Fig 1.
The framework of the MTL-Cox model.
(A) The inner circle shows the main sites of the nine chronic diseases, and the outer circle demonstrates factors that affect chronic diseases in the UK Biobank data, which is detailed in the Materials Section. The figure is created with Biorender. (B) The flow of the MTL-Cox model construction and optimization, which detailed in the Model Section; (C) Concordance index, AUC, specificity, sensitivity, and Youden index are used to evaluate models, which detailed in the Experiments and results Section; (D) Applying the MTL-Cox model for chronic diseases personalized prediction, which detailed in the Experiments and results Section.
Table 1.
Notations of symbols that used in this paper.
Fig 2.
Examples of the static and dynamic cohort survival times.
The static cohorts have a unified starting time; Subjects in dynamic cohorts with sequential enrolling time. For the notation of denotes the i-th specific subject.
Fig 3.
An illustration demonstrating the censoring definition.
Fig 4.
Strategies of parameter sharing in the multitask learning framework.
(A) Hard parameter-sharing mechanism transfers the parameter training representations from hidden layers across all tasks. (B) The soft parameter sharing mechanism shares penalized information between tasks by regularization.
Fig 5.
The censored statistics of the nine chronic diseases.
The definitions of censored and uncensored are presented in the section Preliminaries.
Fig 6.
The selected features of nine chronic diseases.
The color of orange represents the selected features of the corresponding disease; other features are represented in the color of blue.
Table 2.
A summary description of 36 chronic diseases related selected features.
Fig 7.
An example of calculating the number of comparable pairs for the C-index (y1 ≼ y2 ≼ y3 ≼ y4 ≼ y5).
≼ based on the timeline. Black circles denote uncensored observations, and gray circles indicate censored observations.
Fig 8.
Performances of MTL-Cox and competing methods were evaluated using C-index and AUC.
Notes: ‘#’ stands for the word “cancer”, which facilitates the layout of the x-axis labels. ‘*’ denotes p < 0.05, ‘**’ denotes p < 0.01, and ‘***’ denotes p < 0.001.
Fig 9.
Performances of MTL-Cox and competing methods were evaluated using Youden index and Sensitivity.
Notes: ‘#’ stands for the word “cancer”, which facilitates the layout of the x-axis labels. ‘*’ denotes p < 0.05, ‘**’ denotes p < 0.01, and ‘***’ denotes p < 0.001.
Fig 10.
Performances of MTL-Cox and competing methods were evaluated using Specificity.
Notes: ‘#’ stands for the word “cancer”, which facilitates the layout of the x-axis labels. ‘.’ denotes p > 0.05, ‘*’ denotes p < 0.05, ‘**’ denotes p < 0.01, and ‘***’ denotes p < 0.001.
Fig 11.
Personalized absolute risk ranking of nine chronic diseases in the fifth year.
pi denotes the i–th subjects.
Fig 12.
(A) Illustration of Absolute and Basis Risk for a Population: The red line in the figure on the left represents the average basis risk for coronary heart disease (CHD), while the green line in the figure on the left represents the average basis risk for lung cancer. The subject’s absolute risk for CHD is approximately 10.0%, and their absolute risk for lung cancer is 2.5%. (B) Personalized Risk Level Prediction Example: In the third year, AR1 represents the subject’s absolute risk of lung cancer, while AR0 is the basis average risk of lung cancer in the same year. The excess absolute risk is denoted by EAR, and the relative absolute risk is RAR.
Fig 13.
Low-risk, average-risk, and high-risk levels for lung cancer, gastric cancer, and esophagus cancer across four age groups (40∼49, 50∼59, 60∼69, and ≥70).
The horizontal axis denotes the timeline in years, while the vertical axis represents the risk value measured in percentage. The area below the blue line indicates low risk, the area between the blue and green lines denotes average risk, and the area above the green line signifies high risk. Comprehensive outcomes are provided in Supplementary file S3 Table.
Fig 14.
Low-risk, average-risk, and high-risk levels for colorectal cancer, liver cancer, and hypertension across four age groups (40∼49, 50∼59, 60∼69, and ≥70).
The horizontal axis denotes the timeline in years, while the vertical axis represents the risk value measured in percentage. The area below the blue line indicates low risk, the area between the blue and green lines denotes average risk, and the area above the green line signifies high risk. Comprehensive outcomes are provided in Supplementary file S3 Table.
Fig 15.
Low-risk, average-risk, and high-risk levels for diabetes, stroke, and coronary heart disease (CHD) across four age groups (40∼49, 50∼59, 60∼69, and ≥70).
The horizontal axis denotes the timeline in years, while the vertical axis represents the risk value measured in percentage. The area below the blue line indicates low risk, the area between the blue and green lines denotes average risk, and the area above the green line signifies high risk. Comprehensive outcomes are provided in Supplementary file S3 Table.