1. Latent variable models for time-to-event data A joint presentation by Katherine Masyn & Klaus Larsen UCLA PSMG Meeting, 2/13/2002

2. PSMG, 2/13/022 Overview 1) Introduction to survival data 2) Discrete-time survival mixture analysis (Katherine) 3) Latent variable models for (continuous) time-to-event data (Klaus) 4) Extensions

3. PSMG, 2/13/023 Time-to-event Data A record of when events occur (relative to some beginning) for a sample of individuals For example, time from sero-conversion to death in HIV/AIDS patients, age of first alcohol use in school-aged children, time to heroine use following completion of methadone treatment

4. PSMG, 2/13/024 Methods for this type of data must consider an important feature, known as censoring: The event is not observed for all subjects Methods must also handle covariates that may change with time, e.g., CD4 count Data: Time (interval) of event or censoring, indicator for whether or not the event occurred, and relevant covariates

5. PSMG, 2/13/025 Discrete vs. Continuous Time Continuous: The exact time of an event (or censoring) for each subject is known, e.g., time of death Discrete: The time of an event (or censoring) for each subject is only recorded for an interval of time, e.g., grade of school drop out

6. PSMG, 2/13/026

7. Discrete-Time Survival Mixture Analysis (DTSMA) Katherine Masyn, UCLA Based on the work of Muthén and Masyn (2001) and Masyn (2002) Research supported under grants from NIAAA, NIMH, NIDA, and in collaboration with Bill Fals-Stewart at the Research Institute for Addictions at SUNY-Buffalo

8. PSMG, 2/13/028 Let T be the time interval in which the event occurs: T = 1, 2, 3,... S(t), called the survival probability, is defined as the probability of surviving beyond time interval t, i.e., the probability that the event occurs after interval t: S(t) = P(T > t) h(t), called the hazard probability, is defined as the probability of the event occurring in the time interval t, provided it has not occurred prior to t: h(t) = P(T = t | T t)

9. PSMG, 2/13/029 Hazard Probability Plot Survival Probability Plot

10. PSMG, 2/13/0210 DTSMA with Covariates C u1u1 u2u2 uJuJ... Z x1x1 x2x2 xJxJ

11. PSMG, 2/13/0211 Recidivism Intervention

12. PSMG, 2/13/0212 GGMM + DTSMA U M+1 U M+2 U M+3 U M+J... C z Y1Y1 Y2Y2 Y3Y3 YMYM is

13. PSMG, 2/13/0213 Aggression and School Removal

14. PSMG, 2/13/0214 Drinking and Work Absence