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Quantitative Research Using Survival Analysis CBC Final Report, 6/18/01 Section III 1 Section III Survival Analysis: A Quantitative Examination of Children’s Placement Episodes Sarasota and Manatee CBC Programs
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Page 1: Section III Survival Analysis: A Quantitative Examination ... · Quantitative Research Using Survival Analysis CBC Final Report, 6/18/01 Section III 4 Section III: Survival Analysis

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Section IIISurvival Analysis:

A Quantitative Examination of Children’sPlacement Episodes

Sarasota and Manatee CBC Programs

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METHODOLOGY ........................................................................................................... 4

DATA PREPARATION ........................................................................................................ 4SURVIVAL ANALYSES ...................................................................................................... 4

Life Table Method Survival Function Sarasota—Overall .......................................... 7Life Table Method Hazard Function Sarasota—Overall ........................................... 8Life Table Method Survival Function Sarasota—Male and Ethnicity........................ 9Life Table Method Survival Function Sarasota—Female and Ethnicity .................. 10Life Table Method Survival Function Sarasota—Ethnicity ...................................... 11Life Table Method Hazard Function Sarasota—Gender.......................................... 12Life Table Method Hazard Function Sarasota—Ethnicity ....................................... 13Life Table Method Sarasota—Summary Table......................................................... 14Cox Regression Survival Function Sarasota ............................................................ 15Cox Regression Survival Function Sarasota—Permanency Goals .......................... 17

Discussion ............................................................................................................. 18Cox Regression Survival Function Sarasota—Adoption versus all others............... 19

Discussion ............................................................................................................. 19Cox Regression Survival Function Sarasota—Long Term Foster and Relative

Care versus MSF and Reunification ..................................................................... 20Discussion ............................................................................................................. 21

Cox Regression Survival Function Sarasota—Adoption versus LTRC,Reunification, and MSF ............................................................................................ 22

Discussion ............................................................................................................. 23Life Table Method Survival Function Manatee-- Overall ........................................ 25Life Table Method Hazard Function Manatee-- Overall.......................................... 26Life Table Method Survival Function Manatee—Males and Ethnicity .................... 27

Discussion ............................................................................................................. 27Life Table Method Survival Function Manatee—Female and Ethnicity .................. 28

Discussion ............................................................................................................. 28Life Table Method Survival Function Manatee-- Ethnicity ...................................... 29

Discussion ............................................................................................................. 29Life Table Method Hazard Function Manatee-- Ethnicity ....................................... 30

Discussion ............................................................................................................. 30Life Table Method Survival Function Manatee-- Gender......................................... 31

Discussion ............................................................................................................. 31Life Table Method Hazard Function Manatee-- Gender.......................................... 32

Discussion ............................................................................................................. 32Life Table Method Manatee—Summary Table ......................................................... 33Cox Regression Overall Manatee ............................................................................. 34

Discussion ............................................................................................................. 35Cox Regression Survival Function Manatee—Permanency Goals .......................... 36

Discussion ............................................................................................................. 37

Table of Contents and List of Figures

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Cox Regression Survival Function Manatee—Adoption vs. All others .................... 38Discussion ............................................................................................................. 39

Cox Regression Survival Function Manatee—LTFC & LTRC vs. MSF andReunification ......................................................................................................... 40Discussion ............................................................................................................. 41

Cox Regression Survival Function Manatee—Adoption vs. Kinship/Family Pres... 42Discussion ............................................................................................................. 43Limitations ............................................................................................................ 43

OVERALL....................................................................................................................... 43

REFERENCES................................................................................................................ 44

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Section III: Survival Analysis - A Quantitative Examination of Children'sPlacement Episodes

Methodology

Data Preparation

For both the Manatee and Sarasota program databases, the data were manipulatedto create a single file for each client. The data that were included on the unique clientidentifier included all of the placement dates that the child had experienced, date of birthof the child, gender, ethnicity, and initial permanency goal. From this raw data,placement episodes were calculated by subtracting the child’s last ending date inplacement from the child’s earliest placement date. The earliest placement date in theManatee database was 6/1/1999, and for Sarasota it was 4/12/1993. To control for thiswide variability, any case that was outside of 3 standard deviations from the mean wereremoved from the analysis. This also controlled for some data that were enteredincorrectly in the database (i.e., a placement dates of 3/1/1969 and 11/14/2020). Thisresulted in entry cohorts that were similar to the inception time of the community basedcare projects in their respective districts (Sarasota and Manatee).

