Age-dependent topic modelling of comorbidities in UK Biobank identifies disease subtypes with differential genetic risk

doi:10.21203/rs.3.pex-2370/v1

Method Article

Age-dependent topic modelling of comorbidities in UK Biobank identifies disease subtypes with differential genetic risk

https://doi.org/10.21203/rs.3.pex-2370/v1

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Age-dependent topic modelling (ATM) is a method for inferring comorbidity profiles for individuals at Biobank Scale. Details of the Method is available in the paper Age-dependent topic modelling of comorbidities in UK Biobank identifies disease subtypes with differential genetic risk.

ATM assigns to each individual topic weights for several disease topics; each disease topic reflects a set of diseases that tend to co-occur as a function of age, quantified by age-dependent topic loadings for each disease. The model assumes that for each disease diagnosis, a topic is sampled based on the individual’s topic weights (which sum to 1 across topics, for a given individual), and a disease is sampled based on the individual’s age and the age-dependent topic loadings (which sum to 1 across diseases, for a given topic at a given age). The model generalises the latent dirichlet allocation (LDA) model by allowing topic loadings for each topic to vary with age.

The ATM model is implemented as an R package, which is available for download at https://github.com/Xilin-Jiang/ATM/tree/main. We provide example simulated data so that users could easily test before formatting their data.

The main steps involve using the ATM model; a detailed documentary of ATM software is available at https://github.com/Xilin-Jiang/ATM/tree/main.

1. Inferring comorbidity patterns:

Download ATM software following the "Installation" section of https://github.com/Xilin-Jiang/ATM/tree/main.

Following the code example in "Inferring disease topics using diagnosis data". Change the `HES_age_example` using your data.

2. Extract the topic weights.

Topic weights are used for excess PRS analysis, SNP x Topic interaction analysis. You could extract topic weights for each individual from the ATM inference results from previous step. Following the code in section "Inferring comorbidity profiles for individuals" of https://github.com/Xilin-Jiang/ATM/tree/main.

3. Extract diagnosis-specific topic probability.

Diagnosis-specific topic probability is used for excess genetic correlation analysis and F_ST analysis. As an individual has multiple distinct diseases, ATM allows weights for each diagnosis, which is a posterior probability based on the topic weight of the individual and the specific disease. Following the code in section "Inferring comorbidity profiles for individuals" of https://github.com/Xilin-Jiang/ATM/tree/main.

4. Mapping different disease codes.

For mapping between SNOMED and ICD-10 codes, we use mapping downloaded from https://www.nlm.nih.gov/research/umls/mapping_projects/snomedct_to_icd10cm.html and mapping between ICD-10 to Phecodes are downloaded from https://phewascatalog.org/phecodes. We implemented code maps as functions in the ATM software.

5. Genetic analysis of comorbidity subtypes.

We define disease subtypes using topic weights of each patient and diagnosis-specific topic probabilities of each disease diagnosis.

For excess PRS analysis, we use BOLT-LMM 2.3 to compute predictive PRS (five fold cross validation) and perform association between PRS and topic weights.

For genetic correlation analysis, we define discrete disease subtypes based on the largest value of diagnosis-specific topic probabilities. For example, if the model learns 10 comorbidity topics, each diagnosis-specific topic probabilities will be a vector of 10, and each diagnosis is assigned to one of the subtypes based on this value. We then compute three types of genetic correlations: (1) subtype-subtype, (2) subtype-disease, (3) and disease-disease. Here disease means all cases without being assigned to a subtype. We compute excess genetic correlation by comparing the first two types of genetic correlation (subtype-subtype and subtype-disease) to disease-disease genetic correlation.

For excess FST analysis, we first compute observed F_ST estimates (between two subtypes of the same disease, defined the same way as above). We then compute expected null F_ST distribution based on sampling healthy individuals with matched topic weights (i.e. F_ST estimates between two sets of healthy controls with topic weight distributions matched to the respective disease subtypes). We reported the permutation P-values for the 52 diseases with discrete subtypes.

For SNP x topic interactions analysis, we test the interaction between topic weights for each patient and GWAS SNPs (SNPs that reached genome-wide significance in an association analysis, using PLINK 1.9), using diseases as the response variable.

For details of the implementation, refer to the Full Methods section of Supplementary Note of our Associated Nature Genetics publication.

1. Decide the model structure of ATM.

ATM has two model structure parameters to be set. Number of topics: how many distinct topics are needed to capture the comorbidity profile in the data? Degree of freedom of topic profiles: how smooth do we want the disease risk curve to be?

Number of topics could be decided using Evidence Lower Bound (ELBO); simply run the model with different topic numbers (an input of the ATM wrapper function `wrapper_ATM`) and compare the output of the function `multiple_run_ELBO_compare`. Alternatively, you could use cross validation and prediction odds ratio, which is described in details of the section "Inferring disease topics using diagnosis data" on the https://github.com/Xilin-Jiang/ATM page.

Degree of freedom of topic profiles: this is the parameter that controls how smooth the disease risk curve is. We have tested different numbers of degrees of freedom and decided the default number is flexible enough to capture the curve shape while maintaining computational efficiency. We recommend using the default setting unless specifically needing smooth or flexible age curves; in that case, refer to the Full Methods section of the Supplementary Note of the paper for details.

2. Convergence checking of the ATM model.

For large EHR data sets, ATM might not converge easily. By default the ATM is run for 5 times and the best model with the highest evidence lower bound (ELBO) at convergence will be kept. The variational inference should increase ELBOs at each update, but due to the numeric approximation of the inference method, numeric decrease might be observed in certain cases.

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