, PHS and PRS were derived in three ways (1) only using ε2 and ε4 risk alleles, (2) 25 SNPs,

and (3) combining ε2, ε4, and 25 SNPs. We tested whether the addition of either PHS or PRS into the Cox regression model improves the model fit over and above APOE ε4 and ε2 risk alleles using anova() function in R. Since APOE is the strongest predictor of AD risk, we also validated our results in ε3 homozygous individuals (N = 4368). Furthermore, to investigate the stability of the results o for the 25 SNPs of interest, this analysis was repeated for randomly selected subsets of cases and controls (20, 40, 60, 80, and 100% of the whole sample).

We further investigated whether a different (larger) set of SNPs could improve the power of the association and the quality of the prediction of age-specific genetic risk

<table><caption>**Table 1.** APOE variants and the 31 SNPs and, their closest genes, log hazard ratio estimates used for PHS construction in Desikan et al.¹⁰ and their odds ratio estimates as in Lambert et al.⁶</caption><thead><tr><th>SNP</th><th>Chr</th><th>Position</th><th>Gene</th><th>B = log(HR)<br>Desikan et al.<br>(2017)</th><th>-log10(P-value)<br>Desikan et al.<br>(2017)</th><th>B = log(OR)<br>in IGAP</th><th>B = log(OR)<br>IGAP_noGERAD</th><th>A1 IGAP_noGERAD</th></tr></thead><tbody><tr><td>APOE ε2</td><td>19</td><td></td><td>APOE</td><td>-0.47</td><td>>15.0</td><td>-0.66<sup>1</sup></td><td>-0.49<sup>2</sup></td><td>ε2</td></tr><tr><td>APOE ε4</td><td>19</td><td></td><td>APOE</td><td>1.03</td><td>>20.0</td><td>1.12<sup>2</sup></td><td>0.66<sup>2</sup></td><td>ε4</td></tr><tr><td>rs4266886</td><td>1</td><td>207685786</td><td>CR1</td><td>-0.09</td><td>2.7</td><td>-0.1542</td><td>0.1520</td><td>T</td></tr><tr><td>rs61822977</td><td>1</td><td>207796065</td><td>CR1</td><td>-0.08</td><td>2.8</td><td>-0.0805</td><td>-0.0820</td><td>A</td></tr><tr><td>rs6733839</td><td>2</td><td>127892810</td><td>BIN1</td><td>-0.15</td><td>10.5</td><td>-0.1880</td><td>0.1807</td><td>T</td></tr><tr><td>rs10202748</td><td>2</td><td>234003117</td><td>INPP5D</td><td>-0.06</td><td>2.1</td><td>-0.058</td><td>-0.0603</td><td>A</td></tr><tr><td>rs115124923</td><td>6</td><td>32510482</td><td>HLA-DRB5</td><td>0.17</td><td>7.4</td><td>0.1216</td><td>-0.0973</td><td>A</td></tr><tr><td>rs115675626</td><td>6</td><td>32669833</td><td>HLA-DQB1</td><td>-0.11</td><td>3.2</td><td>-0.1246</td><td>0.1040</td><td>A</td></tr><tr><td>rs1109581</td><td>6</td><td>47678182</td><td>GPR115</td><td>-0.07</td><td>2.6</td><td>-0.0651</td><td>0.0601</td><td>T</td></tr><tr><td>rs17265593</td><td>7</td><td>37619922</td><td>BC043356</td><td>-0.23</td><td>3.6</td><td>-0.0659</td><td>-0.0620</td><td>T</td></tr><tr><td>rs2597283</td><td>7</td><td>37690507</td><td>BC043356</td><td>0.28</td><td>4.7</td><td>0.0679</td><td>0.0629</td><td>A</td></tr><tr><td>rs1476679</td><td>7</td><td>100004446</td><td>ZCWPW1</td><td>0.11</td><td>4.9</td><td>0.1741</td><td>0.0712</td><td>T</td></tr><tr><td>rs78571833</td><td>7</td><td>143122924</td><td>AL833583</td><td>0.14</td><td>3.8</td><td>0.0795</td><td>0.2083</td><td>A</td></tr><tr><td>rs12679874</td><td>8</td><td>27230819</td><td>PTK2B</td><td>-0.09</td><td>4.2</td><td>-0.0795</td><td>-0.0748</td><td>A</td></tr><tr><td>rs2741342</td><td>8</td><td>27330096</td><td>CHRNA2</td><td>0.09</td><td>2.9</td><td>0.0916</td><td>-0.0872</td><td>T</td></tr><tr><td>rs7831810</td><td>8</td><td>27430506</td><td>CLU</td><td>0.09</td><td>3.0</td><td>0.083</td><td>-0.0774</td><td>A</td></tr><tr><td>rs1532277</td><td>8</td><td>27466181</td><td>CLU</td><td>0.21</td><td>8.3</td><td>0.1385</td><td>-0.1271</td><td>T</td></tr><tr><td>rs9331888</td><td>8</td><td>27468862</td><td>CLU</td><td>0.16</td><td>5.1</td><td>0.0819</td><td>-0.0806</td><td>C</td></tr><tr><td>rs7920721</td><td>10</td><td>11720308</td><td>CR595071</td><td>-0.07</td><td>2.9</td><td>-0.0713</td><td>-0.0660</td><td>A</td></tr><tr><td>rs3740688</td><td>11</td><td>47380340</td><td>SPI1</td><td>0.07</td><td>2.8</td><td>0.0724</td><td>0.0739</td><td>T</td></tr><tr><td>rs7116190</td><td>11</td><td>59964992</td><td>MS4A6A</td><td>0.08</td><td>3.9</td><td>0.0991</td><td>-0.0968</td><td>A</td></tr><tr><td>rs526904</td><td>11</td><td>85811364</td><td>PICALM</td><td>-0.20</td><td>2.3</td><td>-0.1188</td><td>-0.1130</td><td>T</td></tr><tr><td>rs543293</td><td>11</td><td>85820077</td><td>PICALM</td><td>0.30</td><td>4.2</td><td>0.1257</td><td>-0.1192</td><td>A</td></tr><tr><td>rs11218343</td><td>11</td><td>121435587</td><td>SORL1</td><td>0.18</td><td>2.8</td><td>0.2697</td><td>0.2539</td><td>T</td></tr><tr><td>rs6572869</td><td>14</td><td>53353454</td><td>FERMT2</td><td>-0.11</td><td>3.0</td><td>-0.0947</td><td>0.1006</td><td>A</td></tr><tr><td>rs12590273</td><td>14</td><td>92934120</td><td>SLC24A4</td><td>0.10</td><td>3.5</td><td>0.1348</td><td>0.1231</td><td>T</td></tr><tr><td>rs7145100</td><td>14</td><td>107160690</td><td>abParts</td><td>0.08</td><td>2.0</td><td>0.1047</td><td>-0.1081</td><td>C</td></tr><tr><td>rs74615166</td><td>15</td><td>64725490</td><td>TRIP4</td><td>-0.23</td><td>3.1</td><td>-0.3358</td><td>-0.2986</td><td>T</td></tr><tr><td>rs2526378</td><td>17</td><td>56404349</td><td>BZRAP1</td><td>0.09</td><td>4.9</td><td>0.0762</td><td>0.0754</td><td>A</td></tr><tr><td>rs117481827</td><td>19</td><td>1021627</td><td>C19orf6</td><td>-0.09</td><td>2.5</td><td>-0.1288</td><td>-0.1059</td><td>T</td></tr><tr><td>rs7408475</td><td>19</td><td>1050130</td><td>ABCA7</td><td>0.18</td><td>4.3</td><td>0.0971</td><td>-0.0973</td><td>C</td></tr><tr><td>rs3752246</td><td>19</td><td>1056492</td><td>ABCA7</td><td>-0.25</td><td>8.4</td><td>-0.1345</td><td>-0.1308</td><td>C</td></tr><tr><td>rs7274581</td><td>20</td><td>55018260</td><td>CASS4</td><td>0.10</td><td>2.1</td><td>0.139</td><td>0.1497</td><td>A</td></tr></tbody></table>

First 6th columns are the same as they were presented in Desikan et al. (2017),¹⁰ followed by effect sizes from IGAP and IGAP_noGERAD summary statistics and reference allele as it was presented in IGAP.

¹B estimated on GERAD data when running LR.

²B estimated on GERAD data when running Cox regression.
above, retaining 4100 individuals (2575 cases and 1525 controls).

## Statistical analysis

We calculated PHS for each subject in our GERAD sample using effect sizes as reported in the Desikan et al.¹⁰ (see fifth column of Table 1). The PRS were generated using IGAP_noGERAD effect sizes for the 25 SNPs reported (see seventh column of Table 1). To evaluate the contribution of the 25 SNPs over and above APOE ε2 and ε4 risk alleles, PHS and PRS were derived in three ways (1) only using ε2 and ε4 risk alleles, (2) 25 SNPs,

and (3) combining ε2, ε4, and 25 SNPs. We tested whether the addition of either PHS or PRS into the Cox regression model improves the model fit over and above APOE ε4 and ε2 risk alleles using anova() function in R. Since APOE is the strongest predictor of AD risk, we also validated our results in ε3 homozygous individuals (N = 4368). Furthermore, to investigate the stability of the results o for the 25 SNPs of interest, this analysis was repeated for randomly selected subsets of cases and controls (20, 40, 60, 80, and 100% of the whole sample).

