1. An introduction to Survival analysis and Applications to Predicting Recidivism Rebecca S. Frazier, PhD JBS International

2. Introduction to Survival Analysis
Time-to-event analysis
Allows researchers to investigate the effect of several variables on the time it takes an event to occur and on the probability of that event occurring at any point in time:
Time to death
Time to recovery
Time to recidivism (or relapse)
Or time to any other binary outcome!
Accounts for multiple covariates
Accounts for varying start dates (rolling enrollment)
Accounts for varying observation windows (censoring)
Survival Analysis is a method for researchers to investigate the effect of several variables on the time that it takes for an event to occur
Hazard ratio = Outcome measure of the ratio of:
Hazard for Treatment/ Hazard for Comparison
Hazard = Instantaneous event rate = Probability that an individual at time t has an event at that time (assuming event-free survival to time t)
HR = 1 (event rates are the same in both arms)
HR = 2 (at any time twice as many patients in the treatment group are having an event proportionally to the comparison group)
HR = 0.5 (at any time half as many patients in the treatment group are having an event proportionally to the comparison group)
Can predict not only whether or not an event will occur, but the probability that the event will occur at a particular point in time
Accounts for the fact that individuals may be entering the program at different points in time and the probability of an event occurring increases as time goes on
The model predicts the probability of having a referral based on the number of days since the participant entered the program or became eligible for treatment
The most common methods for survival analysis are life tables, kaplan meier, and cox regression. Life tables are a descriptive procedure for examining the distribution of time to event variables and to compare the distribution by levels of a factor variables. Life tables used with categorical data and subdivide the period of observation into smaller time intervals and then make probability calculations at the mid-point of each interval. Kaplan Meier is used with continuous variables and does calculations at every point of censoring or event occurrence. Cox regression is

3. An Example
Are families who participate in B&B less likely to have a subsequent substantiated child protective services referral than those who do not?

4. To determine this you want to control for individual differences at baseline…
41 years old + White B
29 years old + African American C
34 years old + White

5. What is the likelihood that each person will have an subsequent CPS referral at any point in time?
2010
2011 B
2013
2014 C
2011
2010
2011
2012
2013
2014
2015
2016

6. What is the likelihood that each person will have an subsequent CPS referral at any point in time?
2010
2011 B
2013
2014 C
2011

7. What is the likelihood that each person will have an subsequent referral in 2016?
2010
2011 B
2013
2014 C
2011
2010
2011
2012
2013
2014
2015
2016

8. What is the likelihood that each person will have an subsequent referral in 2016?
2010
2011 B
2013
2014 C
2011
Can predict not only whether or not an event will occur, but the probability that the event will occur at a particular point in time.

9. What are the odds that an event will occur at any given point in time for a treatment individual compared to a comparison person holding everything else constant? A B = ? A …
2010
2011 B
2010

10. Cox Proportional Hazards Regression
Describes how the risk of an event (in this case having a subsequent CPS referral) per time unit changes over time at baseline levels of covariates
Similar to logistic regression, but Cox regression assesses relationship between survival time and covariates
For example:
The risk of having a subsequent CPS referral at any given point in time based on:
Condition: Treatment vs. Comparison
Prior CPS history
Demographic characteristics
Semi-parametric method– Does not make assumptions about the shape of the hazard function, but does make assumptions about how covariates affect the hazard function
Other methods for SA include: non-parametric methods such as the Kaplan-Meier survival analysis which does not include any assumption about the shape of the hazard curve

11. Cox Proportional Hazards Regression
(Event Rate)
Cox regression predicts the risk of recidivism per unit in time (assuming that the event has not yet already occurred), given the baseline hazard rate (which is a function of the amount of time that has passed) and based on a set of covariates (which we are going to control for again in case there are any lingering differences)

12. Cox Proportional Hazards Regression
Recidivism rate at time t = The Baseline hazard of recidivism at time t (based on how many days the person has been in treatment or eligible for treatment) and that person’s values of each of the covariate variables (e.g.- treatment, age, race, etc.)

