Outcome Trajectories among Homeless Individuals with Mental Disorders in a Multisite Randomised Controlled Trial of Housing First

Abstract

Purpose:

Housing First (HF) has been shown to improve housing stability, on average, for formerly homeless adults with mental illness. However, little is known about patterns of change and characteristics that predict different outcome trajectories over time. This article reports on latent trajectories of housing stability among 2140 participants (84% followed 24 months) of a multisite randomised controlled trial of HF.

Methods:

Data were analyzed using generalised growth mixture modeling for the total cohort. Predictor variables were chosen based on the original program logic model and detailed reviews of other qualitative and quantitative findings. Treatment group assignment and level of need at baseline were included in the model.

Results:

In total, 73% of HF participants and 43% of treatment-as-usual (TAU) participants were in stable housing after 24 months of follow-up. Six trajectories of housing stability were identified for each of the HF and TAU groups. Variables that distinguished different trajectories included gender, age, prior month income, Aboriginal status, total time homeless, previous hospitalizations, overall health, psychiatric symptoms, and comorbidity, while others such as education, diagnosis, and substance use problems did not.

Conclusion:

While the observed patterns and their predictors are of interest for further research and general service planning, no set of variables is yet known that can accurately predict the likelihood of particular individuals benefiting from HF programs at the outset.

Clinical Implications

• Staff and funders should be prepared for the path to housing stability in HF programs to vary amongst clients.

• There is no known set of predictors that can accurately determine an individual client’s path to housing stability at the outset.

• All those eligible based on generally identified need should be offered HF, with necessary adaptations made based on need and response observed over time.

Limitations

• Some potentially important variables were not measured in this study, and others were measured only superficially.

• The follow-up period was relatively short for growth mixture modeling studies and for a study population with long-standing risk and vulnerability.

• Classes identified in growth mixture modeling analyses are patterns, not definitive groups.

Homeless people experience poorer physical and mental health, more victimization and violence, and premature mortality.^1–3 Housing First (HF), which involves the immediate provision of permanent housing and supports for homeless individuals with mental disorders without requiring sobriety or treatment adherence, produces substantial improvements in housing stability, moderate improvements in functioning and quality of life (QoL), and reductions in institutional service use.^4–10 However, to date, studies have reported findings based on group averages, and investigators have also sought to determine which subgroups of the homeless population responded to HF and why.⁸ This line of investigation has not borne much fruit. Clinical observation and qualitative data also suggest that there is heterogeneity in response to HF over time that may be explained by client circumstances or external circumstances rather than crude group membership variables.^11,12 There is a need for more nuanced understanding of the complex patterns of change to inform service planning and adaptation of HF programs to unique needs.

From 2009 to 2013, the At Home/Chez Soi (AHCS) trial randomised nearly 2300 individuals to HF and treatment-as-usual (TAU) groups in 5 Canadian cities.¹³ Data were collected every 3 months, over 24 months. Herein we report on the results of person-centered longitudinal data analysis methods, which were applied to the full study sample to examine latent trajectories of outcomes and their predictors.

Growth mixture modeling (GMM)^14–16 is a relatively new analytic approach for longitudinal data that provides a more dynamic picture of outcomes by simultaneously modeling individual paths over time. It contrasts with other longitudinal analytic approaches, which estimate average values for predefined groups and fail to take full advantage of time-specific and person-specific data. GMM produces classes of participants based on latent variables that have statistically derived similar patterns (such as in timing, duration, and sequencing) in relation to an outcome variable and can also identify correlates of latent class membership. Thus, its strength is to “identify rather than assume distinctive groups of trajectories.”^14(p139)

GMM has been used to study trajectories in substance use,^17–22 criminal behaviour,^23,24 mental illness,^25–27 and risky behaviours in specific samples,²⁸ as well as to describe the natural history of phenomena²⁷ and response to interventions,^24,29 including randomised trials.³⁰ To our knowledge, however, only 3 studies have used GMM to examine trajectories of housing stability as an outcome among homeless individuals.