We further investigated whether a different (larger) set of SNPs could improve the power of the association and the quality of the prediction of age-specific genetic risk

<table><caption>**Table 1.** APOE variants and the 31 SNPs and, their closest genes, log hazard ratio estimates used for PHS construction in Desikan et al.¹⁰ and their odds ratio estimates as in Lambert et al.⁶</caption><thead><tr><th>SNP</th><th>Chr</th><th>Position</th><th>Gene</th><th>B = log(HR)<br>Desikan et al.<br>(2017)</th><th>-log10(P-value)<br>Desikan et al.<br>(2017)</th><th>B = log(OR)<br>in IGAP</th><th>B = log(OR)<br>IGAP_noGERAD</th><th>A1 IGAP_noGERAD</th></tr></thead><tbody><tr><td>APOE ε2</td><td>19</td><td></td><td>APOE</td><td>-0.47</td><td>>15.0</td><td>-0.66<sup>1</sup></td><td>-0.49<sup>2</sup></td><td>ε2</td></tr><tr><td>APOE ε4</td><td>19</td><td></td><td>APOE</td><td>1.03</td><td>>20.0</td><td>1.12<sup>2</sup></td><td>0.66<sup>2</sup></td><td>ε4</td></tr><tr><td>rs4266886</td><td>1</td><td>207685786</td><td>CR1</td><td>-0.09</td><td>2.7</td><td>-0.1542</td><td>0.1520</td><td>T</td></tr><tr><td>rs61822977</td><td>1</td><td>207796065</td><td>CR1</td><td>-0.08</td><td>2.8</td><td>-0.0805</td><td>-0.0820</td><td>A</td></tr><tr><td>rs6733839</td><td>2</td><td>127892810</td><td>BIN1</td><td>-0.15</td><td>10.5</td><td>-0.1880</td><td>0.1807</td><td>T</td></tr><tr><td>rs10202748</td><td>2</td><td>234003117</td><td>INPP5D</td><td>-0.06</td><td>2.1</td><td>-0.058</td><td>-0.0603</td><td>A</td></tr><tr><td>rs115124923</td><td>6</td><td>32510482</td><td>HLA-DRB5</td><td>0.17</td><td>7.4</td><td>0.1216</td><td>-0.0973</td><td>A</td></tr><tr><td>rs115675626</td><td>6</td><td>32669833</td><td>HLA-DQB1</td><td>-0.11</td><td>3.2</td><td>-0.1246</td><td>0.1040</td><td>A</td></tr><tr><td>rs1109581</td><td>6</td><td>47678182</td><td>GPR115</td><td>-0.07</td><td>2.6</td><td>-0.0651</td><td>0.0601</td><td>T</td></tr><tr><td>rs17265593</td><td>7</td><td>37619922</td><td>BC043356</td><td>-0.23</td><td>3.6</td><td>-0.0659</td><td>-0.0620</td><td>T</td></tr><tr><td>rs2597283</td><td>7</td><td>37690507</td><td>BC043356</td><td>0.28</td><td>4.7</td><td>0.0679</td><td>0.0629</td><td>A</td></tr><tr><td>rs1476679</td><td>7</td><td>100004446</td><td>ZCWPW1</td><td>0.11</td><td>4.9</td><td>0.1741</td><td>0.0712</td><td>T</td></tr><tr><td>rs78571833</td><td>7</td><td>143122924</td><td>AL833583</td><td>0.14</td><td>3.8</td><td>0.0795</td><td>0.2083</td><td>A</td></tr><tr><td>rs12679874</td><td>8</td><td>27230819</td><td>PTK2B</td><td>-0.09</td><td>4.2</td><td>-0.0795</td><td>-0.0748</td><td>A</td></tr><tr><td>rs2741342</td><td>8</td><td>27330096</td><td>CHRNA2</td><td>0.09</td><td>2.9</td><td>0.0916</td><td>-0.0872</td><td>T</td></tr><tr><td>rs7831810</td><td>8</td><td>27430506</td><td>CLU</td><td>0.09</td><td>3.0</td><td>0.083</td><td>-0.0774</td><td>A</td></tr><tr><td>rs1532277</td><td>8</td><td>27466181</td><td>CLU</td><td>0.21</td><td>8.3</td><td>0.1385</td><td>-0.1271</td><td>T</td></tr><tr><td>rs9331888</td><td>8</td><td>27468862</td><td>CLU</td><td>0.16</td><td>5.1</td><td>0.0819</td><td>-0.0806</td><td>C</td></tr><tr><td>rs7920721</td><td>10</td><td>11720308</td><td>CR595071</td><td>-0.07</td><td>2.9</td><td>-0.0713</td><td>-0.0660</td><td>A</td></tr><tr><td>rs3740688</td><td>11</td><td>47380340</td><td>SPI1</td><td>0.07</td><td>2.8</td><td>0.0724</td><td>0.0739</td><td>T</td></tr><tr><td>rs7116190</td><td>11</td><td>59964992</td><td>MS4A6A</td><td>0.08</td><td>3.9</td><td>0.0991</td><td>-0.0968</td><td>A</td></tr><tr><td>rs526904</td><td>11</td><td>85811364</td><td>PICALM</td><td>-0.20</td><td>2.3</td><td>-0.1188</td><td>-0.1130</td><td>T</td></tr><tr><td>rs543293</td><td>11</td><td>85820077</td><td>PICALM</td><td>0.30</td><td>4.2</td><td>0.1257</td><td>-0.1192</td><td>A</td></tr><tr><td>rs11218343</td><td>11</td><td>121435587</td><td>SORL1</td><td>0.18</td><td>2.8</td><td>0.2697</td><td>0.2539</td><td>T</td></tr><tr><td>rs6572869</td><td>14</td><td>53353454</td><td>FERMT2</td><td>-0.11</td><td>3.0</td><td>-0.0947</td><td>0.1006</td><td>A</td></tr><tr><td>rs12590273</td><td>14</td><td>92934120</td><td>SLC24A4</td><td>0.10</td><td>3.5</td><td>0.1348</td><td>0.1231</td><td>T</td></tr><tr><td>rs7145100</td><td>14</td><td>107160690</td><td>abParts</td><td>0.08</td><td>2.0</td><td>0.1047</td><td>-0.1081</td><td>C</td></tr><tr><td>rs74615166</td><td>15</td><td>64725490</td><td>TRIP4</td><td>-0.23</td><td>3.1</td><td>-0.3358</td><td>-0.2986</td><td>T</td></tr><tr><td>rs2526378</td><td>17</td><td>56404349</td><td>BZRAP1</td><td>0.09</td><td>4.9</td><td>0.0762</td><td>0.0754</td><td>A</td></tr><tr><td>rs117481827</td><td>19</td><td>1021627</td><td>C19orf6</td><td>-0.09</td><td>2.5</td><td>-0.1288</td><td>-0.1059</td><td>T</td></tr><tr><td>rs7408475</td><td>19</td><td>1050130</td><td>ABCA7</td><td>0.18</td><td>4.3</td><td>0.0971</td><td>-0.0973</td><td>C</td></tr><tr><td>rs3752246</td><td>19</td><td>1056492</td><td>ABCA7</td><td>-0.25</td><td>8.4</td><td>-0.1345</td><td>-0.1308</td><td>C</td></tr><tr><td>rs7274581</td><td>20</td><td>55018260</td><td>CASS4</td><td>0.10</td><td>2.1</td><td>0.139</td><td>0.1497</td><td>A</td></tr></tbody></table>

First 6th columns are the same as they were presented in Desikan et al. (2017),¹⁰ followed by effect sizes from IGAP and IGAP_noGERAD summary statistics and reference allele as it was presented in IGAP.

¹B estimated on GERAD data when running LR.

²B estimated on GERAD data when running Cox regression.
for AD. For this we used the full GERAD GWAS dataset (4,997,262 SNPs). The dataset was LD pruned with $r^2 = 0.1$ in a 1000 kb window, retaining 167,188 SNPs (with IGAP_noGERAD summary statistics). A fivefold cross-validation approach was employed splitting the GERAD data randomly into 75%/25% discovery and validation sets, respectively. LR and Cox regression were run in the discovery (75% of GERAD) dataset in order to obtain effect sizes, log(OR) and log(HR), respectively. The PRS and PHS for each individual in the validation set (25% of GERAD) were generated for AD association P-value thresholds of $P \le 5 \times 10^{-8}$, $10^{-5}$, $10^{-3}$, 0.05, 0.1, and 0.5, adjusted for covariates and then standardized. The Cox regression model was run to predict age-specific genetic risk for AD by (1) PHS and (2) PRS in the validation set. Note, in LR analysis age was not included into the model, while Cox regression model has accounted for the age as a censor variable. The proportional hazards assumption for the Cox regression model, that is, that the hazard rate ratio is constant over time, was tested using function cox.zph() in R. P-values of the proportional hazards assumption tests were non-significant indicating that the models were correctly specified.

