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Kessler DP, Sage WM, Becker DJ. Impact of Malpractice Reforms on the Supply of Physician Services. JAMA. 2005;293(21):2618–2625. doi:10.1001/jama.293.21.2618
Context Proponents of restrictions on malpractice lawsuits claim that tort reform
will improve access to medical care.
Objective To estimate the effects of changes in state malpractice law on the supply
Design Differences-in-differences regression analysis that matched data on
the number of physicians in each state between 1985 and 2001 from the American
Medical Association’s Physician Masterfile with data on state tort laws
and state demographic, political, population, and health care market characteristics.
Main Outcome Measure Effect on physician supply of “direct” malpractice reforms
that reduce the size of awards (eg, caps on damages).
Results The adoption of “direct” malpractice reforms led to greater
growth in the overall supply of physicians. Three years after adoption, direct
reforms increased physician supply by 3.3%, controlling for fixed differences
across states, population, states’ health care market and political
characteristics, and other differences in malpractice law. Direct reforms
had a larger effect on the supply of nongroup vs group physicians, on the
supply of most (but not all) specialties with high malpractice insurance premiums,
on states with high levels of managed care, and on supply through retirements
and entries than through the propensity of physicians to move between states.
Direct reforms had similar effects on less experienced and more experienced
Conclusion Tort reform increased physician supply. Further research is needed to
determine whether reform-induced increases in physician supply benefited patients.
Debates about medical malpractice have recurring themes, with tort reformers
emphasizing the threat that liability crises pose to the cost and availability
of medical services and tort defenders emphasizing the importance of liability
to medical quality.1,2 Effects
on access to health care are of particular concern during “malpractice
crises,” when rising liability insurance premiums and uncertain coverage
are said to induce physicians to avoid high-risk patients or procedures, relocate
to other communities, or leave practice altogether. Even between such crises,
however, malpractice climate remains one of many factors determining how many
physicians enter the medical profession, what specialties they choose, and
where they practice.3
We investigated whether and how liability pressure affects long-term
trends in physician supply from state to state. We used data from the American
Medical Association’s Physician MasterFile on the number of physicians
in active practice in each state for each year from 1985 through 2001. We
modeled the number of physicians in a state at a point in time as a function
of state fixed effects, time fixed effects, time-varying state characteristics,
and the presence or absence of certain malpractice reforms. We divided liability-reducing
malpractice reforms into 2 types: reforms that directly reduce expected malpractice
awards and reforms that reduce awards only indirectly. We estimated the simple
average effect of liability-reducing reforms on physician supply. We also
estimated how the effect of reforms varies over time, across different health
care markets, and for different types of physicians.
We modeled the determinants of the supply of physician services in the
United States from 1985 to 2001. In each state s in
year t, we measured supply by the total number of
physicians in the state and by the number of physicians with 20 years or more
vs less than 20 years of experience (defined as the difference between the
current year and year of graduation from medical school). We began our analysis
in 1985, and we omitted 1990 from our analysis because physician-level data
were unavailable for years before 1985 and for 1990. In addition, we modeled
the decisions of 2 subpopulations of physicians whose supply decisions are
likely to be particularly sensitive to malpractice pressure. First, we measured
the supply of physicians in nongroup practice settings because these physicians
may bear a greater share of at least the financial burden of malpractice pressure.
The nongroup designation excluded physicians who reported that they were members
of a group, were members of a health maintenance organization, were hospital-based,
or were in public-sector practice but included physicians who reported that
they were members of a partnership. Second, we measured the supply of physicians
in 5 “high-risk” specialties: obstetrics/gynecology, surgery (including
surgical subspecialties), anesthesiology, emergency medicine, and radiology.
