Integrative analysis of multiple types of genomic data using an accelerated failure time frailty model

Abstract

As the high throughput technologies rapidly develop, multiple types of genomic data become available within and across different studies. It has become a challenging task in modern statistical research to use all types of genomic data to infer some disease-prone genetic information. In this work, we propose an integrative analysis of multiple and different types of genomic data, clinical covariates and survival data under a framework of an accelerated failure time with frailty model. The proposed integrative approach aims to answer some aspects of the complex problem in genomic data analysis by finding relevant genomic features and inferring patients’ survival time using identified features. The proposed integrative approach is developed using a weighted least-squares with a sparse group LASSO penalty as the objective function to simultaneously estimate and select the relevant features. Extensive simulation studies are conducted to assess the performance of the proposed method with two types of genomic data, DNA methylation data and copy number variation data, on 600 genes and three clinical covariates. The simulation results show promises of the proposed method. The proposed method is applied to the analysis of the Cancer Genome Atlas data on Glioblastoma, a lethal brain cancer, and biologically interpretable results are obtained.

Appendix1: Brief summary of the further data processing procedure

The datasets were further processed as follows.

From the methylation data, one can get a probe file, which gives the information for the used probes, including the “probe id”, “gene names”, “chrom”, “chromStart”, “chromEnd” and “strand”.

First, we deleted the probes that are not associated with genes.

In the second step, we grouped the probes according to genes. If one group had more then one gene names, we chose the gene name that was the same as the above group as the representative if one of these gene names was the same as the above group, or just chose one gene name as the representative if there is not any gene name that was the same as the above group; then deleted the remaining if they were the same as the below gene group, or reserved the remaining if they were different from the below gene group and added them into the bottom of the original probe file as new groups.

In the third step, we matched the genes in the probe file with those in the CNV data file, resulting in 288984 probes annotated to 18191 common genes.

For the CNV data with the common genes, matching the samples with those in the original clinical data file, we obtained the final used CNV data file with $p_2=18191$ genes and $n_2=519$ samples: ${\varvec{X}}^{2}_{n_2 \times p_2}$ (the 2-nd genome data).

For the methylation data, deleting the “NA”s in the file, matching the probes in the methylation file with those in the well-handled probe file, and then matching the samples with those in the original clinical dataset, resulted in a data set of $p_1=288984$ probes and $n_1=95$ samples to be used as ${\varvec{X}}^{1}_{n_1\times p_1}$ (the 1-st genome data).

For the clinical covariates to be analyzed with the methylation data, for patient $i (i=1,\ldots , n_1)$, define $Z^{1}_{i1}$ as the age at procedure (mean=61.54, max=85.6, min=23.4) , $Z^{1}_{i2}$ as the gender indicator to be equal to 1 if the patient is female and 0 otherwise (40 females, 55 males), $Z^{1}_{i3}$ to be equal to 1 if the IDH1 status is “WT”, 2 if the IDH1 status is “R132G”, 3 if the IDH1 status is “R132H” and 4 otherwise (86 “WT”, 1 “R132G”, 4 “R132H”, 4 others), $Z^{1}_{i4}$ to be equal to 1 if therapy class is “TMZ Chemoradiation, TMZ Chemo”, 2 if the therapy class is “Nonstandard Radiation”, 3 if the therapy class is “Nonstandard Radiation, TMZ Chemo”, 4 if the therapy class is “Standard Radiation, TMZ Chemo”, 5 if the therapy class is “Standard Radiation”, 6 if the therapy class is “Standard Radiation, Alkylating Chemo”, 7 if the therapy class is “Unspecified Therapy”, 8 if the therapy class is “Unspecified Radiation”, 9 if the therapy class is “Alkylating Chemo”, 10 if the therapy class is “TMZ Chemo” (the number of samples are 42, 4, 11, 14, 4, 1, 6, 11, 1, 1, respectively).

The observed failure time and failure time indicator for the final matching samples can be obtained from the clinical data set along with the methylation. Define $Y^1_{i}$ as the observed failure time in days (min = 24, max = 1788) and $\delta ^1_i$ as the event indicator, which is equal to 1 for death and 0 for censoring (the censoring rate is $57\%$). For the clinical covariates to be analyzed with the CNV data, for patient $j (j=1,\ldots , n_2)$, $Z^2_{j1}, Z^2_{j2}, Z^2_{j3}, Z^2_{j4}, Y^2_j$ and $\delta ^2_j$ are defined in the same way as the above.

The summary information for these covariates are as follows. The mean of $Z^2_{1}$ is equal to 58.25, maximum 89.30 and minimum 10.90. There are 202 females and 317 males for $Z^2_{2}$. The IDH1 status of 375 samples is “WT”, that of 1 sample is “R132G”, that of 26 samples is “R132H”, and that of 116 is “others”. The number of samples for the 10 different therapy class are 209, 29, 19, 85, 54, 28, 13, 58, 7, 4 respectively. The minimum and maximum value for $Y^2$ is equal to 3 and 3881, and the censoring rate is $53\%$ for this clinical data.