The results of the cross-validation procedure are reported as mean and SD of the effect sizes, and as the average of the P-values across cross-validation. We also report the average of the correlation coefficients between individual PHS vs PRS scores.

## Results

In attempt to directly replicate the Desikan et al.¹⁰ results, we performed analysis on 8415 individuals (2384 cases and 6031 controls) for whom APOE genotypes were available. PHS was derived for each individual in the GERAD dataset with APOE ε2 and ε4 risk alleles and the 25 SNPs available in the dataset that were reported in Desikan et al.¹⁰ (see also Table 1). PRS was derived using effect sizes obtained from IGAP_noGERAD summary statistics using the same SNPs as for PHS. As the effect sizes for

APOE ε2 and ε4 risk alleles in IGAP_noGERAD data were unavailable, we used GERAD data to estimate them using LR ($B(ε2) = -0.66$, $B(ε4) = 1.12$). Table 2 presents the results of PHS and PRS models, where risk scores were constructed with (1) APOE ε4 and ε2 risk alleles (columns 2 and 3), (2) PHS and PRS scores based upon 25 SNPs (columns 4 and 5), and (3) PHS and PRS scores + APOE ε4 and ε2 risk alleles (columns 6 and 7). It can be seen from Table 2 that the regression coefficient estimates (B) and P-values for both models are very similar. In both models the strongest association is observed when the risk scores (either PHR or PRS) were constructed using APOE ε2 and ε4 risk alleles. The scores derived with the 25 SNPs also show significant association with age-specific AD risk ($P = 9.7 \times 10^{-8}$, $P = 1.9 \times 10^{-10}$ for PHS and PRS Models, respectively). The last column of Table 2 compares the fit of the APOE-alone model with the model using APOE + 25 SNPs as predictors and shows that the both PHS and PRS significantly improve the association results over and above the predictor variable based upon APOE ε2 and ε4 only. The correlation between individual PHS and PRS was $r = 0.85$ (see Fig. 2) and even higher when APOE variants were included $r = 0.99$. Analysis in ε3 homozygotes (N cases = 846, N controls = 3522) confirmed that PRS is a significant predictor of age specific risk for AD over and above APOE ($B = 0.17$, $P = 9.5 \times 10^{-7}$), and revealed that PHS is a slightly less significant predictor ($B = 0.14$, $P = 2.0 \times 10^{-5}$).

Figure 3 shows survival curves for individuals quantified in 5 groups based on 0–5%, 5–25%, 25–75%, 75–95%, and 95–100% of PHS/PRS distributions. Survival curves were created using PHS (left panel) and PRS (right panel) accounting for APOE ε2, ε4 risk alleles and the 25 SNPs. There is a clear difference in age at onset for individuals that belong to different distribution groups for both models. For example, individuals with the low PHS (bottom 5% of the PHS distribution, purple line in the left panel of Fig. 3) on average have 20 years earlier age at onset as compared to the top 5% of the PHS (red line

<table><caption>**Table 2.** Cox regression analysis results using PHS and PRS based upon (the same) SNPs as in Desikan et al. (2017)¹⁰ in GERAD dataset.</caption><thead><tr><th rowspan="2"></th><th colspan="2">APOE(ε2 + ε4)</th><th colspan="2">25 SNPs</th><th colspan="2">APOE(ε2 + ε4) + 25 SNPs</th><th rowspan="2">Compare: APOE<br/>vs. 25 SNPs +<br/>APOE(ε2 + ε4) P-value</th></tr><tr><th>B [SE]</th><th>P-value</th><th>B [SE]</th><th>P-value</th><th>B<sup>1</sup> [SE], B<sup>2</sup> [SE]</th><th>P-value</th></tr></thead><tbody><tr><td>PHS model with effect<br/>sizes from Desikan<br/>et al. (2017)</td><td>0.41 [0.019]</td><td>1.8 × 10<sup>-101</sup></td><td>0.11 [0.02]</td><td>9.7 × 10<sup>-8</sup></td><td>0.41 [0.019],<br/>0.11 [0.02]</td><td>4.8 × 10<sup>-103</sup></td><td>3.4 × 10<sup>-8</sup></td></tr><tr><td>PRS model with effects<br/>from IGAP_noGERAD</td><td>0.408 [0.018]</td><td>2.7 × 10<sup>-103</sup></td><td>0.13 [0.02]</td><td>1.9 × 10<sup>-10</sup></td><td>0.41 [0.019],<br/>0.13 [0.02]</td><td>2.4 × 10<sup>-105</sup></td><td>8.8 × 10<sup>-10</sup></td></tr></tbody></table>

<footnote n="1">¹B is a coefficient for APOE (ε2 + ε4).</footnote>

<footnote n="2">²B is a coefficient for PRS/PHS without APOE.</footnote>
for AD. For this we used the full GERAD GWAS dataset (4,997,262 SNPs). The dataset was LD pruned with $r^2 = 0.1$ in a 1000 kb window, retaining 167,188 SNPs (with IGAP_noGERAD summary statistics). A fivefold cross-validation approach was employed splitting the GERAD data randomly into 75%/25% discovery and validation sets, respectively. LR and Cox regression were run in the discovery (75% of GERAD) dataset in order to obtain effect sizes, log(OR) and log(HR), respectively. The PRS and PHS for each individual in the validation set (25% of GERAD) were generated for AD association P-value thresholds of $P \le 5 \times 10^{-8}$, $10^{-5}$, $10^{-3}$, 0.05, 0.1, and 0.5, adjusted for covariates and then standardized. The Cox regression model was run to predict age-specific genetic risk for AD by (1) PHS and (2) PRS in the validation set. Note, in LR analysis age was not included into the model, while Cox regression model has accounted for the age as a censor variable. The proportional hazards assumption for the Cox regression model, that is, that the hazard rate ratio is constant over time, was tested using function cox.zph() in R. P-values of the proportional hazards assumption tests were non-significant indicating that the models were correctly specified.

The results of the cross-validation procedure are reported as mean and SD of the effect sizes, and as the average of the P-values across cross-validation. We also report the average of the correlation coefficients between individual PHS vs PRS scores.

## Results

In attempt to directly replicate the Desikan et al.¹⁰ results, we performed analysis on 8415 individuals (2384 cases and 6031 controls) for whom APOE genotypes were available. PHS was derived for each individual in the GERAD dataset with APOE ε2 and ε4 risk alleles and the 25 SNPs available in the dataset that were reported in Desikan et al.¹⁰ (see also Table 1). PRS was derived using effect sizes obtained from IGAP_noGERAD summary statistics using the same SNPs as for PHS. As the effect sizes for

APOE ε2 and ε4 risk alleles in IGAP_noGERAD data were unavailable, we used GERAD data to estimate them using LR ($B(ε2) = -0.66$, $B(ε4) = 1.12$). Table 2 presents the results of PHS and PRS models, where risk scores were constructed with (1) APOE ε4 and ε2 risk alleles (columns 2 and 3), (2) PHS and PRS scores based upon 25 SNPs (columns 4 and 5), and (3) PHS and PRS scores + APOE ε4 and ε2 risk alleles (columns 6 and 7). It can be seen from Table 2 that the regression coefficient estimates (B) and P-values for both models are very similar. In both models the strongest association is observed when the risk scores (either PHR or PRS) were constructed using APOE ε2 and ε4 risk alleles. The scores derived with the 25 SNPs also show significant association with age-specific AD risk ($P = 9.7 \times 10^{-8}$, $P = 1.9 \times 10^{-10}$ for PHS and PRS Models, respectively). The last column of Table 2 compares the fit of the APOE-alone model with the model using APOE + 25 SNPs as predictors and shows that the both PHS and PRS significantly improve the association results over and above the predictor variable based upon APOE ε2 and ε4 only. The correlation between individual PHS and PRS was $r = 0.85$ (see Fig. 2) and even higher when APOE variants were included $r = 0.99$. Analysis in ε3 homozygotes (N cases = 846, N controls = 3522) confirmed that PRS is a significant predictor of age specific risk for AD over and above APOE ($B = 0.17$, $P = 9.5 \times 10^{-7}$), and revealed that PHS is a slightly less significant predictor ($B = 0.14$, $P = 2.0 \times 10^{-5}$).