The age of the child was calculated by subtracting the child’s date of birth fromthe child’s earliest recorded entry in an out-of-home placement setting. Gender wasbrought directly into the current dataset from each of the program datasets. Ethnicity wascreated by combining Hispanic, African American, Asian, and Other into Minority, andfor analytical purposed was coded as 0; for clients who were White, they werecategorized as Majority, and were coded as 1.

Survival Analyses

Survival analysis or Event History Analysis was chosen as it is the preferredmethod in the social sciences for analyzing time dependent data (Allison, 1995; Raftery,2001). Survival or event history analysis is used to examine qualitative changes inevents, from one event to the next. Survival analysis is also useful as it allows for thetesting of theoretical models, that seek to explain and/or predict the dependent variable oftime. Optimally, in creating these models, a wide range of independent variables wouldbe available to help explain the differences in the timing of particular events. Survivalanalysis also controls for the occurrence of censoring; when an event has happenedbefore the study began or a particular case has not experienced the event by the time thestudy or data collection period has ended. For the current data, the event is defined asplacement episode. The database does not include any child cases for which the eventcould have happened prior to the data collection beginning (also known as leftcensoring), however “right censoring” did occur where some children were still in theplacement and were therefore not included in the model.

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To conduct survival analyses, there are multiple methods by which to do this:Kaplan-Meier estimators, life tables, Cox regression, competing risk models, to onlyname a few (Allison, 1995). Life Tables and Cox regression were chosen for the currentanalyses. The Life Table Method was chosen as it allows you to group the data intogroups of times. For the current dataset, the times were calculated as months, and foreach month the survival function1 and hazard function2 were calculated. The hazardfunction “quantifies the instantaneous risk that an event will occur at exactly time t”(Allison, 1995; p. 15).

The survivor function is “the probability of surviving beyond t…Because S is aprobability, we know that it is bounded by 0 and 1. And because T cannot be negative weknow that S (0)=1. Finally as t gets larger, S never increases (and usually decreases)”(Allison, 1995, p. 15). The graphs that were chosen to display the results were theCumulative Survival Estimate and Hazard Function (Y axis) by the number of Monthsthe Child was in the Out of Home Placement (X axis). The Cumulative SurvivalEstimate provides markers as to the percentage of children who “survive” to themaximum amount of time calculated for the entire sample. While the term is “survive”,it is actually counterintuitive in this situation, as the optimal goal is to have children exitout of home care in the quickest amount of time. So “surviving” the longest is actually anegative outcome. It is also possible to graphically depict the median time figure, bylooking at the .50 (50%) percentile by the number of months where the line crosses thispercentile. The Life Table Method was chosen also because of its ability to show thehow different subgroups on the time dependent variable. For these analyses, thesubgroups were Gender and Ethnicity. Graphs are presented for each of these and anoverall graph for the entire group is also provided.

The hazard function provides an estimation of an individuals risk of the eventoccurring (in this instance, the risk of the child leaving out of home care). The hazardfunction has a dimensional quality that allows you to estimate a rate or the number ofevents per interval of time (however time is defined) (Allison, 1995).

The Cox Regression Models were also used to analyze the data. The CoxRegression Model was chosen for two reasons: 1) it is possible to enter covariates intothe model to determine the effect independent variables have on the time dependentvariable (the results are similar to what is provided in logistic regression and multipleregression) and 2) the Cox method “does not require that you choose some particularprobability distribution to represent survival times…and is considerably more robust”(Allison, 1995, p. 112). On another note, the Cox regression is based on proportionalhazard models, which was appropriate with these datasets.

1 Survival function is S(t)=Pr{T>t}=1-F(t)

2 Hazard Function is ( )t

tTttTtth t

∆≤∆+<≤

= →∆}Pr{

0lim

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Sarasota

Life Table MethodCox Regression

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Survival Analysis--Life Table MethodSurvival FunctionSarasota-- Overall

Survival Function--Sarasota

Overall

Life Table Method

n=357

Out of Home Placement Time in Months

60483624120

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

The median survival time for all Sarasota cases in the dataset is 8.31 months. Themedian can be seen above at the point in which the line graph crosses the Y-axis or theCumulative Survival Curve at .50. The median is quite consistent with the Adoption andSafe Families Act outcome of Permanency and the achievement of Permanency within a12-month time frame. Based on this data, the Sarasota program has successfullyachieved this outcome.