13. Hazard Ratios (Exp(β))
HR for Treatment
Hazard Ratio (HR) = exp(β) = the relative hazard (aka recidivism rate) corresponding to a unit change in the associated predictor
HRCategorical = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑛𝑜𝑛−𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡) 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛)
Hazard: The event of interest happening
Hazard rate: The instanteous probability of the event occurring at any point in time
Hazard ratio: The relative risk or Exp(B)
Hazard ratio: The odds that an individual in the treatment group will recidivate first– the odds that a treatment person will have a substantiated referral before a comparison person– the odds that the time to recidivism for the treatment person is less than for the comparison person
Probability of
HRContinuous = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒𝑜𝑛𝑒 𝑤𝑖𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 𝑎+1 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒𝑜𝑛𝑒 𝑤𝑖𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 𝑎

14. Raw Data
Subject Number
Days to Substantiated Referral (time)
Any substantiated referral? (status)
1 = Yes
0= Not yet, Censored
Condition 1= Treat
0 = Comp
White
1= White
0 = Other
Primary Lang English
0 = No
Age in (in years) 1
2000
32.5 2
201
21.3 3 21
50.3 4 56
42.1 5
1450 30 6
652
19.1
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B) (HR) se B
Treatment (versus comparison)
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02

15. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)*
Substantiated Referral
Independent Variable
Exp(B) (HR)
S.E.(b) B
Treatment (versus comparison)
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
*Treatment results are presented for individuals who received treatment services from AmeriCorps volunteers and the current results represent a subset of the full model which includes several additional covariates related to CPS referral history.

16. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B)
(HR) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
HRCategorical = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑛𝑜𝑛−𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡) 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛) =
HRTreatment = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=0.71 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=1
=0.71
**************Maybe cut?
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.

17. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B)
(HR) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02 =
HRTreatment = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=0.71 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛=1
=0.71
**************Maybe cut?
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
Assuming they have not yet had a referral, the odds of a treatment individual having a referral are 0.71 times that of a comparison individual.
Assuming they have not yet had a referral, the odds of a treatment individual having a referral are 29% less than (1-0.71) that of a comparison individual.

18. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B)
(HR) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
HRCategorical = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑛𝑜𝑛−𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡) 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛)
HRTreatment = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=0.71 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛=1 =
**************Maybe cut?
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
=0.71
HRComparison = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛=1 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=0.71 =
=1.41

19. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B)
(HR) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
HRCategorical = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑛𝑜𝑛−𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡) 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑔𝑟𝑜𝑢𝑝 (𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛) =
HRComparison = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛=1 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=0.71
=1.41
**************Maybe cut?
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
Assuming they have not yet had a referral, the odds of a comparison individual having a referral are 1.41 times higher than that of a treatment individual.

20. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B)
(HR) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02 =
HRComparison = 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑎𝑟𝑖𝑠𝑜𝑛=1 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 𝑓𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡=0.71
=1.41
**************Maybe cut?
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
Assuming they have not yet had a referral, the odds of a comparison individual having a referral are 1.41 times higher than that of a treatment individual.
Assuming they have not yet had a referral, the odds of a comparison individual having a referral are 41% greater (1.41-1) than that of a treatment individual.

21. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
There are several different ways to present these results in terms of the relative odds:
At any given point in time, assuming the individual has not yet recidivated:
Treatment individuals have 29% lower odds (1-0.71) of recidivism than comparison
Comparison individuals are 1.41 times more likely to recidivate
Comparison individuals have 41% higher odds (1.41-1) of recidivism than treatment
At any given point in time about 71% as many individuals in the treatment group are recidivating proportionally to the comparison group
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
You have to reach an agreement with your client about what kind of numbers you

22. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
Or the results can be presented in terms of probability:
The probability that a treatment person will recidivate before a comparison individual is 42% (0.71/1.71 = 0.415)
The probability that a comparison person will recidivate before a treatment individual is 58% (1.41/2.41 = 0.585)
There is a 16% greater probability (58-42) that comparison individuals will recidivate first than that treatment individuals will recidivate first
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
You have to reach an agreement with your client about what kind of numbers you

23. Substantiated Referral
Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
O.R. se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
Exp(B) = 1.37 so the odds of a white participant having a referral are 1.37 times higher than the odds for non-whites.
If an OR is 1 that means that the odds are equally likely.
= .37, so the odds of a white participant having a referral are 37% greater than the odds for non-whites.
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.
SAY something about how we’re not goingto interpret the non-significant ones.

24. Substantiated Referral
Table 9 | Cox Regression for Hazard of Recidivism as a Function of Treatment (N=1,478)
Substantiated Referral
Independent Variable
Exp(B) se B
Treatment
0.71
0.15
-0.34 *
Demographics
Person was White (versus nonwhite)
1.37
0.14
0.31
Person's primary language was English (versus any other)
1.09
0.25
0.08
Age in 2015
1.02
0.02
There are several different ways to present these results:
White individuals were 1.37 times more likely to recidivate than non-white individuals
White individuals had 37% higher odds of recidivism than non-white individuals
There were 137 white individuals who would have recidivated at any time point for every 100 non-white individuals who would have recidivated
If Exp(B) < 1 then an increase in one unit for that particular variable will decrease the probability of experiencing an event throughout the observation period. By inverting this value (1/Exp(B)) you can calculate the “Protective effect” or the extent to which being in the treatment condition decreases the probability of having a referral compared to being in the comparison condition.