Figure 3 shows survival curves for individuals quantified in 5 groups based on 0–5%, 5–25%, 25–75%, 75–95%, and 95–100% of PHS/PRS distributions. Survival curves were created using PHS (left panel) and PRS (right panel) accounting for APOE ε2, ε4 risk alleles and the 25 SNPs. There is a clear difference in age at onset for individuals that belong to different distribution groups for both models. For example, individuals with the low PHS (bottom 5% of the PHS distribution, purple line in the left panel of Fig. 3) on average have 20 years earlier age at onset as compared to the top 5% of the PHS (red line

<table><caption>**Table 2.** Cox regression analysis results using PHS and PRS based upon (the same) SNPs as in Desikan et al. (2017)¹⁰ in GERAD dataset.</caption><thead><tr><th rowspan="2"></th><th colspan="2">APOE(ε2 + ε4)</th><th colspan="2">25 SNPs</th><th colspan="2">APOE(ε2 + ε4) + 25 SNPs</th><th rowspan="2">Compare: APOE<br>vs. 25 SNPs +<br>APOE(ε2 + ε4) P-value</th></tr><tr><th>B [SE]</th><th>P-value</th><th>B [SE]</th><th>P-value</th><th>B<sup>1</sup> [SE], B<sup>2</sup> [SE]</th><th>P-value</th></tr></thead><tbody><tr><td>PHS model with effect<br>sizes from Desikan<br>et al. (2017)</td><td>0.41 [0.019]</td><td>1.8 × 10<sup>-101</sup></td><td>0.11 [0.02]</td><td>9.7 × 10<sup>-8</sup></td><td>0.41 [0.019],<br>0.11 [0.02]</td><td>4.8 × 10<sup>-103</sup></td><td>3.4 × 10<sup>-8</sup></td></tr><tr><td>PRS model with effects<br>from IGAP_noGERAD</td><td>0.408 [0.018]</td><td>2.7 × 10<sup>-103</sup></td><td>0.13 [0.02]</td><td>1.9 × 10<sup>-10</sup></td><td>0.41 [0.019],<br>0.13 [0.02]</td><td>2.4 × 10<sup>-105</sup></td><td>8.8 × 10<sup>-10</sup></td></tr></tbody></table>

<footnote n="1">¹B is a coefficient for APOE (ε2 + ε4).</footnote>

<footnote n="2">²B is a coefficient for PRS/PHS without APOE.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Scatter plot of individual's PRS and PHS that were derived using 25 SNPs from Desikan et al.¹⁰ in the GERAD sample.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Survival curves for PHS and PRS scores + APOE ε4 and ε2 risk alleles for 8,415 individuals (2,384 cases and 6,031 controls) for whom APOE genotypes were available. Individuals are split into 5 groups based on 0–5%, 5–25%, 25–75%, 75–95%, and 95–100% of PHS/PRS distributions.</figcaption></figure>

in the left panel of Fig. 3), given a probability of 0.25 of developing AD. For both models the curves are almost identical and there is clear difference in age at onset for individuals that belong to different distribution groups for both models.

The results of age-specific predictions using PHS and PRS analyses based upon 25 SNPs for different sample sizes are presented in Figure 4. As before, the age-specific

risk effect sizes for both PRS and PHS were similar and (as expected) were lowest in the smallest subset of the GERAD data, gradually increasing with sample size.

To increase the power of the analysis we attempted to increase the sample size and the number of SNPs included in the analysis. We utilized the full GERAD dataset (2626 cases and 7277 controls), and included *APOE* locus via the best (imputed) proxies as not all individuals in the GEARD
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Scatter plot of individual's PRS and PHS that were derived using 25 SNPs from Desikan et al.¹⁰ in the GERAD sample.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Survival curves for PHS and PRS scores + APOE ε4 and ε2 risk alleles for 8,415 individuals (2,384 cases and 6,031 controls) for whom APOE genotypes were available. Individuals are split into 5 groups based on 0–5%, 5–25%, 25–75%, 75–95%, and 95–100% of PHS/PRS distributions.</figcaption></figure>

in the left panel of Fig. 3), given a probability of 0.25 of developing AD. For both models the curves are almost identical and there is clear difference in age at onset for individuals that belong to different distribution groups for both models.

The results of age-specific predictions using PHS and PRS analyses based upon 25 SNPs for different sample sizes are presented in Figure 4. As before, the age-specific

risk effect sizes for both PRS and PHS were similar and (as expected) were lowest in the smallest subset of the GERAD data, gradually increasing with sample size.

To increase the power of the analysis we attempted to increase the sample size and the number of SNPs included in the analysis. We utilized the full GERAD dataset (2626 cases and 7277 controls), and included *APOE* locus via the best (imputed) proxies as not all individuals in the GEARD
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Results of age-specific predictions using PRS and PHS analyses in GERAD subsamples of 20, 40, 60, 80, and 100% randomly selected individuals. The PHS and PRS are derived based upon 25 SNPs reported by Desikan et al.¹⁰</figcaption></figure>

sample had direct *APOE* genotypes. The correlation between *APOE* ε2 allele and rs41290120 was *r* = 0.74 and between *APOE* ε4 allele and rs7259620 was *r* = −0.41. To include more SNPs into the PHS, we increased the *P*-value association threshold to 0.5 and LD pruned SNPs while keeping the most significantly AD-associated SNPs (in IGAP_noGERAD) for the analysis. For the pruned SNPs we re-estimated the *B* coefficients with Cox regression and LR in the 75% of the GERAD sample, and ran the age specific prediction analyses in the remaining 25% with

fivefold cross-validation (see Results in Table 3). The Cox regression analysis suggests that significant age-specific prediction when using either PHS or PRS is achieved with the SNP selection threshold at *P* ≤ 10⁻³. The Pearson's correlation coefficient between individual PHS and PRS is high for SNP selection thresholds up to *P* ≤ 10⁻⁵ (Table 3, last column). Age-specific predictions are no longer significant when SNPs *P*-value thresholds are higher than 10⁻³. Since the age distribution was quite different in cases and controls (see Fig. 1), the same analyses were performed for

<table><caption>**Table 3.** Cox regression analyses results of 5-fold cross-validation for PHS and PRS in GERAD dataset.</caption><thead><tr><th rowspan="2">SNP selection<br/>P-value<br/>threshold</th><th rowspan="2">N SNPs</th><th colspan="2">PHS</th><th colspan="2">PRS</th><th rowspan="2">Correlation<br/>between PHS<br/>and PRS</th></tr><tr><th>B [SD]</th><th>P-value</th><th>B [SD]</th><th>P-value</th></tr></thead><tbody><tr><td>5 × 10<sup>-8</sup></td><td>31</td><td>0.28 [0.04]</td><td>4.3 × 10<sup>-13</sup></td><td>0.28 [0.04]</td><td>2.5 × 10<sup>-12</sup></td><td>0.96</td></tr><tr><td>10<sup>-5</sup></td><td>80</td><td>0.26 [0.02]</td><td>2.8 × 10<sup>-11</sup></td><td>0.29 [0.05]</td><td>5.7 × 10<sup>-11</sup></td><td>0.79</td></tr><tr><td>10<sup>-3</sup></td><td>1460</td><td>0.13 [0.025]</td><td>3.4 × 10<sup>-3</sup></td><td>0.18 [0.04]</td><td>1.9 × 10<sup>-4</sup></td><td>0.17</td></tr><tr><td>0.05</td><td>29998</td><td>0.07 [0.027]</td><td>0.12</td><td>0.1 [0.034]</td><td>0.04</td><td>0.21</td></tr><tr><td>0.1</td><td>49247</td><td>0.06 [0.031]</td><td>0.18</td><td>0.09 [0.028]</td><td>0.05</td><td>0.27</td></tr><tr><td>0.5</td><td>128952</td><td>0.08 [0.024]</td><td>0.07</td><td>0.08 [0.035]</td><td>0.13</td><td>0.42</td></tr></tbody></table>

First column shows the *P*-value thresholds for AD associated SNP selection (from an independent IGAP_noGERAD data). Second column represents the number of SNPs that were included to the PRS/PHS score. PHS and PRS effect sizes (mean and SD) and averaged *P*-values across 5-fold cross-validation subsampling are shown in columns 3–6. The last column shows the average of Pearson's correlation coefficients between PHS and PRS.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Results of age-specific predictions using PRS and PHS analyses in GERAD subsamples of 20, 40, 60, 80, and 100% randomly selected individuals. The PHS and PRS are derived based upon 25 SNPs reported by Desikan et al.¹⁰</figcaption></figure>

sample had direct APOE genotypes. The correlation between APOE ε2 allele and rs41290120 was r = 0.74 and between APOE ε4 allele and rs7259620 was r = −0.41. To include more SNPs into the PHS, we increased the *P*-value association threshold to 0.5 and LD pruned SNPs while keeping the most significantly AD-associated SNPs (in IGAP_noGERAD) for the analysis. For the pruned SNPs we re-estimated the *B* coefficients with Cox regression and LR in the 75% of the GERAD sample, and ran the age specific prediction analyses in the remaining 25% with

fivefold cross-validation (see Results in Table 3). The Cox regression analysis suggests that significant age-specific prediction when using either PHS or PRS is achieved with the SNP selection threshold at $P \le 10^{-3}$. The Pearson's correlation coefficient between individual PHS and PRS is high for SNP selection thresholds up to $P \le 10^{-5}$ (Table 3, last column). Age-specific predictions are no longer significant when SNPs *P*-value thresholds are higher than $10^{-3}$. Since the age distribution was quite different in cases and controls (see Fig. 1), the same analyses were performed for