Lennon and colleagues³¹ studied homelessness trajectories among 96 men with mental illness in New York City randomised to a shelter-based critical time intervention or usual care and followed for 18 months. Four latent classes were identified for the TAU group and 3 for the experimental group. The sample was relatively small for such a computationally demanding method; 1 class represented only 4 individuals. Predictors were not reported. Tevendale et al.³² used GMM to describe housing trajectories among 426 homeless youth followed for 2 years in Los Angeles County. Three trajectories of shelter use over time were identified. The ability to return home, age, type of drugs used, and informal sector activity involvement predicted class membership. Aubry and colleagues¹ examined trajectories of 329 homeless individuals in Ottawa over 2 time points and 2 years of follow-up. Variables that distinguished 4 classes were mental and physical health problems (diagnosis, substance use, and chronic conditions) and health care use. The authors noted a single type of recruitment site, a mixed-age sample, and relatively high attrition (40%) as limitations. These early experiences with GMM in homeless samples are promising, but samples have been relatively small and geographically limited.

Methods

The HF Intervention and Participants

The AH/CS trial was conducted in Vancouver, Winnipeg, Toronto, Montreal, and Moncton, with data collection from October 2009 to June 2013. Participants were recruited from community agencies, shelters, clinics, and directly from the street. Eighty-four percent were interviewed at the end point. The intervention was based on the Pathways to Housing model.⁴ Fidelity was assessed twice, with good results.^33,34 Participants were stratified by need level^* and randomly assigned to HF or TAU (any other housing or supports locally available). Those with high needs received assertive community treatment (ACT) and those with moderate needs received intensive case management (ICM).^** Participants were eligible if they were legal adults, were absolutely or precariously housed, and had a mental disorder (including substance use disorders). Fifty-seven percent of the sample was 35 to 54 years old, 67% were male, 81% were born in Canada, and 22% were Aboriginal. Fifty-five percent had not completed high school, 93% were unemployed at baseline, and 24% had an income of less than 300 CAD in the prior month. Eighty-two percent were absolutely homeless. Thirty-four percent met criteria for a psychotic disorder and 67% for substance abuse or dependence. Thirty-six percent were at moderate or high risk of suicide at baseline; 66% reported a history of traumatic brain injury, and the average number of adverse childhood experiences was 4.6 on a scale of 10. The trial was approved by 11 research ethics boards.

Measures and Operational Definitions

The outcome of interest was days in stable housing in each of eight 90-day follow-up periods (secondary outcomes were included in the main study, but they are not considered in this paper; see¹³). The Residential Time-Line Follow-Back Calendar (RTLFB)³⁷ was used to document housing status over time. Housing stability was defined as living in one’s own room, apartment, or house or with family, with an expected duration of residence ≥6 months and/or tenancy rights. Unstable housing was defined as living on the street or in temporary residences (with expected duration <6 months and no tenancy rights), emergency shelters, crisis units, or institutions.

Probable diagnosis was documented using the Mini International Neuropsychiatric Interview (MINI)³⁶ and categorized as mood disorder with psychotic features, psychotic disorders, mania/hypomania, major depression, panic disorder, and posttraumatic stress disorder (PTSD). Psychiatric symptoms were measured using the Colorado Symptom Index, a 14-item scale that documents past month presence and frequency of symptoms.³⁸ Past month substance use problems were measured using the Global Assessment of Individual Need Short Screener, a 5-item scale capturing high-frequency use, social problems, dysfunction at home or work, time spent procuring the substance, and withdrawal circumstances.³⁹ Age at first use of alcohol and drugs and number of police contacts were ascertained with self-report items.

Childhood trauma was assessed using the Adverse Childhood Experiences (ACE) Scale, which consists of 17 questions pertaining to events experienced before age 18 years.⁴⁰ It includes 3 categories of childhood abuse (psychological, physical, and sexual) and 2 categories of neglect (emotional and physical), and it also measures exposure to household dysfunction (parental separation/divorce, substance abuse, mental illness, domestic violence, and incarceration). For comorbid physical health conditions, a list of 28 long-term conditions was developed for the trial and administered at baseline.