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Survival Analysis--Life Table MethodHazard Function

Sarasota—Overall

Hazard Function

Sarasota

Out of Home Placement Time in Months

403020100

Haz

ard

.4

.3

.2

.1

0.0

The Hazard Function provides a more descriptive picture of a child’s risk ofmoving out of a home placement. As is evident above, within the first 10 months, thehazard function varies between approximately .18 and .05. This indicates the changingsurvival rates for each group in regards to when the children will exit out of care. Whatis most notable, is as the number of months increase, so does the hazard rate.Specifically, around the 30 month, the child’s rate of exit out of care is about .35, thusindicating that children who are in an out of home placement for this extended period oftime are substantially likely to exit out of care at significant rates.

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Survival Analysis—Life Table MethodSurvival Function

Sarasota—Male and Ethnicity

Survival Function--Sarasota

GENDER = Male

Life Table Method

n=175

Out of Home Placement Time in Months

60483624120

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

ETHNICITY

majority

minority

Based on this graph, among males in out of home placements, the graphdemonstrates that male children who are minorities are more likely to stay in out-of-homeplacements longer than their majority (white) counterparts. The Cumulative Survivalpoint at .50, indicates the median length of time in care. As is evident in the graph, thereis considerable differences between the points in which the two lines cross the .50 mark.White males exit out of care significantly earlier than do the minorities.

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Survival Analysis--Life Table MethodSurvival Function

Sarasota—Female and Ethnicity

Survival Function--Sarasota

GENDER = Female

Life Table Method

n=181

Out of Home Placement Time in Months

60483624120

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

ETHNICITY

majority

minority

The differences between females who are minorities or majority (white) is morecomplicated to explain. As is evident above that the two lines cross, two times, indicatingchanges overtime in the likelihood that the children will exit out of care. The differencein out of home placement time for these 4 groups is more similar than the males, howeveras you can see in the above graph, white (majority) females exit out of care a little earlier.

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Survival Analysis--Life Table MethodSurvival Function

Sarasota—Ethnicity

Survival Function

Sarasota

Life Table Method

n=357

Out of Home Placement Time in Months

6050403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

ETHNICITY

majority

minority

When only ethnicity is examined in relation to the time to exit out of care, againthere is some difference, especially when the survival estimate goes below .50. Thiswould indicate that as was seen in the earlier graphs, those children in the majoritycategory usually exit out of care at a quicker rate than minority children.

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Survival Analysis--Life Table MethodHazard Function

Sarasota—Gender

Hazard Function

Sarasota

Out of Home Placement in Months

403020100

Haz

ard

.6

.5

.4

.3

.2

.1

0.0

GENDER

Female

Male

The hazard rate for these two groups is quite difficult to interpret as there isconsiderable crossing of the lines throughout the entire period. As with the hazard rateoverall, towards the 25 month and beyond, the rate of exit out of care is significantlyincreased. On another note, however, the parallel nature of the hazard rates indicates thatthe two lines are somewhat proportional to each other, which ensures that the analyticalmodels that have been used with this data meet the basic assumptions.

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Survival Analysis--Life Table MethodHazard Function

Sarasota—Ethnicity

Hazard Function

Sarasota

Out of Home Placement Time in Months

403020100

Haz

ard

.7

.6

.5

.4

.3

.2

.1

0.0

ETHNICITY

majority

minority

This graph illustrates that ethnicity does play a role in the rate at which childrenexit out of home care. Initially (from 1 to 18 months), the majority group demonstrates ahigher hazard rate/risk of leaving out of home placement as compared to the minoritygroup. As can be seen around 22 months and after 30 months, minority children have anincreased hazard rate of exiting out of care. To interpret this, the following example isprovided. At the 32 month, among 100 minority children who are still in care will exit ata rate of .68 (given that everything else remains constant). For this particular month inthe data, eight children were exposed to the risk of exiting care (a positive outcome), andof these eight children, four left care that month. Thus indicating a significant level ofrisk for the children to leave care. In sum, as time increases, the risk of leaving careincreases as well, which is inline with what is expected theoretically.