<table><caption>**Table 3.** Cox regression analyses results of 5-fold cross-validation for PHS and PRS in GERAD dataset.</caption><thead><tr><th rowspan="2">SNP selection<br>P-value<br>threshold</th><th rowspan="2">N SNPs</th><th colspan="2">PHS</th><th colspan="2">PRS</th><th rowspan="2">Correlation<br>between PHS<br>and PRS</th></tr><tr><th>B [SD]</th><th>P-value</th><th>B [SD]</th><th>P-value</th></tr></thead><tbody><tr><td>5 × 10<sup>-8</sup></td><td>31</td><td>0.28 [0.04]</td><td>4.3 × 10<sup>-13</sup></td><td>0.28 [0.04]</td><td>2.5 × 10<sup>-12</sup></td><td>0.96</td></tr><tr><td>10<sup>-5</sup></td><td>80</td><td>0.26 [0.02]</td><td>2.8 × 10<sup>-11</sup></td><td>0.29 [0.05]</td><td>5.7 × 10<sup>-11</sup></td><td>0.79</td></tr><tr><td>10<sup>-3</sup></td><td>1460</td><td>0.13 [0.025]</td><td>3.4 × 10<sup>-3</sup></td><td>0.18 [0.04]</td><td>1.9 × 10<sup>-4</sup></td><td>0.17</td></tr><tr><td>0.05</td><td>29998</td><td>0.07 [0.027]</td><td>0.12</td><td>0.1 [0.034]</td><td>0.04</td><td>0.21</td></tr><tr><td>0.1</td><td>49247</td><td>0.06 [0.031]</td><td>0.18</td><td>0.09 [0.028]</td><td>0.05</td><td>0.27</td></tr><tr><td>0.5</td><td>128952</td><td>0.08 [0.024]</td><td>0.07</td><td>0.08 [0.035]</td><td>0.13</td><td>0.42</td></tr></tbody></table>

First column shows the *P*-value thresholds for AD associated SNP selection (from an independent IGAP_noGERAD data). Second column represents the number of SNPs that were included to the PRS/PHS score. PHS and PRS effect sizes (mean and SD) and averaged *P*-values across 5-fold cross-validation subsampling are shown in columns 3–6. The last column shows the average of Pearson's correlation coefficients between PHS and PRS.
<table><caption>**Table 4.** Cox regression analysis results of 5-fold cross-validation for PHS and PRS in GERAD dataset for individuals age at onset 55 and above.</caption><thead><tr><th rowspan="2">P-value threshold</th><th rowspan="2">N SNPs</th><th colspan="2">PHS</th><th colspan="2">PRS</th><th rowspan="2">Pearson's correlation between PHS and PRS</th></tr><tr><th>B [sd]</th><th>P-value</th><th>B [sd]</th><th>P-value</th></tr></thead><tbody><tr><td>5 × 10<sup>-8</sup></td><td>31</td><td>0.3 [0.01]</td><td>1.3 × 10<sup>-12</sup></td><td>0.29 [0.03]</td><td>5.8 × 10<sup>-12</sup></td><td>0.96</td></tr><tr><td>10<sup>-5</sup></td><td>80</td><td>0.25 [0.05]</td><td>8.4 × 10<sup>-7</sup></td><td>0.31 [0.04]</td><td>5.3 × 10<sup>-10</sup></td><td>0.76</td></tr><tr><td>10<sup>-3</sup></td><td>1460</td><td>0.12 [0.04]</td><td>0.03</td><td>0.1 [0.03]</td><td>0.03</td><td>0.16</td></tr><tr><td>0.05</td><td>29998</td><td>0.03 [0.04]</td><td>0.42</td><td>0.004 [0.02]</td><td>0.62</td><td>0.32</td></tr><tr><td>0.1</td><td>49247</td><td>0.04 [0.03]</td><td>0.34</td><td>0.001 [0.02]</td><td>0.62</td><td>0.4</td></tr><tr><td>0.5</td><td>128952</td><td>0.05 [0.03]</td><td>0.29</td><td>0.008 [0.02]</td><td>0.59</td><td>0.59</td></tr></tbody></table>

First column shows the P-value thresholds for AD associated SNP selection (from an independent IGAP_noGERAD data). Second column represents the number of SNPs that were included to the PRS/PHS score. PHS and PRS effect sizes (mean and SD) and averaged P-values across 5-fold cross-validation subsampling are shown in columns 3–6. The last column shows the average of Pearson's correlation coefficients between PHS and PRS.

individuals aged 55 and above, retaining 4100 samples for the analysis (see Results in Table 4). Despite the substantial reduction in sample size, the pattern of the results stays the same across tables.

## Discussion

Polygenic risk score approach is typically used to predict risk of the disease and does not account for age at onset of cases and the fact that controls may develop the disease later in their lives. Implementation of the polygenic hazard score provides prediction for individuals' age-specific risk of AD development and can potentially be used for future investigation of the disease progression, intervention, and treatment of the disease.

There are two components to the risk prediction analyses by polygenic scores. The first component is the construction of the scores. Both PRS and PHS are derived as a sum of the number of risk alleles weighed by the SNP effect sizes, either logarithm of the odds ratio (log (OR)) or logarithm of the hazards ratio (log(HR)), respectively, which in turn are obtained with two different regression models (Logistic or Cox Proportional Hazard regression models). Ideally, for the construction of these scores, the SNP selection should be informed by the corresponding summary statistic from an independent dataset. For example case/control GWAS results should be used for PRS SNP selection, and Cox regression GWAS results, should be used for PHS SNP selection. The second component is the actual risk prediction. The choice of the regression model for this component of the analysis depends upon the question of interest and available data. If one is interested in predicting age-specific risk for AD then PHS should be used as the predictor in the Cox regression model, given that the age for controls and age at onset for cases is available for the analysis.

In this study, we tested whether there is an advantage in using PHS over the PRS for age-specific risk

prediction. First, we attempted to directly replicate the results of Desikan et al.¹⁰ using SNPs available in the GERAD dataset. Then we constructed PRS using the same SNPs and tested how well PRS can predict the age-specific risk in the GERAD sample. Finally, we attempted to enhance the PHS by adding more SNPs related to AD risk.

Desikan et al.¹⁰ selected AD associated SNPs with $P \le 10^{-5}$ in the IGAP, currently the largest publicly available GWAS dataset, then generated individual PHS in their (ADGC) dataset and tested this PHS for association with the AD age-specific risk. We have replicated their findings in our (GERAD) data. These were as expected given previous studies, comparing LR and Cox regression,¹⁴,¹⁷ show that the predictors with the largest effects stay significant in both Cox and Logistic regression analyses. When the effect sizes of the associated SNPs are large, the period between the age at onset and age at assessment is short (follow-up period is 5 years or less) and survival rate is high, then both Cox regression and LR will show similar estimates of the regression coefficients.¹⁶ A typical AD GWAS design falls into this category. In our data the mean difference between the age of the last assessment and age at onset was 4.7 years; there were more controls than cases; and the SNPs were selected on the basis of significant association with the disease risk. Therefore, it is expected that the IGAP genome-wide significant SNPs combined into PHS will show strong association in the ADGC and GERAD datasets as these datasets both contribute to the IGAP study.

When the SNPs were selected based upon AD association results in a sample set independent of GERAD (IGAP_noGERAD), both PHS and PRS were significantly associated with AD age-specific risk ($P < 10^{-3}$). For less stringent significance thresholds the age-specific risk prediction was not significant with either PHS or PRS. The results of Cox regression analysis have shown no significant difference in model fits when using PRS or PHS, if SNPs are selected on the basis of strong association to
<table><caption>**Table 4.** Cox regression analysis results of 5-fold cross-validation for PHS and PRS in GERAD dataset for individuals age at onset 55 and above.</caption><thead><tr><th rowspan="2">P-value threshold</th><th rowspan="2">N SNPs</th><th colspan="2">PHS</th><th colspan="2">PRS</th><th rowspan="2">Pearson's correlation between PHS and PRS</th></tr><tr><th>B [sd]</th><th>P-value</th><th>B [sd]</th><th>P-value</th></tr></thead><tbody><tr><td>5 × 10<sup>-8</sup></td><td>31</td><td>0.3 [0.01]</td><td>1.3 × 10<sup>-12</sup></td><td>0.29 [0.03]</td><td>5.8 × 10<sup>-12</sup></td><td>0.96</td></tr><tr><td>10<sup>-5</sup></td><td>80</td><td>0.25 [0.05]</td><td>8.4 × 10<sup>-7</sup></td><td>0.31 [0.04]</td><td>5.3 × 10<sup>-10</sup></td><td>0.76</td></tr><tr><td>10<sup>-3</sup></td><td>1460</td><td>0.12 [0.04]</td><td>0.03</td><td>0.1 [0.03]</td><td>0.03</td><td>0.16</td></tr><tr><td>0.05</td><td>29998</td><td>0.03 [0.04]</td><td>0.42</td><td>0.004 [0.02]</td><td>0.62</td><td>0.32</td></tr><tr><td>0.1</td><td>49247</td><td>0.04 [0.03]</td><td>0.34</td><td>0.001 [0.02]</td><td>0.62</td><td>0.4</td></tr><tr><td>0.5</td><td>128952</td><td>0.05 [0.03]</td><td>0.29</td><td>0.008 [0.02]</td><td>0.59</td><td>0.59</td></tr></tbody></table>

First column shows the P-value thresholds for AD associated SNP selection (from an independent IGAP_noGERAD data). Second column represents the number of SNPs that were included to the PRS/PHS score. PHS and PRS effect sizes (mean and SD) and averaged P-values across 5-fold cross-validation subsampling are shown in columns 3–6. The last column shows the average of Pearson's correlation coefficients between PHS and PRS.

individuals aged 55 and above, retaining 4100 samples for the analysis (see Results in Table 4). Despite the substantial reduction in sample size, the pattern of the results stays the same across tables.

