This short report investigates scale effects in family substance abuse treatment programs. In Massachusetts, the family substance abuse treatment programs were much more costly than other adult residential treatment models. State officials were concerned that the "scale" or size of these programs (averaging just eight families) was too small to be economical. Although the sample size (just nine programs) was too small to permit reliable inference, the data clearly signalled the importance of "scale effects" in these family substance abuse treatment programs. To further investigate scale effects in family substance abuse treatment programs, data from the Center for Substance Abuse Treatment's (CSAT's) Residential Women and Children and Pregnant and Postpartum Women (RWC-PPW) Demonstration were re-analyzed, focusing on the relationship between cost per family-day and the estimated average family census. This analysis indicates strong economies of scale up until an average family census of about 14, and less apparent scale effects beyond that point. In consideration of these and other study findings, a multidisciplinary interagency team redesigned the Massachusetts' family treatment program model. The new programs are larger than the former family treatment programs, with each new program having capacity to treat 11 to 15 families depending on family makeup

A Beaston-Blaakman

A James Lee

AJ Lee

Center for Substance Abuse Treatment

HJ Harwood

SQ Duffy

English

PubMed

Springer - Publisher Connector

Lee Substance Abuse Treatment, Prevention, and Policy 2010, 5:14
http://www.substanceabusepolicy.com/content/5/1/14
Open AccessSHORT REPORTShort ReportAn investigation of scale effects in family substance 
abuse treatment programs
A James Lee
Abstract
This short report investigates scale effects in family substance abuse treatment programs. In Massachusetts, the family 
substance abuse treatment programs were much more costly than other adult residential treatment models. State 
officials were concerned that the "scale" or size of these programs (averaging just eight families) was too small to be 
economical. Although the sample size (just nine programs) was too small to permit reliable inference, the data clearly 
signalled the importance of "scale effects" in these family substance abuse treatment programs. To further investigate 
scale effects in family substance abuse treatment programs, data from the Center for Substance Abuse Treatment's 
(CSAT's) Residential Women and Children and Pregnant and Postpartum Women (RWC-PPW) Demonstration were re-
analyzed, focusing on the relationship between cost per family-day and the estimated average family census. This 
analysis indicates strong economies of scale up until an average family census of about 14, and less apparent scale 
effects beyond that point. In consideration of these and other study findings, a multidisciplinary interagency team 
redesigned the Massachusetts' family treatment program model. The new programs are larger than the former family 
treatment programs, with each new program having capacity to treat 11 to 15 families depending on family makeup.
Short report
The Massachusetts Bureau of Substance Abuse Services
(BSAS) contracts with licensed not-for-profit vendors to
provide residential rehabilitation services to individuals
and families recovering from addiction to alcohol and
other drugs [1]. In FY2002, BSAS funded nine family
treatment programs, ranging in size from five to 12 fami-
lies. The programs provided shelter and coordinated sub-
stance abuse treatment on behalf of predominantly
female-headed "homeless" families. The women had
long-term substance abuse problems, and many referrals
were involuntary. The programs themselves provided
case management services and some "life skills" educa-
tion, but most individual and group counseling was pro-
vided on a fee-for service basis and paid separately by
Medicaid and others.
In conducting this study, we collected and analyzed the
program-specific Schedule B reports included in the
audited FY 2002 Uniform Financial Reports (UFRs) sub-
mitted by the parent organizations of all nine family
treatment programs. The UFRs provided a reasonably
authoritative source for facility cost and statistical infor-
mation. In addition, we conducted in-depth site visit
interviews with eight of the nine programs and collected
additional, substantially qualitative information on pro-
gram operations.
The nine family treatment programs had a total capac-
ity of 73 families, which is, an average of just 8.1 families
per program. The programs' average lengths-of-stay var-
ied from 104 days to 215 days, and the program average
length-of-stay was 176 days (nearly half a year). More-
over, for those who actually completed treatment (and
did not leave against advice), the program average length-
of stay was 331 days (nearly a year), and ranged from 200
days to 492 days. The number of children per family (i.e.,
the child-to-family ratio) varied from 1.1 to 2.2, and aver-
aged 1.6
Averaging over the nine programs, the average total
cost per family-day (counting only adults) was $224, and
the total cost per family-day varied from $157 to $312.
Excluding program and administrative expense, the
direct care cost per family-day averaged $159, varying
from $108 to $207 per family-day. The average total cost
per person-day was $86, varying from $55 to $115 per
* Correspondence: AJames_Lee@uml.edu
1 Department of Community Health and Sustainability, School of Health and 
Environment, University of Massachusetts Lowell, 300 Weed Hall, 3 Solomont 
Way Lowell, MA 01854, USA
Full list of author information is available at the end of the article© 2010 Lee; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribu-
tion License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any me-
dium, provided the original work is properly cited.
Lee Substance Abuse Treatment, Prevention, and Policy 2010, 5:14