Participants’ assessments of their recovery was measured using the Recovery Assessment Scale (RAS), which has 22 items in 5 subscales (personal confidence/hope, help seeking, goal orientation, reliance on others, and not being dominated by symptoms).⁴¹ Self-esteem and self-efficacy were operationalized using individual RAS items 4 and 9. Overall health status was measured using the visual analog scale item on the EQ-5D.⁴² Cognitive impairment was operationalized as an endorsement of the following item: Did you ever get extra help with learning in school? Ethnicity was self-reported from a standard Census Canada listing and collapsed into major groups of interest.

The Modelling Approach

The literature on outcomes of HF programs is rich, but there is less coherent literature on the predictors of housing outcomes in homeless individuals with mental health issues specifically, but variables likely to be important were inferred from research on broader outcomes such as QoL or studies including homelessness among other variables for high-risk populations.^26,43,44 These studies identified that severity of mental illness, poor physical health, the presence of chronic medical conditions, lack of social support, and victimization are important. We also used the original HF logic model, qualitative findings from a 10% sample of trial participants interviewed at baseline and 18 months,^12,45 and quantitative analyses for 2 subsamples (predictors of persistent homelessness in one site and predictors for those in the intervention that did not achieve stable housing^46,47) to build an initial theoretical model of the variables (and their timing) that might distinguish trajectories (Figure 1). Predictors from the qualitative sources included adverse childhood events, leaving school early, early justice system involvement, early drug use, early hospitalization, loss/lack of social support, loss of hope, sense of security, housing quality, substance use, self-reflection, positive identity, type of social contacts, perceived failure, social isolation, and poor self-esteem. Predictors from the quantitative analyses included gender, age, age first homeless, educational level, substance use, site, duration of prior homelessness, preenrolment incarceration, greater psychological integration with street living, and diagnosis.

Figure 1.

Theoretical model.

Analysis

Data were available for 2140 participants (1234 HF and 906 TAU). The HF and TAU group data were combined for 2 reasons. First, participants in both groups had positive and negative housing histories; second, we used group membership as an observed class variable, making each group distinct and independent where appropriate. This allowed for the identification and estimation of both common and different trajectories to occur freely for the 2 groups simultaneously. The objective of the analysis was to determine if factors over and above group membership were predictive of outcome type and trajectory. Multigroup, multilevel GMM, as developed by Muthén,¹⁶ was used. It allows for combinations of categorical or continuous latent variables and predictor variables, integrates variable-centred analysis with person-centred analysis, and also allows for clustering in the data. Key clusters were treatment group and site.

For the outcome variable, there was a preponderance of values at both extremes, 0 days and 90 days housed at all time points. These boundary conditions led to over- and underestimates of the location of the latent class means at each respective boundary, reducing the ability to identify unique trajectory classes. To address this issue, a secondary parallel process was introduced into the model and linked to class membership using a 2-step procedure.

First, a second primary outcome variable was created from the original housing variable. The new outcome was a decomposition of the original variable, by participant over time, into a single growth measure, which is the participant-specific deviance about his or her mean number of days in stable housing over the study period. This decomposition recentred the variable relative to the centre of the participant-specific trajectory. For example, a participant starting at 0 days housed and increasing monotonically to 90 days over the study period would have a centre (mean) to this trajectory of 45 days housed, and recentring would result in values of –45, –22.5, 0, 22.5, and 45 days housed. Given that this was a randomised controlled trial with an expected intercept value of 0 days housed on the original variable, the newly recentred variable now has variability in the intercepts and is not subject to the boundary conditions. The added variable was a multimodal, aggregate, approximately normal overall distribution that eliminated the ceiling and floor effects, increased the uniqueness of the observations, and increased variability.