## Discussion

Polygenic risk score approach is typically used to predict risk of the disease and does not account for age at onset of cases and the fact that controls may develop the disease later in their lives. Implementation of the polygenic hazard score provides prediction for individuals' age-specific risk of AD development and can potentially be used for future investigation of the disease progression, intervention, and treatment of the disease.

There are two components to the risk prediction analyses by polygenic scores. The first component is the construction of the scores. Both PRS and PHS are derived as a sum of the number of risk alleles weighed by the SNP effect sizes, either logarithm of the odds ratio (log (OR)) or logarithm of the hazards ratio (log(HR)), respectively, which in turn are obtained with two different regression models (Logistic or Cox Proportional Hazard regression models). Ideally, for the construction of these scores, the SNP selection should be informed by the corresponding summary statistic from an independent dataset. For example case/control GWAS results should be used for PRS SNP selection, and Cox regression GWAS results, should be used for PHS SNP selection. The second component is the actual risk prediction. The choice of the regression model for this component of the analysis depends upon the question of interest and available data. If one is interested in predicting age-specific risk for AD then PHS should be used as the predictor in the Cox regression model, given that the age for controls and age at onset for cases is available for the analysis.

In this study, we tested whether there is an advantage in using PHS over the PRS for age-specific risk

prediction. First, we attempted to directly replicate the results of Desikan et al.¹⁰ using SNPs available in the GERAD dataset. Then we constructed PRS using the same SNPs and tested how well PRS can predict the age-specific risk in the GERAD sample. Finally, we attempted to enhance the PHS by adding more SNPs related to AD risk.

Desikan et al.¹⁰ selected AD associated SNPs with $P \le 10^{-5}$ in the IGAP, currently the largest publicly available GWAS dataset, then generated individual PHS in their (ADGC) dataset and tested this PHS for association with the AD age-specific risk. We have replicated their findings in our (GERAD) data. These were as expected given previous studies, comparing LR and Cox regression,¹⁴,¹⁷ show that the predictors with the largest effects stay significant in both Cox and Logistic regression analyses. When the effect sizes of the associated SNPs are large, the period between the age at onset and age at assessment is short (follow-up period is 5 years or less) and survival rate is high, then both Cox regression and LR will show similar estimates of the regression coefficients.¹⁶ A typical AD GWAS design falls into this category. In our data the mean difference between the age of the last assessment and age at onset was 4.7 years; there were more controls than cases; and the SNPs were selected on the basis of significant association with the disease risk. Therefore, it is expected that the IGAP genome-wide significant SNPs combined into PHS will show strong association in the ADGC and GERAD datasets as these datasets both contribute to the IGAP study.

When the SNPs were selected based upon AD association results in a sample set independent of GERAD (IGAP_noGERAD), both PHS and PRS were significantly associated with AD age-specific risk ($P < 10^{-3}$). For less stringent significance thresholds the age-specific risk prediction was not significant with either PHS or PRS. The results of Cox regression analysis have shown no significant difference in model fits when using PRS or PHS, if SNPs are selected on the basis of strong association to
AD risk. However when SNPs are prioritized for associa-
tion with AD age at onset rather than general AD risk by
a powerful discovery study (e.g., Cox-regression AD
GWAS), the PHS is likely to be advantageous over the
PRS for age specific AD risk prediction. As such discovery
study was not available to us, we could not demonstrate
this advantage in our paper. We emphasize, that this is
the main limitation of our study. Since we only had
access to the AD GWAS summary statistics, obtained with
Logistic Regression, we could not prioritize SNPs specifi-
cally associated with AD age at onset, but only used SNPs
associated with AD risk overall. To overcome this issue
we divided the GERAD data into a discovery and valida-
tion sub-samples, however this reduced the power of our
further analyses. Another limitation of this study is the
lack of replication in a similar dataset since we did not
have access to individual genotypes of another AD case/
control study that was independent from IGAP. To
address this limitation, we employed cross-validation and
resampling approaches to the GERAD data. The main
results remained consistent in all analyses.

In conclusion, when SNPs are selected based upon case/
control AD GWAS with *P*-values thresholds up to
*P* ≤ 10<sup>-3</sup>, comparison of PRS and PHS suggests no advan-
tage of using effects of PHS over PRS for age-specific risk
prediction. Using less stringent significance thresholds for
SNP selection, the age-specific risk prediction results are
not significant by either PHS or PRS. To further enhance
and validate the PHS approach for AD age at onset risk
prediction, a large Cox regression GWAS needs to be con-
ducted, and used for SNP prioritization prior to construc-
tion of the PHS for each individual.

We have demonstrated that PRS is a robust measure of
the genetic liability to Alzheimer's disease. In addition to
general AD risk, it predicts the age-specific risk of AD.
The PHS, when constructed using significant SNPs identi-
fied by case/control GWAS, has potential disadvantages
which are similar to PRS, as outlined in Tan et al.¹⁸
Development of PHS based up on Cox Hazard Regression
model GWAS is a potential way forward to validate the
PHS approach.

Acknowledgments

We thank the MRC Centre for Neuropsychiatric Genetics and Genomics and Dementia Research Institute (DRI), Dementia Platform UK (DPUK). Data used in the preparation of this article was obtained from the Genetic and Environmental Risk for Alzheimer's disease (GERAD) Consortium, see Table S1. We thank the International Genomics of Alzheimer's Project (IGAP) for providing summary results data for these analyses. The investigators within