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Survival Analysis--Life Table MethodSarasota—Summary Table

Group Median Time in Out-of-Home PlacementMinority Males (n=65) 12.5 monthsMajority Males (n=110) 7.3 monthsMinority Females (n=64) 9.0 monthsMajority Females (n=117) 7.6 monthsMinority (n=130) 11.0 monthsMajority (n=227) 7. 5 monthsPermanency GoalsAdoption (n=55) 19.3 monthsIndependent Living (n=18) 20.5 monthsLTFC (n=20) 27.0 monthsLTRC (n=23) 11.8 monthsMSF (n=76) 4.8 monthsReunification (n=163) 5.4 months

Overall (n=357) 8.3 months

This summary table provides the different median times for children to be in outof home care based on the categories provided on the left. Minority males stay in care forthe longest periods of time, whereas majority males stay in the shortest. For females,ethnicity has less of an influence. When the genders are combined it is evident thatminorities stay in out of home care for the longest (11.0 months) compared to themajority’s stay in out of home care of 7.5 months. With these numbers broken out, theissue becomes clearer and points to recommendations to be made in regards to creatingstrategies to assist children who are minorities to exit from out of home care at a quickerrate. On a positive note, most of these amounts are within the time frame specified in theAdoption and Safe Families Act of 1997. In regards to the different goals established forchildren, there is considerable difference in the amount of time a child spends in out ofhome care as it relates to the child’s initial permanency goal. Children who are in longterm foster care have the longest placement episodes, which is understandable, yetunfortunate for these children. Children who have adoption as their goal on averagespend 19.3 months in foster care, which falls within the 24-month time frame on freeingchildren for adoption. On a more positive note, the time children who have reunificationas their goal have a median time of 5.4 months.

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Survival Analysis—Cox RegressionSurvival Function

Sarasota

Survival Function at mean of covariates

Sarasota

Cox Regression

n=355

Out of Home Placement Time in Months

9080706050403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

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Variable BetaStandard

Error Wald Significance Exp(B) MeanAge -.036 .011 11.331 .001 .964 6.482Gender(1=female)

.168 .113 2.211 .137 1.183 .637

Ethnicity(1=majority)

.040 108 137 .711 1.041 .510

The only statistically significant indicator was age, which had an inverserelationship with time in out of home placement (β=-.036). While this was significant, itwas not however a large effect.

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Survival Analysis—Cox RegressionSurvival Function

Sarasota—Permanency Goals

Survival Function for Goals

Sarasota

Out of Home Placement Time in Months

9080706050403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

PERM GOAL

Reunification

Maintain Safe Family

Long Term Relative C

Long Term Foster Car

Independent living

Adoption

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.002 .012 .024 .876 .998Gender (1=female) .002 .109 .000 .982 1.002Ethnicity(1=majority)

.254 .117 4.673 .031 1.289

Goals 62.137 .000Independent Living -.291 .294 .978 .323 .747LTFC -.410 .283 2.103 .147 .664LTRC .720 .254 8.042 .005 2.055MSF 1.059 .183 33.41 .000 2.884Reunification .845 .160 27.862 .000 2.327Adoption is the Reference Category and =0

Discussion

The table above provides the findings that support the graph. Each of thecategories are compared to the reference category of Adoption, which was coded as 0.As was demonstrated in the graph, Maintain and Support Family had the shortest lengthsof stay (1.059) and Long Term Foster Care had the longest length of stay (-.410). In thismodel ethnicity was significant and contributed and those in the majority category had adecreased length of stay.

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Survival Analysis—Cox RegressionSurvival Function

Sarasota—Adoption versus all others

Survival Function for patterns

Adoption versus others

Sarasota

Out of Home Placement Time in Months

9080706050403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL

adoption

il,ltfc,ltrc,msf,reu

Variable Beta Standard Error Wald Significance Exp(B)Age -.045 .011 17.289 .000 .956Gender(1=female)

.008 .108 .006 .941 .992

Ethnicity(1=majority)

.145 .113 1.632 .201 1.156

Adoption=1 .690 .150 21.179 .000 1.993

Discussion

Adoption resulted in an increase in time over all of the other types of permanencygoals. In this model, age resulted in a decrease length of time in out of home placement.

