I* I V APPLICATION OF SURVIVAL ANALYSIS ^ TO RECIDIVISM DATA OF PSYCHIATRIC PATIENTS Barbara S. Arndorfer MMSS Senior Thesis May 17, 1989 ABSTRACT: The present study employed survival analyses to the recidivism data of 291 Chicago area psychiatric hospital patients. First, a comparison was made between regular and incomplete survival distributions which are based on opposing assumptions regarding eventual "failure," i.e. readmission to the hospital. Second, the effects of several subject variables on the length of time a discharged patient "survives" in the community were investigated. Results indicated that the lognormal, a regular distribution based on the assumption that eventually everyone will fail provided the closest data fit. In addition, race, age and number of previous admissions were significantly related to the length of survival time.
Transcript
I *
I V APPLICATION OF SURVIVAL ANALYSIS ^ TO RECIDIVISM DATA OF PSYCHIATRIC PATIENTS
Barbara S. Arndorfer MMSS Senior Thesis
May 17, 1989
ABSTRACT: The present study employed survival analyses to the recidivism data of 291 Chicago area psychiatric hospital patients. First, a comparison was made between regular and incomplete survival distributions which are based on opposing assumptions regarding eventual "failure," i.e. readmission to the hospital. Second, the effects of several subject variables on the length of time a discharged patient "survives" in the community were investigated. Results indicated that the lognormal, a regular distribution based on the assumption that eventually everyone will fail provided the closest data fit. In addition, race, age and number of previous admissions were significantly related to the length of survival time.
The population of state mental hospitals has been decreasing since
the mid-1960s as a result of the policy of deinstitutionalization. Although
these hospitals have been successful in shortening the length of one's stay,
as well as discharging an increasing number of patients, many of those
released continue to be rehospitalized (Munley, et al.# 1977).
"Approximately 60 percent of all admissions to state hospitals are
readmissions with some variance by state and hospital (Kalifon, 1985)."
Related to readmission is the concept of recidivism which, in a
mental health context can be defined as the reversion to previous unstable
behavioi—following hospitalization, treatment, and discharge into the
community—which results in readmission to the hospital. Recidivism
rates differ from readmission rates because the former usually describe a
small population involved in a specific program or hospital (Kalifon, 1985).
Numerous studies have been done in attempt to determine the
factors which predict recidivism. One consistent finding after more than
20 years of research is that a correlation exists between the number of
previous admissions and the likelihood of subsequent admissions (Anthony,
et al., 1972; Buell and Anthony, 1973; Rosenblatt and Mayer, 1 974; Munley,
et al., 1 977; Byers, et al., 1 978; Pokorny, et al. ; 1 983; Lewis, et a l , 1 988).
"Apparently one of the best predictors of psychiatric patients future
behavior has been past behavior (Munley, et a l , 1 977)."
Other variables such as diagnosis, type of treatment, and length of
hospitalization are not consistently related to recidivism (Lewis, et a l .
1988). Rosenblatt and Mayer (1974) found the number of previous
admissions to be the only predictor of recidivism. Buell and Anthony
(1973) agreed with i ts importance, but added the length of last
hospitalization as a significant factor. Byers, et al. (1978) found a
patient's family and living situation to be more important when predicting
recidivism, but could not overlook the role of the number of previous
admissions.
Munley, et al. (1977) found that the type of discharge had a
stronger relationship to readmission than the number of previous
hospitalizations. The follow-up period in this study was only three months
however. "Because percentage of readmissions increases with length of
the follow up period (Anthony, Buell, Sharrat, & Althoff) the relationship
between type of discharge and readmission may well decrease as
increasing numbers for regularly discharged patients are readmitted
(Munley, et al., 1977)." Pokorny, et al. (1983) found the number of previous
hospital admissions to be significant, but unlike Rosenblatt and Mayer
(1974) and Munley, et al. (1977), added diagnosis as an important predictor.
In addition to the inconsistent variable findings stated above,
studies do not provide a clear relationship between the variables of race
and age and hospital readmission. Munley, et al. (1 977) determined that
age was not a significant predictor for readmission; race remaining "open
to speculation." The data from Turkat (1980) indicated "a significant
overrepresentation of young black males among hospital recidivists." Buell
and Anthony (1973) found race and age to be nonsignificant predictors of
recidivism.
Some of the inconsistencies reported in the l i terature are due to
the nature of the variable being studied. For example, recidivism is more
clearly defined (Anthony, et al., 1972), whereas the measurement of the
length of hospitalization may vary from length of last hospital stay (Buell
and Anthony, 1973) to cumulative months of prior hospitalization
(Pokorny, et al., 1983). Thus, results from various studies often cannot be
compared due to discrepancies in variable definition.
Survival Analysis
Survival analysis is a methodology developed and implemented
most often in the areas of engineering and medical research. It can be
util ized when the dependent variable represents the length of t ime
between an initial event (e.g. date of discharge from hospital) and a
termination event (e.g. date of readmission) (SPSSX User's Guide, 1986).