IGAP contributed to the design and implementation of
IGAP and/or provided data but did not participate in anal-
ysis or writing of this report. Members of the GERAD con-
sortium are listed below, and their affiliations and
contributions are provided in a separate file (File S1).
Magda Tsolaki, David Craig, Despoina Avramidou, Anto-
nia Germanou, Maria Koutroumani, Olymbia Gkatzima,
Harald Hampel, Patrick G Kehoe, Seth Love, David C
Rubinsztein, Lutz Frölich, Bernadette McGuinness, Janet A
Johnston, Peter Passmore, Dmitriy Drichel, Martin Rossor,
Jonathan M Schott, Jason D Warren, Jose Bras, Rita Guer-
reiro, Amit Kawalia Joseph T Hughes, Yogen Patel,
Michelle K Lupton, Petra Proitsi, John Powell, John S K
Kauwe, Michelangelo Mancuso, Ubaldo Bonuccelli, James
Uphill, Elizabeth Fisher, Carlo Masullo, Hilkka Soininen,
Gina Bisceglio, Li Ma, Dennis W Dickson, Neill R Graff-
Radford, Minerva M Carrasquillo, Steven G Younkin, San-
dro Sorbi, Makrina Daniilidou, Angela Hodges, Daniela
Galimberti, Elio Scarpini, Martin Scherer, Oliver Peters,
Alfredo Ramirez, Markus Leber, Sabrina Pichler, Manuel
Mayhaus, Wei Gu, Matthias Riemenschneider, Jens Wilt-
fang, Reinhard Heun, Heike Kölsch, Johannes Kornhuber,
Isabella Heuser, Dan Rujescu, Annette M Hartmann, Ina
Giegling, Michael Hüll, Simon Lovestone, Carlos Cruchaga,
John Morris, Kevin Mayo, Thomas Feulner, Rebecca Sus-
sams, Clive Holmes, David Mann, Stuart Pickering-Brown,
Nigel M Hooper, Andrew McQuillin, Gill Livingston,
Nicholas J Bass, Maria Vronskaya, Taniesha Morgan,
Nicola Denning, Thomas D Cushion, Lesley Jones, Rachel
Marshall, Alun Meggy, Georgina Menzies, Detelina Gro-
zeva, Michael C O'Donovan, Michael J Owen, Peter A
Holmans, Francesca Salani, Giancarlo Russo, Wolfgang
Maier, Frank Jessen, H-Erich Wichmann, Kevin Morgan,
Alison M Goate, Bruno Vellas, Emma Vardy, Susanne
Moebus, Karl-Heinz Jöckel, Martin Dichgans, Norman
Klopp, James Turton, Jenny Lord, Kristelle Brown,
Christopher Medway, Markus M Nöthen, Per Hoffmann,
Antonio Daniele, Anthony Bayer, John Gallacher, Hendrik
van den Bussche, Carol Brayne, Steffi Riedel-Heller, John F
Powell, Ammar Al-Chalabi, Christopher E Shaw, Iwona
Kloszewska, Pau Pastor, Monica Diez-Fairen, Aoibhinn
Lynch, Brian Lawlor, Michael Gill, Eliecer Coto, Victoria
Alvarez, Andrew B Singleton, John Collinge, Simon Mead,
Natalie Ryan, Benedetta Nacmias, Sara Ortega-Cubero,
Eloy Rodriguez-Rodriguez, Pascual Sanchez-Juan, Jacob
Shofany, Nerisa Banaj, Valentina Ciullo, Eleonora Sacchi-
nelli, Robert Clarke, A David Smith, Donald Warden, Yoav
Ben-Shlomo, Chiara Cupidi, Raffaele Giovanni Maletta,
Amalia Cecilia Bruni, Maura Gallo, Denise Harold, Roberta
Cecchetti, Patrizia Mecocci, Virginia Boccardi, Nick War-
ner, Gordon Wilcock, Panagiotis Deloukas, Rhian Gwil-
liam, Chris Corcoran, JoAnn Tschanz, Ron Munger.
AD risk. However when SNPs are prioritized for associa-
tion with AD age at onset rather than general AD risk by
a powerful discovery study (e.g., Cox-regression AD
GWAS), the PHS is likely to be advantageous over the
PRS for age specific AD risk prediction. As such discovery
study was not available to us, we could not demonstrate
this advantage in our paper. We emphasize, that this is
the main limitation of our study. Since we only had
access to the AD GWAS summary statistics, obtained with
Logistic Regression, we could not prioritize SNPs specifi-
cally associated with AD age at onset, but only used SNPs
associated with AD risk overall. To overcome this issue
we divided the GERAD data into a discovery and valida-
tion sub-samples, however this reduced the power of our
further analyses. Another limitation of this study is the
lack of replication in a similar dataset since we did not
have access to individual genotypes of another AD case/
control study that was independent from IGAP. To
address this limitation, we employed cross-validation and
resampling approaches to the GERAD data. The main
results remained consistent in all analyses.

In conclusion, when SNPs are selected based upon case/
control AD GWAS with *P*-values thresholds up to
*P* ≤ 10<sup>-3</sup>, comparison of PRS and PHS suggests no advan-
tage of using effects of PHS over PRS for age-specific risk
prediction. Using less stringent significance thresholds for
SNP selection, the age-specific risk prediction results are
not significant by either PHS or PRS. To further enhance
and validate the PHS approach for AD age at onset risk
prediction, a large Cox regression GWAS needs to be con-
ducted, and used for SNP prioritization prior to construc-
tion of the PHS for each individual.

We have demonstrated that PRS is a robust measure of
the genetic liability to Alzheimer's disease. In addition to
general AD risk, it predicts the age-specific risk of AD.
The PHS, when constructed using significant SNPs identi-
fied by case/control GWAS, has potential disadvantages
which are similar to PRS, as outlined in Tan et al.¹⁸
Development of PHS based up on Cox Hazard Regression
model GWAS is a potential way forward to validate the
PHS approach.

Acknowledgments

We thank the MRC Centre for Neuropsychiatric Genetics and Genomics and Dementia Research Institute (DRI), Dementia Platform UK (DPUK). Data used in the preparation of this article was obtained from the Genetic and Environmental Risk for Alzheimer's disease (GERAD) Consortium, see Table S1. We thank the International Genomics of Alzheimer's Project (IGAP) for providing summary results data for these analyses. The investigators within

IGAP contributed to the design and implementation of
IGAP and/or provided data but did not participate in anal-
ysis or writing of this report. Members of the GERAD con-
sortium are listed below, and their affiliations and
contributions are provided in a separate file (File S1).
Magda Tsolaki, David Craig, Despoina Avramidou, Anto-
nia Germanou, Maria Koutroumani, Olymbia Gkatzima,
Harald Hampel, Patrick G Kehoe, Seth Love, David C
Rubinsztein, Lutz Frölich, Bernadette McGuinness, Janet A
Johnston, Peter Passmore, Dmitriy Drichel, Martin Rossor,
Jonathan M Schott, Jason D Warren, Jose Bras, Rita Guer-
reiro, Amit Kawalia Joseph T Hughes, Yogen Patel,
Michelle K Lupton, Petra Proitsi, John Powell, John S K
Kauwe, Michelangelo Mancuso, Ubaldo Bonuccelli, James
Uphill, Elizabeth Fisher, Carlo Masullo, Hilkka Soininen,
Gina Bisceglio, Li Ma, Dennis W Dickson, Neill R Graff-
Radford, Minerva M Carrasquillo, Steven G Younkin, San-
dro Sorbi, Makrina Daniilidou, Angela Hodges, Daniela
Galimberti, Elio Scarpini, Martin Scherer, Oliver Peters,
Alfredo Ramirez, Markus Leber, Sabrina Pichler, Manuel
Mayhaus, Wei Gu, Matthias Riemenschneider, Jens Wilt-
fang, Reinhard Heun, Heike Kölsch, Johannes Kornhuber,
Isabella Heuser, Dan Rujescu, Annette M Hartmann, Ina
Giegling, Michael Hüll, Simon Lovestone, Carlos Cruchaga,
John Morris, Kevin Mayo, Thomas Feulner, Rebecca Sus-
sams, Clive Holmes, David Mann, Stuart Pickering-Brown,
Nigel M Hooper, Andrew McQuillin, Gill Livingston,
Nicholas J Bass, Maria Vronskaya, Taniesha Morgan,
Nicola Denning, Thomas D Cushion, Lesley Jones, Rachel
Marshall, Alun Meggy, Georgina Menzies, Detelina Gro-
zeva, Michael C O'Donovan, Michael J Owen, Peter A
Holmans, Francesca Salani, Giancarlo Russo, Wolfgang
Maier, Frank Jessen, H-Erich Wichmann, Kevin Morgan,
Alison M Goate, Bruno Vellas, Emma Vardy, Susanne
Moebus, Karl-Heinz Jöckel, Martin Dichgans, Norman
Klopp, James Turton, Jenny Lord, Kristelle Brown,
Christopher Medway, Markus M Nöthen, Per Hoffmann,
Antonio Daniele, Anthony Bayer, John Gallacher, Hendrik
van den Bussche, Carol Brayne, Steffi Riedel-Heller, John F
Powell, Ammar Al-Chalabi, Christopher E Shaw, Iwona
Kloszewska, Pau Pastor, Monica Diez-Fairen, Aoibhinn
Lynch, Brian Lawlor, Michael Gill, Eliecer Coto, Victoria
Alvarez, Andrew B Singleton, John Collinge, Simon Mead,
Natalie Ryan, Benedetta Nacmias, Sara Ortega-Cubero,
Eloy Rodriguez-Rodriguez, Pascual Sanchez-Juan, Jacob
Shofany, Nerisa Banaj, Valentina Ciullo, Eleonora Sacchi-
nelli, Robert Clarke, A David Smith, Donald Warden, Yoav
Ben-Shlomo, Chiara Cupidi, Raffaele Giovanni Maletta,
Amalia Cecilia Bruni, Maura Gallo, Denise Harold, Roberta
Cecchetti, Patrizia Mecocci, Virginia Boccardi, Nick War-
ner, Gordon Wilcock, Panagiotis Deloukas, Rhian Gwil-
liam, Chris Corcoran, JoAnn Tschanz, Ron Munger.
## Author Contribution

GL, RS, and MS involved in data analysis, drafting the manuscript, or part of it. AF involved in data analysis. PB, GS, and NF involved in critical review of the manuscript. JW, JH, and VE-P involved in conception and design of the study, drafting and critical review of the manuscript.

## Conflicts of Interest

JH-grants from Cytox, outside the submitted work; JW-patent for diagnostics on some SNPs identified as associated with AD; VE-P – personal fees from Consultancy, outside the submitted work. GL, RS, MS, AF, PB, GS, and NF have nothing to report.

## References

1. Sloane PD, Zimmerman S, Suchindran C, et al. The Public Health Impact of Alzheimer's Disease, 2000-2050: potential Implication of Treatment Advances [Internet]. Annu Rev Public Health 2002;23:213-231.

2. Prince M, Wimo A, Guerchet M, et al. World Alzheimer Report 2015: the Global Impact of Dementia - An analysis of prevalence, incidence, cost and trends. Alzheimer's Dis Int 2015;84:425.

3. Gatz M, Reynolds CA, Fratiglioni L, et al. Role of genes and environments for explaining Alzheimer disease. Arch Gen Psychiatry 2006;63:168-174.