Second, exploiting the direct linkage between the processes behind the growth measure of days in stable housing and the original variable,⁴⁸ the estimates of class membership were conditioned on both processes. This parallel process approach corrected the estimates of class membership and growth parameters in the days of stable housing process as the data differed only in the centring. Therefore, the intercepts differed, while the slope estimates, which are the variables of interest, were the same.^49,50

GMM was conducted using MPlus version 7.1.^16,51 Because there was heterogeneity by treatment group, it was incorporated as a known class variable. Linear, quadratic, cubic, and piecewise continuous growth trajectories over time were all considered, over a range of up to 7 latent classes. The selection of the best model to describe the data followed suggestions made by Nylund and colleagues⁵² and information provided in the Schwartz-Bayesian information criterion,⁵³ the Lo-Mendell-Rubin likelihood ratio test,⁵⁴ and the bootstrapped likelihood ratio test⁵⁵ with the classification precision evaluated by the estimated entropy.⁵⁶

For the person-centred growth process, the latent intercept variance was not identifiable as it was completely determined by the slope variance as a result of the centring. Furthermore, estimates of the slope parameter variances were extremely small and nonsignificant, meaning that the within-class trajectories were all extremely similar overall and represented well by the mean of the trajectory without adjustment. The person-centred growth process was therefore treated as an unconditional latent class growth analysis, while the days in stable housing remained a GMM with class probabilities and trajectories conditioned upon baseline and time-varying covariates.

For all predictor variables, multiple imputation of missing data was generated in Mplus version 7.1 using a Markov chain Monte Carlo simulation where the missing data posterior distribution was estimated from the simulation using an unrestricted variance-covariance method that demonstrates good convergence properties and is robust to model misspecification.⁵⁷ The approach was also guided by the recommendations of Rubin,⁵⁸ Snijders and Bosker,⁵⁹ and Graham et al.⁶⁰ Imputed proportions ranged from 0% to 17% for the predictor variables. The outcome variable was not imputed as it had a low proportion of missing data over time (less than 10% at all occasions prior to study end), and no visible or statistical patterns to the remaining missing data were observed. Allowing missingness on the outcome variable resulted in an overall proportion of participants included in the analysis of 94.9% (2140 of a possible 2255). All subsequent analyses using the imputed data were treated according to the missing-at-random assumption using maximum likelihood.

Results

The best-fitting model (Figure 2) produced a set of 6 latent class trajectories for each treatment group; all trajectories except one (class 4) are common or shared (parallel) between the treatment groups. As such, the trajectory lines are separated by treatment group only for class 4. While most participants started at nearly zero days housed at study enrolment, the figure reveals that some participants spent some time in stable housing in the 3 months prior to enrolment. Results for correlates of class membership (with reference to class 1) are shown in Table 1. As with all regression results, the findings represent the joint effect of all variables modeled rather than of individual variables.

Figure 2.

Trajectories of housing stability outcomes based on growth mixture modelling. HF, Housing First; TAU, treatment as usual.

Table 1.

Predictors of Class Membership.