http://www.substanceabusepolicy.com/content/5/1/14
Page 2 of 4person-day; and the average direct care cost per person-
day was $61, varying from $38 to $76 per person-day.
Since the administrative and facility costs are largely
uncontrollable at the program level, this direct care cost
measure more fairly reflects differences in program cost
structure (and arguably program efficiency). It includes
the cost of all on-site program personnel, any profes-
sional service contracting, groceries and other supplies
expense.
Now what accounts for these cost differences across
programs? Could it be the scale differences in these com-
paratively small programs? In Figure 1, the direct care
cost per family-day is plotted against the number of fam-
ily-days. The downward sloping line represents the best
bivariate linear fit to the data. As we see, a simple linear
regression model suggests that the direct care costs fall
pretty sharply as client volume increases. In Figure 2, the
direct care cost per person-day is similarly plotted against
the number of person-days, and the result is much the
same. The bivariate regression line likewise suggests that
the direct care costs decline quickly as client volume
increases. In both cases, the right-hand-side scale vari-
ables are significant at the 0.05 level or better.
How confident can we be that we are accurately model-
ing costs per day and that the model correctly indicates
scale effects? As the reader can plainly see from Figures 1
and 2, the fit to the data is not tight. So what else might
account for the cost variances? Adding just one variable
to these models--the child-to-family ratio--dramatically
improves the goodness of fit. The percentage of variance
explained in the direct care cost per family-day model
increases from 48 percent to 68 percent, and the percent-
age of variance explained in the direct care cost per per-
son-day model increases from 43 percent to 80 percent.
Moreover, both variables in these models are significant
at the 0.10 level or better, and the volume relationships
are essentially unchanged from those depicted in Figures
1 and 2. Indeed, the person-day model predicts that
increasing the average program size by just three families
would reduce the average direct care cost by 24 percent,
from $61 per person-day to $46 per person-day. The find-
ings are little different if looking at total cost per family-
day or total cost per person-day (i.e., also including the
program and administrative costs). Although the sample
size (just nine observations) is too small to permit reliable
inference, the findings clearly signal the importance of
"scale effects" in family substance abuse treatment pro-
grams.
Two recent studies--Beaston-Blaakman, Shepard, Hor-
gan and Ritter [2] and: Duffy, Dunlap, Feder and Zarkin
[3]--report finding substantial scale economies in outpa-
tient substance abuse treatment. However, little evidence
of systematic efforts to investigate scale effects in family
and other residential substance abuse treatment pro-
grams is found in the literature. One study [4] analyzed
data from the RWC-PPW Demonstration [5] and found
fairly compelling evidence for the cost advantages of
increasing program size. In particular, Harwood, Kallinis
and Liu [4] conducted a series of regression analyses of
the relationship between cost and scale in the RWC-PPW
Demonstration. The executive summary of this report
concludes (p. i), "This analysis demonstrates that larger
residential substance abuse providers, on average, have
lower costs per day than smaller providers." The empiri-
Figure 1 Plot of Direct Care Cost per Family-Day Vs. Total Family-
Days. Massachusetts Family Treatment Providers, FY 2002 (N = 9). 
Source: Program-specific Schedule B's included in FY 2002 Uniform Fi-
nancial Reports submitted to the Executive Office of Health and Hu-
man Services.
Figure 2 Plot of Direct Care Cost per Person-Day Vs. Total Person-
Days. Massachusetts Family Treatment Providers, FY 2002 (N = 9). 
Source: Program-specific Schedule B's included in FY 2002 Uniform Fi-
nancial Reports submitted to the Executive Office of Health and Hu-
man Services.
Lee Substance Abuse Treatment, Prevention, and Policy 2010, 5:14
http://www.substanceabusepolicy.com/content/5/1/14
Page 3 of 4cal relationship is a strong one. For the RWC programs,
their analyses indicate that a 10 percent increase in cli-
ents would be associated with about a 6 percent decrease
in cost per client day. Moreover, the report concludes (p.
26) that, "Small providers should be conscious of poten-
tial benefits that could be realized from growth or
merger/consolidation with other providers." While unde-
niably germane, these findings are nevertheless some-
what difficult to generalize to the family treatment
programs because the analysts focus on the relationship
between cost per person-day and the average total census
(i.e., counting both women and children).
To further investigate scale effects in family substance
abuse treatment programs, we conducted a new analysis
of the RWC-PPW Demonstration data, focusing on the
relationship between cost per family-day and the esti-
mated average family census. For this purpose, we used
the demonstration data as included in the 2000 N-SSATS
public use data file [6]. Although the public use data file
does not include a bed-size variable, it includes informa-
tion sufficient to estimate the average daily family census.
For the 22 RWC programs reporting in 1997, the esti-
mated average family census was 14, and the estimated
median was 11. The estimated average daily family census
ranged from a low of 6 to a high of 43. Only two programs
had an average family census larger than 20. Of course,
the program bed-sizes would have been somewhat larger.
The RWC-PPW Demonstration data were re-analyzed,
focusing on the relationship between cost per family-day
and estimated average family census. This relationship is
