Personalized screening intervals for biomarkers using joint models for longitudinal and survival data Dimitris Rizopoulos, Jeremy Taylor, Joost van Rosmalen, Ewout Steyerberg, Hanneke Takkenberg Department of Biostatistics, Erasmus University Medical Center, the Netherlands [email protected]Joint Statistical Meetings August 1st, 2016, Chicago, USA
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Personalized screening intervals for biomarkers using ... · Dimitris Rizopoulos, Jeremy Taylor, Joost van Rosmalen, Ewout Steyerberg, Hanneke Takkenberg Department of Biostatistics,
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Personalized screening intervals for biomarkers using jointmodels for longitudinal and survival data
Dimitris Rizopoulos, Jeremy Taylor, Joost van Rosmalen, Ewout Steyerberg,Hanneke Takkenberg
Department of Biostatistics, Erasmus University Medical Center, the Netherlands
* zi(t) and bi: Random-effects part, bi ∼ N (0, D)
JSM – August 1st, 2016, Chicago 8/30
2.1 Joint Modeling Framework (cont’d)
• The two processes are associated ⇒ define a model for their joint distribution
• Joint Models for such joint distributions are of the following form(Tsiatis & Davidian, Stat. Sinica, 2004; Rizopoulos, CRC Press, 2012)
p(yi, Ti, δi) =
∫p(yi | bi)
{h(Ti | bi)δi S(Ti | bi)
}p(bi) dbi
where
◃ bi a vector of random effects that explains the interdependencies
◃ p(·) density function; S(·) survival function
JSM – August 1st, 2016, Chicago 9/30
2.2 Estimation
• Joint models can be estimated with either Maximum Likelihood or Bayesianapproaches (i.e., MCMC)
• Here we follow the Bayesian approach because it facilitates computations for our laterdevelopments. . .
JSM – August 1st, 2016, Chicago 10/30
3.1 Prediction Survival – Definitions
• We are interested in predicting survival probabilities for a new patient j that hasprovided a set of aortic gradient measurements up to a specific time point t
• Example: We consider Patients 20 and 81 from the Aortic Valve dataset
JSM – August 1st, 2016, Chicago 11/30
3.1 Prediction Survival – Definitions (cont’d)
Follow−up Time (years)
Aor
tic G
radi
ent (
mm
Hg)
0
2
4
6
8
10
0 5 10
Patient 200 5 10
Patient 81
JSM – August 1st, 2016, Chicago 12/30
3.1 Prediction Survival – Definitions (cont’d)
Follow−up Time (years)
Aor
tic G
radi
ent (
mm
Hg)
0
2
4
6
8
10
2 4 6 8 10 12
Patient 202 4 6 8 10 12
Patient 81
JSM – August 1st, 2016, Chicago 12/30
3.1 Prediction Survival – Definitions (cont’d)
Follow−up Time (years)
Aor
tic G
radi
ent (
mm
Hg)
0
2
4
6
8
10
2 4 6 8 10 12
Patient 202 4 6 8 10 12
Patient 81
JSM – August 1st, 2016, Chicago 12/30
3.1 Prediction Survival – Definitions (cont’d)
• What do we know for these patients?
◃ a series of aortic gradient measurements
◃ patient are event-free up to the last measurement
• Dynamic Prediction survival probabilities are dynamically updated as additionallongitudinal information is recorded
JSM – August 1st, 2016, Chicago 13/30
3.1 Prediction Survival – Definitions (cont’d)
• Available info: A new subject j with longitudinal measurements up to t