Quantitative Research Using Survival AnalysisCBC Final Report, 6/18/01 Section III
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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
Quantitative Research Using Survival AnalysisCBC Final Report, 6/18/01 Section III
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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
Quantitative Research Using Survival AnalysisCBC Final Report, 6/18/01 Section III
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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
Quantitative Research Using Survival AnalysisCBC Final Report, 6/18/01 Section III
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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.
Quantitative Research Using Survival AnalysisCBC Final Report, 6/18/01 Section III
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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
Quantitative Research Using Survival AnalysisCBC Final Report, 6/18/01 Section III
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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.