4. Farrer LA, Cupples LA, Haines JL, et al. Effects of age, sex, and ethnicity on the association between apolipoprotein E Genotype and Alzheimer Disease: a Meta-analysis. JAMA J Am Med Assoc 1997;278:1349-1356.

5. Corder EH, Saunders AM, Strittmatter WJ, et al. Gene Dose of Apolipoprotein-E Type-4 Allele and the Risk of Alzheimers-Disease in Late-Onset Families. Science 1993;261:921-923.

6. Lambert JC, Ibrahim-Verbaas CA, Harold D, et al. Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease. Nat Genet 2013;45:1452-1458.

7. Jones L, Lambert JC, Wang LS, et al. Convergent genetic and expression data implicate immunity in Alzheimer's disease. Alzheimer's Dement 2015;11:658-671.

8. Escott-Price V, Sims R, Bannister C, et al. Common polygenic variation enhances risk prediction for Alzheimer's disease. Brain 2015;138:3673-3684.

9. Escott-Price V, Myers AJ, Huentelman M, Hardy J. Polygenic risk score analysis of pathologically confirmed Alzheimer disease. Ann Neurol 2017;82:311-314.

10. Desikan RS, Fan CC, Wang Y, et al. Genetic assessment of age-associated Alzheimer disease risk: development and

validation of a polygenic hazard score. PLoS Med 2017;14: e1002289.

11. Cox DR. Regression models and life tables. J R Stat Soc Ser B 1972;34:187-220.

12. Ingram DD, Kleinman JC. Empirical comparisons of proportional hazards and logistic regression models. Stat Med 1989;8:525-538.

13. Staley JR, Jones E, Kaptoge S, et al. A comparison of Cox and logistic regression for use in genome-wide association studies of cohort and case-cohort design. Eur J Hum Genet 2017;25:854-862.

14. Moriguchi S, Hayashi Y, Nose Y, et al. A comparison of the logistic regression and the Cox proportional hazard models in retrospective studies on the prognosis of patients with gastric cancer. J Surg Oncol 1993;52:9-13.

15. Hashemian AH, Garhasbi M, Pourhoseingholi MA, Eskandari S. A comparative study of cox regression vs. log-logistic regression (with and without its frailty) in estimating survival time of patients with colorectal cancer. J Med Biomed Sci. 2017; 6:35-43.

16. Annesi I, Moreau T, Lellouch J. Efficiency of the logistic regression and Cox proportional hazards models in longitudinal studies. Stat Med 1989;8:1515-1521.

17. Moghimi-Dehkordi B, Safaee A, Tabei SZ. A comparison between Cox proportional hazard models and logistic regression on prognostic factors in gastric cancer. East Afr J Public Health 2009;6(Suppl 1):20-22.

18. Tan CH, Desikan RS. Interpreting Alzheimer disease polygenic scores. Ann Neurol 2018;83:443-445.

19. Purcell SM, Wray NR, Stone JL, et al. Common polygenic variation contributes to risk of schizophrenia and bipolar disorder. Nature 2009;40(AuGuST):8192.

20. Harold D, Abraham R, Hollingworth P, et al. Genome-wide association study identifies variants at CLU and PICALM associated with Alzheimer's disease. Nat Genet 2009;41:1088-1093.

21. McCarthy S, Das S, Kretzschmar W, et al. A reference panel of 64,976 haplotypes for genotype imputation [Internet]. 2015. Available from: http://biorxiv.org/content/ early/2015/12/23/035170 abstract

22. Tan CH, Fan CC, Mormino EC, et al. Polygenic hazard score: an enrichment marker for Alzheimer's associated amyloid and tau deposition. Acta Neuropathol 2018;135:85-93.

## Supporting Information

Additional supporting information may be found online in the Supporting Information section at the end of the article.

**Table S1.** Sample size and descriptive statistics for the GERAD dataset. Legend.

**File S1.** GERAD authorship list.
## Author Contribution

GL, RS, and MS involved in data analysis, drafting the manuscript, or part of it. AF involved in data analysis. PB, GS, and NF involved in critical review of the manuscript. JW, JH, and VE-P involved in conception and design of the study, drafting and critical review of the manuscript.

## Conflicts of Interest

JH-grants from Cytox, outside the submitted work; JW-patent for diagnostics on some SNPs identified as associated with AD; VE-P – personal fees from Consultancy, outside the submitted work. GL, RS, MS, AF, PB, GS, and NF have nothing to report.

## References

1. Sloane PD, Zimmerman S, Suchindran C, et al. The Public Health Impact of Alzheimer's Disease, 2000-2050: potential Implication of Treatment Advances [Internet]. Annu Rev Public Health 2002;23:213-231.

2. Prince M, Wimo A, Guerchet M, et al. World Alzheimer Report 2015: the Global Impact of Dementia - An analysis of prevalence, incidence, cost and trends. Alzheimer's Dis Int 2015;84:425.

3. Gatz M, Reynolds CA, Fratiglioni L, et al. Role of genes and environments for explaining Alzheimer disease. Arch Gen Psychiatry 2006;63:168-174.

4. Farrer LA, Cupples LA, Haines JL, et al. Effects of age, sex, and ethnicity on the association between apolipoprotein E Genotype and Alzheimer Disease: a Meta-analysis. JAMA J Am Med Assoc 1997;278:1349-1356.

5. Corder EH, Saunders AM, Strittmatter WJ, et al. Gene Dose of Apolipoprotein-E Type-4 Allele and the Risk of Alzheimers-Disease in Late-Onset Families. Science 1993;261:921-923.

6. Lambert JC, Ibrahim-Verbaas CA, Harold D, et al. Meta-analysis of 74,046 individuals identifies 11 new susceptibility loci for Alzheimer's disease. Nat Genet 2013;45:1452-1458.

7. Jones L, Lambert JC, Wang LS, et al. Convergent genetic and expression data implicate immunity in Alzheimer's disease. Alzheimer's Dement 2015;11:658-671.

8. Escott-Price V, Sims R, Bannister C, et al. Common polygenic variation enhances risk prediction for Alzheimer's disease. Brain 2015;138:3673-3684.

9. Escott-Price V, Myers AJ, Huentelman M, Hardy J. Polygenic risk score analysis of pathologically confirmed Alzheimer disease. Ann Neurol 2017;82:311-314.

10. Desikan RS, Fan CC, Wang Y, et al. Genetic assessment of age-associated Alzheimer disease risk: development and

validation of a polygenic hazard score. PLoS Med 2017;14: e1002289.

11. Cox DR. Regression models and life tables. J R Stat Soc Ser B 1972;34:187-220.

12. Ingram DD, Kleinman JC. Empirical comparisons of proportional hazards and logistic regression models. Stat Med 1989;8:525-538.

13. Staley JR, Jones E, Kaptoge S, et al. A comparison of Cox and logistic regression for use in genome-wide association studies of cohort and case-cohort design. Eur J Hum Genet 2017;25:854-862.

14. Moriguchi S, Hayashi Y, Nose Y, et al. A comparison of the logistic regression and the Cox proportional hazard models in retrospective studies on the prognosis of patients with gastric cancer. J Surg Oncol 1993;52:9-13.

15. Hashemian AH, Garhasbi M, Pourhoseingholi MA, Eskandari S. A comparative study of cox regression vs. log-logistic regression (with and without its frailty) in estimating survival time of patients with colorectal cancer. J Med Biomed Sci. 2017; 6:35-43.

16. Annesi I, Moreau T, Lellouch J. Efficiency of the logistic regression and Cox proportional hazards models in longitudinal studies. Stat Med 1989;8:1515-1521.

17. Moghimi-Dehkordi B, Safaee A, Tabei SZ. A comparison between Cox proportional hazard models and logistic regression on prognostic factors in gastric cancer. East Afr J Public Health 2009;6(Suppl 1):20-22.

18. Tan CH, Desikan RS. Interpreting Alzheimer disease polygenic scores. Ann Neurol 2018;83:443-445.

19. Purcell SM, Wray NR, Stone JL, et al. Common polygenic variation contributes to risk of schizophrenia and bipolar disorder. Nature 2009;40(AuGuST):8192.

20. Harold D, Abraham R, Hollingworth P, et al. Genome-wide association study identifies variants at CLU and PICALM associated with Alzheimer's disease. Nat Genet 2009;41:1088-1093.

21. McCarthy S, Das S, Kretzschmar W, et al. A reference panel of 64,976 haplotypes for genotype imputation [Internet]. 2015. Available from: http://biorxiv.org/content/ early/2015/12/23/035170 abstract

22. Tan CH, Fan CC, Mormino EC, et al. Polygenic hazard score: an enrichment marker for Alzheimer's associated amyloid and tau deposition. Acta Neuropathol 2018;135:85-93.

## Supporting Information

Additional supporting information may be found online in the Supporting Information section at the end of the article.

**Table S1.** Sample size and descriptive statistics for the GERAD dataset. Legend.

**File S1.** GERAD authorship list.