Thus, this methodology "analyzes rates over time in which 'terminal
events' or 'failures' occur for a given population group (Illinois Criminal
Justice Information Authority, 1986)."
"The distinguishing mark of survival analysis is the allowance for
the censoring of the dependent variable which renders the data incomplete
(Steinberg and Colla, 1988)." For example, some patients are not
rehospitalized by the termination date of the study; in this case the data
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would be right censored because the dependent variable is known to be
greater than the length of time from hospital discharge to the end of the
study, but it 's true value is not known. Another advantage of survival
analysis is that unlike a fixed interval observation which determines the
percentage of a population who fail within a specific time period, i t can
specify the proportion recidivating across specified time intervals within
the follow-up period. Furthermore, this type of analysis allows
comparisons to be made between two samples or different subgroups
within a sample (Illinois Criminal Justice Information Authority, 1986).
Limitations exist, however, within survival analysis programs of
current statistical software packages. For example, SYSTAT (Steinberg
and Colla, 1988) allows for censorship but i ts models are all based on the
underlying assumption that every subject will eventually "fai l" (i.e.
recidivate). Thus i ts models do not allow for a patient to be "cured" and
never return to the hospital. Maltz (1989) on the other hand, is in the
process of developing a computer program entit led SURFIT (SURvival
FITting software) which f i ts the survival data to both regular and
incomplete distributions. While the former are based on the same
assumption as SYSTAT, the lat ter "admit the possibil i ty that some fraction
of the population under study may survive forever (where "eternal survival"
is relative to the focus of the study) (Maltz, 1989)." Maltz's program is in
the early stages of development. "Software is currently being developed
for SURFIT to permit covariate analysis along with incomplete
distributions"; as of now, no programs are available (Maltz, 1989).
METHOD
This study investigated 1) the application of SURFIT (Maltz, 1989)
to mental health survival data, employing both regular and irregular
distributions, and 2) the effects of race, age and number of previous
admissions on the length of time a discharged psychiatric patient survives
in the community. The lat ter was analyzed by SURVIVAL within SYSTAT
(Steinberg and Colla, 1988).
Subjects. The subjects were 313 Chicago area psychiatric hospital
patients who were discharged between July 24, 1 985, and February 1 7,
1987. Data collection terminated on March 1, 1987. Five patients were
excluded from the analyses due to incomplete hospital records. Another
f i fteen patients were dropped because they were not discharged from the
hospital prior to the termination date of the study; thus no "survival t ime"
could be calculated. Finally, two patients who were discharged and
readmitted on the same day were excluded because the computer programs
specified that survival times must be positive.
Variables. The dependent variable of the two data analyses was
the length of t ime a patient survived in the community following discharge
from the hospital. This was computed by subtracting the date of discharge
from the date of readmission.
Subject variables were examined for their relationship to the
preceding dependent variable. Prior to statistical significance
calculations, six variables had been selected: sex, race, age, number of
previous admissions, diagnosis, and where patients stay when they leave
the hospital. Significance calculations, however, forced the rejection of
the final two: diagnosis, p>.l 0; where stay, p>.25. Further Cox regression
calculations resulted in rejection of sex as well ( t -s ta t= 1.645). Thus,
three variables were significant to test; their frequencies are as follows:
Race: White (33%) Non-White (57%)
Age: 18-34(67%) 35-49(23%) 50+(10%)
No. Previous Admissions: 0(38%) 1-5(30%) 6+(32%)
Procedure. Data was collected by a Mental Health Policy Project
research team headed by Dr. Dan Lewis, Northwestern University. The 291
patients eligible for this analysis were interviewed prior to their
discharge from various psychiatric hospitals in the Chicago area.
Readmission data were obtained from hospital records.
RESULTS
SURFIT Analysis. SURFIT uses the method of maximum
likelihood to estimate the parameters of a distr ibution (Maltz, 1989). The
intent of this study was to compare analyses based on the following
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/
assumptions: 1) eventually every person will "fai l" (i.e. be readmitted to
the hospital), and 2) some people will be "cured" (i.e. never recidivate). As
a result of this intent, the available distributions in SURFIT (where
S(t)=the proportion expected to survive after time t ;nrepresents the
probability of eventual failure) were grouped according to assumption.
When determining goodness of f i t , therefore, the mixed exponential, which
st i l l "assumes that everyone fails, but that one part of the population fails
at a relatively high rate compared to the other part (Maltz, 1989)," was
compared to regular distributions rather than irregular.
Based on the goodness of f i t cr i teria and the rule for comparing
distributions with varying numbers of parameters, the lognormal provided
the best f i t for the assumption that eventually everyone will fail (see
Table 1). Although the goodness of f i t cri teria determined that the mixed
exponential had the closest f i t , the rule for comparing distributions with
varying numbers of parameters forced its rejection. According to Maltz
(1989), "if the addition of a parameter increases the maximum of the
likelihood function by around 3, resulting in a height ratio of about 20,
then the additional parameter is warranted." Because this guideline is not
very precise and the height ratio of maximum likelihoods of the lognormal
and the mixed exponential was only 17.5, the lat ter was rejected. Thus, i t
was concluded that the lognormal distribution provided the best f i t when
the analysis was based on the assumption of eventual failure (see Table 2
and Figure 1).