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Survival Analysis—Cox RegressionSurvival Function

Sarasota—Long Term Foster and Relative Care versusMSF and Reunification

Survival Function for patterns

LTFC and LTRC versus MSF and Reunification

Sarasota

Out of Home Placement Time in Months

9080706050403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL3

ltfc,ltrc

msf and reunif

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.001 .013 2.833 .920 .999Gender(1=female)

.080 .122 .430 .512 1.083

Ethnicity(1=majority)

.215 .128 2.833 .092 1.240

LTFC,LTRC=1 .723 .187 14.924 .000 2.060

Discussion

Long Term Foster Care and Long Term Relative Care as permanency goals resultin an increase in time over the Maintain and Support Family and Reunification.

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Survival Analysis—Cox RegressionSurvival Function

Sarasota—Adoption versus LTRC, Reunification, and MSF

Survival Function for patterns

Adoption versus Kinship and Family Pres.

Sarasota

Out of Home Placement in Months

6050403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL4

adoption

ltrc,reuni,msf

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.006 .013 .247 .619 .994Gender(1=female)

.086 .114 .569 .451 1.090

Ethnicity(1=majority)

.303 .120 6.388 .011 1.354

Adoption .896 .155 33.510 .000 2.449

Discussion

The Adoption permanency goal increases time over the child’s permanency goalof long term relative care (LTRC), Reunification with the family, and maintain andsupport the family.

Each of these models demonstrated that the placement time was indeed associatedwith the permanency goal that was originally set for the child. However, each of thesemodels demonstrate that there is room for improvement, now that the time has beendefined for each group, strategies can be developed to assist with lowering these times sothat they may be more inline with the permanency expectations in the Adoption and SafeFamilies Act.

As has been stated elsewhere, it is unfortunate that additional explanatoryvariables have not been captured in the two datasets. These additional variables mightinclude, for example, maltreatment type, chronicity in the child welfare system, servicesprovided, and risks present could provide a more detailed description of what influencesout of home placement time.

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Manatee

Life Table MethodCox Regression

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Survival Analysis--Life Table MethodSurvival FunctionManatee-- Overall

Survival Function

Manatee

Life Table Method

n=412

Out of Home Placement Time in Months

20100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

The Survival Function for all of Manatee demonstrates a consistent step downover time. The median survival time for all children is 6.6 months. The remaininggraphs demonstrate the differences between groups based on demographics and for thechild’s permanency goal.

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Survival Analysis--Life Table MethodHazard Function

Manatee-- Overall

Hazard Function

Manatee

Out of Home Placement Time in Months

20100

Haz

ard

2.5

2.0

1.5

1.0

.5

0.0

The hazard functions above, demonstrates that past the 10 month point, the risk ofexiting out of home care increases dramatically, which is a positive sign. From 0-10months the hazard is fairly consistent, with a steady number of children leaving out ofhome care.

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Survival Analysis--Life Table MethodSurvival Function

Manatee—Males and Ethnicity

Survival Function- Manatee

GENDER = male

Life Table Method

n=193

Out of Home Placement Time in Months

403020100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

ETHNICITY

majority

minority

Discussion

Ethnicity is less of an influence than what was seen in Sarasota. Based on thegraph above, each group changes over time as to their exit from out of home care.

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Survival Analysis--Life Table MethodSurvival Function

Manatee—Female and Ethnicity

Survival Function-Manatee

GENDER= female

Life Table Method

n=207

Out-of-home Placement Time in Months

403020100

Cum

ulta

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

ETHNICITY

majority

minority

Discussion

When gender is broken out and female majority and minority is compared, thereis more of a discrepancy between the two. As can be seen, females that are in themajority exit out of care sooner throughout the extent of placement time. Only initiallyare the two groups similar.

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Survival Analysis--Life Table MethodSurvival Function

Manatee-- Ethnicity

Survival Function

Manatee

Life Tables Method

n=412

Out of Home Placement Time in Months

20100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

ETHNICITY

majority

minority

Discussion

Initially, the two groups start out very similarly, however around the median time(.50), the majority group starts to exit out of care sooner. However after about 10months, the two groups become equivalent.