depicted in Figure 3 for the 20 RWC programs with a
daily family census of 30 or less in 1997. It was thought
unlikely that anyone in Massachusetts would choose to
develop a program with capacity for more than 30 fami-
lies. A simple linear regression model accounts for
approximately one-third of the variance in cost per family
day, and the family census variable is significant at the
0.01 level. The data clearly indicate scale effects.
Although the sample size is too small to fit a non-linear
model, the data scatter in Figure 3 nevertheless suggests
that scale effects quickly plateau. In particular, for five of
the six programs with a family census of approximately 14
or more, the estimated costs per family-day are similar,
varying only from $140 to $178 per family-day, and aver-
aging $157. The average cost per family-day for the 14
smaller programs is $255.
For the 16 PPW programs that reported in 1997, the
estimated average family census was 15 and the median
was 14. The estimated average daily family census ranged
from a low of 5 to a high of 50. Five programs had an aver-
age family census larger than 20. Figure 4 similarly
depicts the relationship between cost per family-day and
average daily family census in the 15 PPW programs with
a daily family census of 30 or less in 1997. It indicates a
pattern remarkably similar to that in Figure 3. In particu-
lar, it similarly indicates that the family-day cost initially
falls rather sharply with program size and then seems to
plateau once an average family census of 14 or so is
reached. The estimated costs per family-day are little
more than $200 or less for all seven programs with a fam-
ily census of 14 or more. For these larger programs, the
cost-per-family days averages $152, compared to $392 for
the eight smaller programs.
In summary, our re-analysis of CSAT's RWC-PPW
demonstration cost data finds strong economies of scale
up until an average family census of about 14. It is impor-
tant to acknowledge, however, that this and other cost
findings reported herein are altogether unadjusted for
case mix differences. Nor did we have any outcome data
Figure 3 Plot of Cost per Family-Day Vs. Daily Family Census. Res-
idential Women and Children (RWC) Programs, 1997 (N = 20)
Figure 4 Plot of Cost per Family-Day Vs. Daily Family Census. 
Pregnant and Postpartum Women (PPW) Programs, 1997 (N = 15)
Lee Substance Abuse Treatment, Prevention, and Policy 2010, 5:14
http://www.substanceabusepolicy.com/content/5/1/14
Page 4 of 4available to similarly investigate the relationship between
cost and outcomes.
In consideration of the cost analysis and other study
findings, a multidisciplinary interagency team redesigned
the Commonwealth's family treatment program model.
In 2005, BSAS introduced a new modality, Family Resi-
dential Substance Abuse Treatment Services, to replace
both its costly family treatment programs and its under-
utilized Special Residential Services for Women (and
children) programs. These new programs are larger than
the former family treatment programs, with each new
program having capacity to treat 11 to 15 families
depending on family makeup. Eight such programs were
funded at an average cost of no more than $162 to $221
per family-day, and this included the cost of treatment
services formerly paid by Medicaid but now provided by
the programs themselves. The new modality also
included a variety of clinical enhancements, namely,
improved outcome monitoring and intensive case man-
agement services.
Author information
A. James Lee, Ph.D., is Associate Professor within the
Department of Community Health and Sustainability,
School of Health and Environment, University of Massa-
chusetts at Lowell (Lowell, Massachusetts). He is a
healthcare economist.
Competing interests
The author declares that they have no competing interests.
Acknowledgements
The author thanks Matthew R. Cornish for his support and assistance with the 
project. At the time of the study, he was Director of Administration and 
Finance, Bureau of Substance Abuse Services, Massachusetts Department of 
Public Health. The study was funded by the Center for Substance Abuse Treat-
ment (CSAT) under CSAT's State Health Care Reform Technical Assistance, and 
Knowledge Synthesis and Dissemination Project (Contract No. 270-00-7071). The 
opinions expressed herein are the views of the author and do not necessarily 
reflect the official position of CSAT or any other part of the U.S. Department of 
Health and Human Services.
Author Details
Department of Community Health and Sustainability, School of Health and 
Environment, University of Massachusetts Lowell, 300 Weed Hall, 3 Solomont 
Way Lowell, MA 01854, USA
References
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the adult residential rehabilitation programs in Massachusetts.  J Public 
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2. Beaston-Blaakman A, Shepard D, Horgan C, Ritter G: Organizational and 
client determinants of cost in outpatient substance abuse treatment.  J 
Ment Health Policy Econ 2007, 1:3-13.
3. Duffy SQ, Dunlap J, Feder M, Zarkin GA: A hybrid cost function for 
outpatient nonmethadone substance abuse treatment facilities.  In 
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4. Harwood HJ, Kallinis S, Liu C: Do larger residential service delivery units 
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doi: 10.1186/1747-597X-5-14
Cite this article as: Lee, An investigation of scale effects in family substance 
abuse treatment programs Substance Abuse Treatment, Prevention, and Policy 
2010, 5:14
Received: 23 March 2010 Accepted: 5 July 2010 
Published: 5 July 2010
This article is available from: http://www.substanceabusepolicy.com/content/5/1/14© 2010 Lee; licensee BioMed Central Ltd. is an Open Acc ss article distributed under th  terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Substan  Abuse Treatment, Prevention, and Policy 2010, 5:14