25. Predicted Substantiated Referral Rate at Time X
Uses hazard curves to predict the likelihood of an event at a given point in time controlling for all relevant covariates…
Predicted Substantiated Referral Rate at Time X
This shows the estimated degree to which people over time you would have higher degrees. This curve shows the cumulative hazard rate

26. Predicted Substantiated Referral Rate at Time X
You can also use hazard curves to predict the likelihood of an event at a given point in time… Y1 Y2 Y3 Y4
Predicted Substantiated Referral Rate at Time X
Given that the event has not yet occurred…
The function of a cumulative hazard curve net of the covariates.

27. Predicted Substantiated Referral Rate at Time X
Uses hazard curves to predict the likelihood of an event at a given point in time…
Predicted Substantiated Referral Rate at Time X

28. Strengths of Survival Analysis
Allows you to predict the likelihood of dichotomous outcomes over time
Accounts for covariates and time-varying covariates
Controls for the length of time people have been in the study or the program
Includes individuals with very different start dates and durations in a single model
Accounts for censoring (varying observation windows)

29. Limitations of Survival Analysis
Requires certain statistical assumptions:
Can only be used with independent observations where each person is only included once and with binary outcomes
Assumes non-informative (random) censoring–
No systematic differences between censored and uncensored cases (i.e.- censored cases should have the same survival prospects as uncensored ones)
Assumes survival curves with proportional hazards–
Hazard functions for two different levels of a covariate must be proportional over time (survival prospects remain constant and covariates don’t interact with time)
Example: If men have twice the risk of heart attack compared to women at age 50, they also have twice the risk of heart attack at age 60, or any other age
Non-informative (random) censoring:
Those censored at time ti should be representative of all subjects still alive at ti (with the same covariate values).
At any particular point in time there should be no systematic differences between censored and uncensored cases– men should be more likely to have a censored case than women.
Two people with identical covariate values should be equally likely to be censored vs. not at a particular point in time.
Non-informative (random) censoring: Individuals lost to follow-up or those that have yet to experience the event should have the same risk of experiencing the event as those that actually did
Proportional hazards: All individuals must have an equal probability of experiencing the event of study over the period of observation. As an example, consider a research study that recruits smokers without asking the number of years each person has been smoking. The probability of developing health problems for a new smoker vs. a long time smoker are markedly different depending on the time interval observed. In this case, the decision to observe a specific period impacts the analysis.

30. Limitations of Survival Analysis
Requires certain statistical assumptions (see handout)
Can be difficult to explain to lay audiences and audiences who are used to seeing mean differences and may want simple effect sizes
Need to provide descriptive information as well to contextualize results, here are some hypothetical examples:
Example 1: Recidivism rates at certain time points
About half the people who participated in treatment recidivated within 500 days, and 80% recidivated within 800 days. Meanwhile, about 50% of the people who did not participate in treatment recidivated within 200 days and 80% recidivated within 700 days.
Example 2: Median recidivism time ratio
Median recidivism date for treatment: 500 days
Median recidivism date for comparison: 250 days
Ratio = 500/250 = 0.50
Non-informative (random) censoring:
Those censored at time ti should be representative of all subjects still alive at ti (with the same covariate values).
At any particular point in time there should be no systematic differences between censored and uncensored cases– men should be more likely to have a censored case than women.
Two people with identical covariate values should be equally likely to be censored vs. not at a particular point in time.
Non-informative (random) censoring: Individuals lost to follow-up or those that have yet to experience the event should have the same risk of experiencing the event as those that actually did
Proportional hazards: All individuals must have an equal probability of experiencing the event of study over the period of observation. As an example, consider a research study that recruits smokers without asking the number of years each person has been smoking. The probability of developing health problems for a new smoker vs. a long time smoker are markedly different depending on the time interval observed. In this case, the decision to observe a specific period impacts the analysis.

31. Conclusions
SA can be an effective tool for evaluators to account for complex data and covariates and to predict time to an event
SA has wide applicability to contexts such as:
Health– predicting death, disease, healing time, etc.
Criminal justice– predicting crime, recidivism, etc.
Education- predicting graduation, college enrollment, dropout, course completion
Social services – time in foster care, time to employment, length of sobriety
Nonprofits – Predicting length of program services, dropout, recovery, other positive program outcomes

32. Thank you!
Questions?
Additional resources including step by step instructions for conducting a survival analysis in SPSS with test data and syntax will be available
on the AEA website, or you can