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Survival Analysis--Life Table MethodHazard Function

Manatee-- Ethnicity

Hazard Function

Manatee

Out of Home Placement Time in Months

20100

Haz

ard

2.5

2.0

1.5

1.0

.5

0.0

ETHNICITY

majority

minority

Discussion

The Hazard Functions demonstrate that each group’s risk of exit from out ofhome care is fairly constant up to the 10 month mark. After 10 months the level of riskof exiting out of home care increases significantly, as is to be expected.

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Survival Analysis--Life Table MethodSurvival FunctionManatee-- Gender

Survival Function

Manatee

Out of Home Placement Time in Months

3020100

Cum

ulat

ive

Sur

viva

l

1.2

1.1

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GENDER

female

male

Discussion

The pattern represented above also provides a complicated picture. Initially malesexit placement earlier than females. At the 60th percentile females exit care earlier,however these trends continue to constantly change with females being in care slightlylonger than males.

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Survival Analysis--Life Table MethodHazard Function

Manatee-- Gender

Hazard Function

Manatee

Out of Home Placement Time in Months

20100

Haz

ard

2.5

2.0

1.5

1.0

.5

0.0

GENDER

female

male

Discussion

The hazard functions are very similar, proportionate and little difference existsbetween these two groups.

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Survival Analysis--Life Table MethodManatee—Summary Table

The following chart provides findings on each group (ethnicity:minority/majority; gender: male/female) median length of stay in out of home care. Thisis presented in number of months and was calculated using the life tables method.

Group Median Time in Out-of-Home PlacementMinority Males (n=61) 7.1 monthsMajority Males (n=132) 6.8 monthsMinority Females (n=82) 8.1 monthsMajority Females (n=125) 5.9 monthsMinority (n=150) 7.4 monthsMajority (n=262) 6.2 monthsPermanency GoalAdoption (n=49) 11.75 monthsLong Term Foster Care (n=35) 12.12 monthsLong Term Relative Care(n=41)

6.50 months

Maintain and Support Family(n=118)

5.20 months

Reunification (n=158) 4.0 monthsOverall (n=412) 6.6 months

Based on these calculations, females who are considered minorities have thelongest median time in out-of-home placement (8.14); whereas females who are in themajority culture, have the shortest length of stay (5.92 months). For the males, there wasa small difference between the majority and minority group, however this difference wasmuch smaller than that for the females. In regards to permanency goal, Long TermFoster Care had the longest length of stay (12.12 months) followed by those withAdoption (11.75) as the permanency goal. The shortest length of stay was reunification(4.0 months), which was surprising, given that those with Maintain and Support Familyas a goal had longer out of home placement times (5.20 months).

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Survival Analysis-- Cox RegressionOverall

Manatee3

Survival Function at mean of covariates

Manatee

Cox Regression

n=390

Out-of-Home Placement Time in Months

24181260

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

3 Three cases were removed as their time exceeded 200 months and also exceeded 3standard deviations from the mean.

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Variable BetaStandard

Error Wald Significance Exp(B) MeanAge -.054 .011 25.268 .000 .948 8.240Gender(1=female)

.097 .102 .900 .343 1.102 .633

Ethnicity(1=majority)

.128 .107 1.408 .235 1.136 .518

Discussion

Only age was statistically significant in influencing out-of-home placement time;specifically, as age increases the amount of time in out of home placement timedecreased. The R2 for the model of age, ethnicity, and gender was only 7%, indicatingthat additional variables, not measured or captured in the database could additionallycontribute to the explanation of time spent in out-of-home placements. The Exp(B) isanalogous to a log odds ratio. Allison writes the “Risk Ratio, is just eβ. For indicator(dummy) variables with values of 1 and 0, you can interpret the risk ratio as the ratio ofthe estimated hazard for those with a value of 1 to the estimated hazard for those with avalue of 0 (controlling for other covariates)” (Allison, 1995, p. 117). For these data, thehazard risk for age was 10% greater for those who are female and 13% risk for those whoare in the majority. Age, on the other hand has an inverse effect.

