1. NEMO English Seminar
Dynamic predictions using flexible joint models of longitudinal and time-to-event data
Jessica Barrett
University of Cambridge, U.K.
Li Su
University of Cambridge Robinson Way, U.K.
Statistics in Medicine, 36(9): , 2017.
Speaker JUNGJU PARK
Date 18th July 2018

2. Introduction Key words Limited traditional predictive modeling
Joint model for longitudinal and time-to-event data
Predictions of patient prognosis (e.g., patient survival)
Biomarker information
Limited traditional predictive modeling
Simple linear model
Static prediction
Contribution
Including time-dependent random effects with non-stationary covariance structure
Individualized dynamic predictions

3. Example (HIV Epidemiology Research Study, HERS)

4. Few equations 𝜇 𝑖 𝑡 = 𝐱 𝑖 𝑡 T 𝜶+ 𝑚 𝑖 𝑡 Functions Base model
Patient 𝑖, time 𝑡
𝜇 𝑖 𝑡 is the mean function of process 𝑌 𝑖 𝑡
𝐱 𝑖 𝑡 is the vector of covariates
𝑚 𝑖 𝑡 is the true underlying time trajectory
Base model
To estimate the coefficients of 𝜶
𝜇 𝑖 𝑡 = 𝐱 𝑖 𝑡 T 𝜶+ 𝑚 𝑖 𝑡
Handling error with P-splines
𝑚 𝑖 𝑡 = 𝑙=0 𝑀 𝛽 𝑙 + 𝑏 𝑖𝑙 𝐵 𝑙 𝑡

5. 𝜆 𝑖𝑟 =1−Φ 𝐱 𝑖𝑟 T 𝜶 + 𝜸 𝑟 𝑇 𝐖 𝑖𝑟 𝐛 𝑖
Some details
Survival sub-model (discrete hazard rate)
𝜆 𝑖𝑟 =1−Φ 𝐱 𝑖𝑟 T 𝜶 + 𝜸 𝑟 𝑇 𝐖 𝑖𝑟 𝐛 𝑖
Maximum penalized likelihood estimation
Dynamic predictions of survival probabilities

6. Result

7. NEMO English Seminar
Deep multi-task gaussian processes for survival analysis with competing risks
Ahmed M. Alla
University of California, Los Anageles
Mihaela van de Schaar
University of Oxford
31st Conference on Neural Information Processing Systems (NIPS 2017)

8. Introduction Key words Difficulties in real world Contributions
Competing Risks
Deep multi-task Gaussian Processes (DMGP)
Difficulties in real world
Patients with comorbidities (renal disease and diabetes)
Contributions
Survival analysis with competing risks (or diseases)
Patient-specific and cause-specific incident model

9. How to handle the competing risks
Key assumption: The earliest event is observable.
Data set 𝐷= 𝐗 𝑖 , 𝑇 𝑖 , 𝑘 𝑖 𝑖=1 𝑛
𝐗 𝑖 , vector of covariates
𝑇 𝑖 , time until an event occur
𝑘 𝑖 , type of event

10. Results Definition of cause-specific concordance index (C-index)
Performance comparisons