Variable	1 Reference: Almost No Time Stably Housed	2 Rapid and Sustained Path to Stable Housing	3 Slow Path to Housing Stability	4 Large and Rapid Divergence by Treatment Group	5 Early Housing Gradually Lost	6 Rapid Gain First Year and Then Steep Decline
TAU, n (%)	456 (50.3)	164 (18.1)	130 (14.4)	38 (4.20)	31 (3.40)	87 (9.60)
HF, n (%)	170 (13.8)	537 (43.5)	101 (8.20)	79 (6.40)	42 (3.40)	305 (24.70)
Age (years)	40.5	41.8*	40.9	41.6	39.1	39.9
Gender (% female)	26.2	32.7*	33.1*	40.2*	43.9**	34.1
Ethnocultural status (%)
Caucasian (reference class)
Aboriginal	27.0	20.3**	20.9*	21.2	11.0*	18.1**
Other minority	35.5	38.3	39.1	35.1	46.5	39.2
Education (%)
< High school (reference class)
Completed high school/some  higher education	29.1	32.0	29.3	39.4	26.0	35.0
Completed trade school/ undergraduate	11.6	12.4	12.1	11.1	13.7	13.4
Income ($/prior month)	527.8	577.0	562.6	583.2	629.3	625.7*
Total time homeless (years)	7.5	6.6***	7.6	5.2***	5.1*	7.1
Age first drink (years)	14.4	14.4	14.0	15.4	14.9	14.9
Age first drug use (years)	16.1	16.1	15.4	16.8	15.8	16.4
Justice involvement (number of police contacts)	1.4	1.1	1.3	0.9	0.9	1.1
Diagnosisa	2.7	2.6	2.6	2.6	2.5	2.6
Previous hospitalizations (n)	1.9	2.1**	2.2*	1.8	2.4***	2.0*
Overall health (EQ-5D VAS score)	61.5	58.2	58.4	55.1*	60.9	60.9
Mental illness symptoms (CSI total score)	38.7	39.6	40.2	39.3	38.5	39.8*
Comorbidity (>1 condition)	0.434	0.495*	0.484	0.503	0.493	0.425
Cognitive impairment (% help in school)	41.5	39.1	44.1	36.8	38.3	37.3
Substance problems (GAIN SPS total score)	3.0	2.8	3.1	2.8	2.6	2.7
Childhood trauma (ACE total score)	4.3	4.4	4.5	4.2	4.3	4.5
Baseline self-esteem indicator score	3.5	3.4	3.4	3.5	3.6	3.4
Baseline self-efficacy indicator score	3.6	3.6	3.5	3.6	3.8	3.7

ACE, Adverse Childhood Experiences; CSI, Colorado Symptom Index; GAIN SPS, Global Assessment of Individual Need Substance Problem Scale; HF, Housing First; TAU, treatment as usual; VAS, Visual Analog Scale.

^aDiagnosis is a quasi-quantitative variable coded as follows: 1) mood disorder with psychotic features, 2) psychotic disorders, 3) mania/hypomania, 4) depression, 5) panic disorder, or 6) posttraumatic stress disorder.

*P < 0.05. **P < 0.01. ***P < 0.001.

Class 1, almost no time housed, represents 29% of the sample and is the reference condition. This group had the poorest outcomes; they were not housed at all or for only very brief periods. Participants in this class were predominantly (73%) in TAU, had low monthly income prior to study enrolment, had longer histories of homelessness, and were more likely to be male and Aboriginal.

Class 2, the best outcome, describes a trajectory of rapid and sustained housing, with many achieving virtually full-time housing by 6 months with additional incremental stability by 12 and 18 months and almost no loss by completion of follow-up. This class was also the largest, comprising 33% of the sample. Most of these participants (77%) were in HF. Compared to class 1, they tended to be older, were more likely to be female, were less likely to be Aboriginal, were homeless fewer years before study entry, and had more physical comorbidities.

Those in Class 3, gradual gains sustained, also had a good outcome. While their path into stable housing was much slower, it was maintained at the study’s end. About 11% of the sample showed this pattern; of these, 44% were in HF and 56% in TAU. They differed from the reference group in that they were more likely to be female and to have had more prior hospitalizations. They were also less likely to be Aboriginal.

Class 4, divergence by treatment arm, with 117 individuals (5.5% of the sample) had a mixed outcome despite a very similar starting point in terms of prior days housed. The 79 HF participants (67.5%) maintained and even improved on their initial higher number of days housed, while the 38 people in TAU (32.5%) were initially more stably housed but then lost that stability rapidly after enrolment. While trajectories differed between treatment arms, the composition of the class did not statistically differ, allowing for the predictors of class membership to be pooled. The common characteristics of this class were that members were more likely female, were homeless for a shorter time, and had poorer general health.

The smallest group was class 5, early housing gradually lost, including 3% of the sample (73 participants, of whom 58% were in HF). These individuals had some stable housing prior to the study but tended to lose it after the first year. This group had the highest proportion of females, participants with the greatest number of previous hospitalizations, the least time previously homeless, and the lowest proportion of individuals of Aboriginal heritage.