Next the incomplete distributions were compared to determine
which model provided the best f i t for the assumption that some people are
"cured," hence never returning to the hospital. Once again, comparisons
were based on the goodness of f i t criteria. The incomplete lognormal was
found to provide the data with the closest f i t (see Table 2 and Figure 2).
Because the incomplete lognormal provided a slightly bet ter f i t
when compared to the lognormal distribution, the ratio of likelihood
function heights was computed to determine if the additional parameter
was warranted. The ratio was a mere 2.4, certainly not a significant
difference. Thus overall, according to SURFIT, the lognormal distribution
based on the assumption that eventually everyone will fail provided the
best data f i t (see Figure 3).
SYSTAT's SURVIVAL Analysis
As stated above, SURFIT determined the lognormal to be the best
distribution to f i t the data. Consequently i t was used within SYSTAT's
SURVIVAL Analysis when the effects of race, age and number of previous
admissions on "survival t ime" were analyzed (see Table 3).
Race. Af ter setting age (AGETHREE) and number of previous
admissions (PREVADM) equal to their means, the two categories of race
(RACETWO) were compared. As can be seen in the Table 4, whites
(RACETWO = 0) have a higher probability of surviving (equivalent to the
estimated rel iabi l i ty) at every time specification (measured in days).
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Age. Following a procedure similar to the one stated above, the
three age groups (18-34= 1, 35-49=2, 50+=3) were compared. One can see
that as age increases the probability of not recidivating also increases
(see Table 5).
Number of Previous Admissions. Race and age were set equal to
their means while the three categories of the number of previous
admissions (0 = 0, 1 -5 = 2, 6+ = 2) were analyzed. Table 6 shows the
significant effect this variable has on the length of time a patient
survives in the community. After two years, 51.4% and 32.4% of those
hospitalized zero and 1 -5 times, respectively, are expected to survive
while only 17.2% of those recidivists with six or more previous
hospitalizations are not expected to require readmission.
DISCUSSION
Unlike Munley, et al. (1977) and Buell and Anthony (1 973), the
results of this study found significant relationships between race, age and
the length of t ime a patient remains in the community without
recidivating. Nonwhites and those aged 1 8-34 have the lowest predicted
chance of survival, thus confirming the results of Turkat (1 980).
In concurrence with several previous studies (Anthony, et al.,
I 972; Buell and Anthony, 1 973; Rosenblatt and Mayer, 1974; Munley, et al.,
1977; Byers, et al., 1978; Pokorny, et a l , 1 983; Lewis, et a l , I 988), the
number of previous admissions consistently relates to readmission after
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discharge. Thus past behavior is a significant predictor of future actions.
Of interest in this present study is the final result of the SURFIT
Analysis (Maltz, 1989). One would expect an incomplete distribution which
doesn't assume eventual failure for everyone to provide the closest data
f i t . However, tests indicated that the addition of the third parameter
wasn't warranted. Consequently the lognormal survival distr ibution, based
on the opposing assumption was found to f i t the data most accurately.
Unfortunately due to the recent development of the SURFIT
Analysis, findings from similar studies were not found in the l i terature. It
seems l ikely though that the above result is due to the nature of the
lognormal survival distribution. As can be seen with any of the variables
in Appendix B, the length of time for eventual failure for the total patient
population is longer than the expected lifespan of the human race. For
example, after lOOyears the estimated probability of survival of
individuals with no previous admissions is 5.5%. Because of the great
length of t ime before eventual failure, the lognormal survival distr ibt ion
provides an accurate data fit.
In conclusion, the present study identif ied three variables with
significant relationships to the length of t ime a patient remains (i.e.
"survives") in the community without recidivating. Findings regarding the
number of previous admissions replicated results from numerous past
studies. Race and age, however, were both of consistent and inconsistent
nature due to incompatabilities in the l i terature.
0
Unfortunately, from a social policy point of view, the variables
which remained significant to test within survival analysis provide l i t t le
insight as towhy patients recidivate. This study only determined that
these characteristics—aged 18-34, nonwhite, having six or more previous
admissions—describe the person most likely to be readmitted to the
hospital. Because policymakers are unable to change the past, further
research successfully employing characteristics related to a patient's
future (such as where he/she stays when discharged from the hospital) in
addition to those variables which generate an understanding of his/her
past (e.g. number of previous admissions) is in great demand.
Finally, the present study determined that the lognormal survival
distr ibution, based on the assumption that eventually every patient will
recidivate, provided the best data f i t . Although this finding is contrary to
what one would assume, i t seems that the nature of this distribution—the
length of t ime i t takes to reach zero—accounts for this result. As the
SURFIT program (Maltz, 1 939) becomes more accessible, popular, and
refined to include covariate analysis, future research util izing its survival
distributions may contradict this study's finding.
1 1
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