An investigation of scale effects in family substance abuse treatment programs

Abstract This short report investigates scale effects in family substance abuse treatment programs. In Massachusetts, the family substance abuse treatment programs were much more costly than other adult residential treatment models. State officials were concerned that the "scale" or size of these programs (averaging just eight families) was too small to be economical. Although the sample size (just nine programs) was too small to permit reliable inference, the data clearly signalled the importance of "scale effects" in these family substance abuse treatment programs. To further investigate scale effects in family substance abuse treatment programs, data from the Center for Substance Abuse Treatment's (CSAT's) Residential Women and Children and Pregnant and Postpartum Women (RWC-PPW) Demonstration were re-analyzed, focusing on the relationship between cost per family-day and the estimated average family census. This analysis indicates strong economies of scale up until an average family census of about 14, and less apparent scale effects beyond that point. In consideration of these and other study findings, a multidisciplinary interagency team redesigned the Massachusetts' family treatment program model. The new programs are larger than the former family treatment programs, with each new program having capacity to treat 11 to 15 families depending on family makeup.</p

Lee A James

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Substance Abuse Treatment Prevention and Policy

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Data on Substance Abuse Treatment Programs.

Do larger residential service delivery units have lower costs? Falls Church, VA: The Lewin Group;

GA: A hybrid cost function for outpatient nonmethadone substance abuse treatment facilities.

MR: Toward greater equity and efficiency in rate setting: the adult residential rehabilitation programs in Massachusetts. J Public Health Manag Pract

Organizational and client determinants of cost in outpatient substance abuse treatment.

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An investigation of scale effects in family substance abuse treatment programs

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