Class 6, rapid gain then steep decline, had 392 members (18% of the sample with 78% from HF). Those in this group started out with almost no housing stability, were housed after enrolment, but then returned to homelessness after the first year. The group had a higher monthly income than the reference group, had higher levels of psychiatric symptoms, and were less likely to be Aboriginal.

Trajectory plots were also generated for all classes separated by treatment group (not shown but available as supplementary material). In most cases, the trajectories were better for HF participants, ranging from slightly better (classes 1, 2, and 6) to moderately better (class 3) to dramatically better (class 4). Class 5 suggests that despite a similar starting point and the intervention, a small number of TAU participants held onto their housing slightly better than HF participants with similar characteristics at the outset.

Discussion

Conventional analyses have shown that HF is successful in keeping participants stably housed. Our results explore the heterogeneous response trajectories not apparent in nondynamic group-based analyses. They confirm the relatively immediate, strong, and sustained response to the HF intervention for many participants. HF participants predominate in classes with positive outcomes and TAU participants in those with negative ones. Even so, many TAU participants also had positive pathways to housing stability. This may reflect access to universal health care and an array of other social and housing interventions in the Canadian context and perhaps other positive events (e.g., recovery after a crisis, family reunification, employment).

Many study participants had complex and less predictable responses over the course of the study. Class 4 best represents the theoretical ideal for the intervention response, but this group is relatively small. Heterogeneity of response may be the rule rather than the exception for a population with entrenched disadvantage. Decades of trauma and vulnerability are often not undone “overnight,” although for many, a rapid and dramatic housing response is possible. While our childhood trauma variable did not differentiate trajectories, future research should consider accumulated trauma over the entire period of homelessness.

Predictors of poorer outcomes were somewhat consistent across classes. Aboriginal persons were less common in classes with better outcomes, as were males. Note that most Aboriginal participants were from the Winnipeg site, so these variables were strongly correlated. However, site was accounted for in the model, and Aboriginal status was significant above and beyond site. The youngest mean age was associated with class 5, but this was likely partly confounded by total time homeless. Prebaseline income seemed to play a role in class 6, but it is unclear why those with more initial resources would have rapid gains followed by a later return to homelessness.

Some variables were not significantly associated with any trajectory; these included education, diagnosis, early substance exposure, self-esteem, and self-efficacy that emerged in qualitative analyses. This may be due in part to joint dependence in the model. The GMM analysis illuminates heterogeneity, but difficulty in capturing all complexity underlying individual paths remains. We made an initial attempt to include some relatively unstudied variables such as self-esteem and self-efficacy but had only simple indicators of these available. We also believe that other variables that we did not model and that operate at higher levels (e.g., housing quality, neighbourhood acceptance, systemic stigma/discrimination) may have substantial influence on housing outcomes.

Strengths of this analysis include data from a large heterogeneous multisite sample with low attrition and comprehensive measurement. Despite these strengths, Kertesz et al. caution that “trajectory analyses represent statistical approximations rather than identifiable ‘types’. Causal inferences are tentative.”^22(p808) The modelling approach is aimed at finding longitudinal patterns in data, and the results are not entirely consistent with our classical analyses. Even though we specified a theoretical model in advance, the analysis is very exploratory and the class compositions should not be considered precise. While follow-up was long relative to other studies, it is short relative to many studies using GMM. Some variables were not comprehensively assessed, and self-report variables are prone to numerous biases. Our suggestions for research include longer follow-up, modeling variable groupings as higher level dimensions, and examining other outcomes (e.g., Qol, recovery). Further description of specific patterns of housing for each class is also possible and warranted.

While our identified predictors are of interest for further research and general service planning, it is not recommended that they be used to make decisions about the likelihood of particular individuals benefiting from HF. Our findings do, however, point to some variables that are relevant to intervention success to guide further adaptation. They also underscore the importance of multipronged, individualized interventions that attend to longstanding individual and system-level trauma. This type of analysis can also contribute to a discourse aimed at recognizing the complexity of homelessness.