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Survival Analysis—Cox RegressionSurvival Function

Manatee—Permanency Goals

Survival Function for patterns

All permanency goals

Manatee

Out of Home Placement Time in Months

20100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL

Reunification

MSF

LTRC

LTFC

Adoption

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.031 .013 5.857 .016 .969Gender(1=female)

.148 .108 1.893 .169 1.160

Ethnicity(1=majority)

.009 .118 .006 .936 1.010

PermanencyGoal

86.365 .000

LTFC .405 .240 2.838 .092 1.500LTRC 1.204 .278 18.790 .000 3.334MSF 1.394 .190 53.580 .000 4.030Reunification 1.568 .190 68.245 .000 4.797Adoption as 0 is reference category

Discussion

In relation to the other categories, the children who had adoption as their initialgoal experienced the longest time in out of home placement. Adoption as the referencecategory provides the basis for which the others are measured. As the number increases,the less time the child spends in out of home Based on the table above, long term fostercare (LTFC) was the second longest predictor of time in placement as compared toadoption (.405), followed by long term relative care (LTRC) at 1.204. The children whoexperience the shortest period of time in out of home care are those with a reunification(1.568) goal and Maintain and Support Family (1.394) goal, as compared to those whohave a goal of Adoption.

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Survival Analysis—Cox RegressionSurvival Function

Manatee—Adoption vs. All others

Survival Function for patterns

Adoption vs. LTFC,LTRC,MSF, & Reunify

Manatee

Out of Home Placement Time

20100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL2

Adoption

LTFC,LTRC,MSF,Reunif

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.063 .012 29.152 .000 .939Gender(1=female)

.181 .107 2.848 .091 1.199

Ethnicity(1=majority)

.037 .113 .110 .740 1.038

LTFC, LTRC,MSF, &Reunify

-1.242 .173 51.522 .000 .289

Adoption Reference Category

Discussion

All of the other goals reduce the child’s length of time in out of home care (-1.242), as compared to those with adoption as the goal. Age was also a significantpredictor of change in out of home placement; as the child’s age increased, the amount oftime spent in out of home care is decreased.

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Survival Analysis—Cox RegressionSurvival Function

Manatee—LTFC & LTRC vs. MSF and Reunification

Survival Function for patterns

LTFC,LTRC vs. MSF Reunification

Out of Home Placement Time in Months

20100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL3

LTFC,LTRC

MSF & Reunification

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.044 .014 9.751 .002 .957Gender(1=female)

.167 .116 2.064 .151 1.181

Ethnicity(1=majority)

.010 .122 .007 .934 1.101

MSF &Reunify

-.738 .171 18.627 .000 .478

Discussion

Maintain and Support Family and Reunification goal significantly decrease theamount of time the child spends in out of home care (-.738) as compared to those withadoption. Age, again is a significant predictor, however has a minor influence onplacement time.

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Survival Analysis—Cox RegressionSurvival Function

Manatee—Adoption vs. Kinship/Family Pres.

Survival Function for patterns

Adoption vs. LTRC,MSF. Reunification

Manatee

Out of Home Placement Time in Months

20100

Cum

ulat

ive

Sur

viva

l

1.0

.9

.8

.7

.6

.5

.4

.3

.2

.10.0

GOAL4

Adoption

LTRC,MSF, & Reunific

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Variable BetaStandard

Error Wald Significance Exp(B)Age -.036 .013 8.272 .004 .965Gender(1=female)

.104 .112 .852 .356 1.109

Ethnicity(1=majority)

.146 .118 1.534 .215 1.157

LTRC, MSF,Reunification

-1.373 .178 59.736 .000 .253

Discussion

The goals of long term relative care, maintain and support family, andreunification reduce the amount of time the child spends in foster care significantly ascompared to adoptions. Age, again, had an inverse effect on placement time.

Limitations

The independent variables of age, gender, and ethnicity are not good predictorvariables of time spent in out-of-home care. This limitation is unfortunate as theopportunity to capture additional variables in the databases has not been done and couldpossibly contribute to more understanding of the placement episodes.

Overall

The differences between the permanency goals, on the whole, are in the intendeddirection. The graphs that were provided demonstrated pictorially the time childrenspend in out of home care based on several different independent variables. On thewhole, both programs are working on meeting the permanency outcome as stated in theAdoption and Safe Families Act. As was mentioned above, there are several limitationsand future evaluation activities should be pursued that include working with the differentprograms to assist them in capturing additional information.

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References

Allison, P.D. (1995). Survival analysis using the SAS system: A practical guide. Cary, North Carolina: SAS Institute.

Raftery, A.E. (2001). Statistics in Sociology: A selective review. Technical Report 389.Seattle, Washington: Department of Statistics—University of Washington.


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