1. Comparisons of Modeling Methods on Longitudinal and Survival Data: Identifying Use of Repeat Biomarker Measurements to Predict Time-to-Event Outcome in Cancer Research
Meng Ru, MS
Erin Moshier, MS
Vernon Wu, MD
Ajai Chari, MD
Madhu Mazumdar, PhD
Icahn School of Medicine at Mount Sinai
Tisch Cancer Institute
July 30, 2018

2. Time-to-Event Outcome:
MOTIVATION
Disease: Smoldering Multiple Myeloma (SMM)
Data: Biomarkers (Hemoglobin, etc) measured longitudinally during monitoring window) Progression
Objective:
Modeling Methods
Longitudinal Data:
Biomarker Levels
Link
Time-to-Event Outcome:
Progression
This project was inspired by a clinical collaborative study with the multiple myeloma group at Mount Sinai. As a cancer biostatistician, we are constantly reminded by our collaborators of the importance of biomarkers. It’s everywhere and it tells so much not only about patients’ current stage but also the likelihood of a future event which might help clinical decision making. Our study here was designed to identify longitudinal profiles of various biomarkers, collected from smoldering multiple myeloma patients, that were associated with an increased risk of progression to active myeloma.. We hope to find out the patients with early time to progression who may benefit more from early interventional therapies. There are several modeling available to associate longitudinal profiles and time to event outcomes.
of The retrospective study recently published in Blood Advances sets out to identify longitudinal profiles, of various biomarkers collected during routine monitoring of smoldering multiple myeloma patients (such as hemoglobin, free light chain ratios, bone marrow plasma cells and m-protein), that were associated with an increased risk of progression to active myeloma. The clinical importance of this research question is that patients with biomarker profiles associated with early time to progression may benefit from early interventional therapies. Historically, many risk prediction models only accounted for the biomarker levels at diagnosis, but current research in many cancer disease groups including multiple myeloma, lymphoma and prostate cancer have focused on not only the static value of the biomarker at a particular point in time but the rate of change or trajectory of the biomarker over time which can be clinically important.
The purpose of this project is to review and compare the various methods available for associating longitudinal biomarker profiles and time to event outcomes.
Prediction

3. Longitudinal Analysis
METHODS
Longitudinal Analysis
Link
Survival Analysis
Time-dependent Cox Model (TDCM):
TDCM with time-varying covariate
Mixed Model(MM):
Joint Model (JMM) vs. Two-Stage Approach (TSMM)
Longitudinal: Mixed model on (current value/current value + current slope)
Survival: Piecewise PH model (JMM); TDCM (TSMM)
Latent Class Model (LCM):
Joint Model (JLCM) vs. Two-Stage Approach (TSLCM)
Longitudinal: Latent class model (JLCM); Group-based trajectory model (TSLCM)
Survival: Piecewise PH model (JLCM); Cox PH (TSLCM)
The go-to method for many statisticians is the time-dependent cox model with the repeated measures of biomarker entered as a time-varying covariate, however this method does not specify a particular model for the longitudinal profile component of the data.
Two more sophisticated methods in the literature now are the joint and two stage modeling approaches. As the names suggest the joint model simultaneously models the longitudinal and survival components of the data while the two stage approach separately models the longitudinal and survival components of the data in two different stages.
Both longitudinal and survival components can be specified with different submodels. the longitudinal submodel is usually estimated with either a mixed or latent class model. Latent class modeling is not currently as popular as mixed modeling, it assumes the biomarker profile is better described by multiple distinct trajectories rather than the single trajectory assumed by a mixed model. We do find that it has a much more clinically meaningful interpretation in many settings and lends itself well to risk stratification studies.
We applied all methods to our dataset, which we will share in more detail in our poster, and compared the estimates obtained.
When using a mixed model you assume that the biomarker profile can be appropriately described with a single trajectory whereas a latent class model assumes that the biomarker profile is better described by multiple distinct trajectories. Latent class modeling is not currently as popular as mixed modeling, however we do find that it has a much more clinically meaningful interpretation in many settings and lends itself well to risk stratification studies. With the mixed model method you can use various specifications of the longitudinal profile (current value, current slope, cumulative slope, etc.) to test for association each with answering a different research question.
The joint modeling approach is the gold standard however the two-stage approach remains popular due to its convenience to implement and interpret.

4. RESULTS TDCM vs. Joint Model/ Two-stage:
TDCM produced larger estimates of HRs and SEs than Joint Model and Two-stage approaches for current value specification.
Joint Model vs. Two-stage:
Two-stage yielded smaller estimates of HRs and SEs than Joint Model with both MM and LCM approaches. (simulation: Sweeting et. al (2011))
*Forest plot of HR in Poster.
We found that the time dependent cox tends to produce larger estimates of the hazard ratio than joint and two-stage modeling approaches using mixed modeling to estimate the longitudinal component. The two-stage approach produced smaller and more conservative estimates of the hazard ratio than the joint modeling approach with both mixed models and latent class analysis methods used to model the longitudinal profile. This finding also corresponds to another simulation study by Sweeting et al.
We present all hazard ratios from all methods in forest plot in our poster.
The time dependent cox model can only be compared to the current value specification of the longitudinal profile estimated with the mixed modeling approach; it’s not comparable to results from latent class modeling of the longitudinal profile.

5. RECOMMENDATIONS A* C,A A S D Scenarios TDCM JM TS JMM JLCM TSMM TSLCM
Events concurrent to (C) or after (A) longitudinal exposure window A*
C,A A
Single (S) or Distinct (D) trajectory best captures longitudinal process S D
To summarize, we describe some scenarios where the methods discussed may be most suitable.
If the outcome event can only occur after the longitudinal exposure window, then all methods are appropriate to varying degrees of accuracy of estimates and assuming if missingness in the longitudinal measures is not a problem for time dependent cox. However, if the outcome event can occur concurrent to the longitudinal exposure window then time dependent cox and two-stage approach (without landmark). With either the joint or two stage approaches we recommend using the latent class model for the longitudinal component if your research goal is to identify heterogeneous risk groups.
One thing that should be noted is that our example here is a cancer study, but the application for joint models is not limited to cancer research, people in the field of chronic disease, psychology and social science.
with larger estimates of the association likely with the two stage approach and TDCM only appropriate.
One thing that should be noted is that our example here is a cancer study, but the application for joint models is not limited to cancer research, people in the field of chronic disease, psychology and social science have been using this method for quite a while to do research like, using maternal depression symptoms during pregnancy and the first 12 months postpartum to predict children’s behaviors like hyperactivity/inattention and physical aggression at a young age.

6. THANKS, QUESTIONS? Poster Number #9 Session #215942
Time: 7/30/2018 2:00 PM – 2:45 PM
Location: Vancouver Convention Centre, West Hall B.
Presenter Contact Info:
Meng Ru, MS