These specialties paid the highest reported malpractice premiums in 1994,
a year in the middle of our study period for which comprehensive premium data
by specialty were available.4
We modeled the supply of care as a function of state and year fixed
effects (αs and θt), the natural log of the population of state s in year t (Pst),
the political parties of the governor and each house of the legislature of
state s in year t (Wst), the number of residency programs and the
number of residents per capita in state s in year t (R1st and R2st, respectively, with Rst defined as the 2-element vector containing R1st and R2st), managed care
enrollment per capita in state s at year t (Mst), and state malpractice
Our models identified the effect of state malpractice laws by comparing
the change in physician supply in states that altered their laws between 1986
and 2001 to the change in supply in states that did not. As in previous work
by one of us (D.P.K.), this involved using differences-in-differences between
reforming and nonreforming states to identify effects.
Our differences-in-differences approach has advantages and disadvantages.
By identifying the effect of interest based only on states that changed their
laws between 1986 and 2001, we can control completely for fixed differences
between states and for national trends that affect all states, as well as
for the time-varying characteristics of states affecting physician supply
that are most likely to be correlated with states’ propensity to adopt
legal reforms. However, we cannot assess the impact of reforms adopted in
1985 or earlier. For example, the effect of a reform adopted in 1985 (that
remained in force through 2001) would be indistinguishable from other fixed
differences between states.
We categorized state malpractice laws according to the presence of 2
types of reforms: reforms that directly reduce expected malpractice awards
and reforms that reduce awards only indirectly (Table 1). “Direct” reforms include caps on damage awards,
abolition of punitive damages, abolition of mandatory prejudgment interest,
and collateral source rule reforms. “Indirect” reforms include
caps on attorney contingency fees, mandatory periodic payment of future damages
awards, joint-and-several liability reforms, statute of limitations reforms,
and patient compensation funds. We chose to group reforms into these 2 categories
because several studies in the literature have found that reforms that directly
reduce expected malpractice awards have the largest effect on malpractice
pressure and physician behavior.6-8
We defined our 2 law variables as follows. If a state adopted any direct
reform between 1986 and 2001, then we set the binary variable L1st = 1 for the year of adoption t and all years subsequent to t; L1st = 0 for all years before t.
If, after adoption of reforms, a state repealed all its direct reforms between
1986 and 2001, then we reset the binary variable L1st = 0 for the year of repeal t and all years subsequent to t; L1st = 1 for the year of adoption and all years after
adoption but before t. For all other states, L1st = 0 for all years. We defined
L2st similarly for indirect reforms. Lst was defined as the 2-element vector containing
L1st and L2st.
We began by estimating Poisson models of the following form:
where ln(λst) = αs + θt + βPst + Wstγ
+ Rstρ + Mstδ + Lstφ. Although
we were unable to distinguish the effect of reforms adopted in 1985 or earlier
from differences caused by other factors influencing either the level or growth
of physician supply, we estimated different baseline time trends θt for states adopting direct and indirect reforms
before 1986 (which generally were adopted before 1980) and for nonadopting
states to impose as few constraints as possible on the empirical model. Because
it is impossible to consistently estimate the fixed effects in a nonlinear
model of this form, we conditioned them out of the likelihood function according
to the method described by Hausman et al.9 In
this model, E(Nst | Pst, Wst, Rst, Lst) = λst, so dlnE(Nst)/dLst = φ. In other words, φ
represents the approximate percentage change in the supply of physicians that
results from tort reform. We calculated the SE of φ, allowing the number
of physicians to be correlated within a state over time; we assumed only that
the number of physicians is independent across states.10
We also estimated 3 sets of expanded Poisson models. The first set of
models estimated separately the long-term and short-term effects of reforms.
In these models, we denoted the existence of direct reforms by using 2 binary
variables. If a state adopted any direct reform between 1986 and 2001, then
we set the binary variable L1st = 1
for the year of adoption t, t +1, and t +2; L1st = 0
for all years before t. We set the binary variable
L2st = 1 for all years after t +2; L2st = 0
for all years through t +2. If, after adoption, a
state repealed all its direct reforms between 1986 and 2001, then we reset
the binary variables L1st and L2st = 0 for the year of repeal t and all years after t; L1st = 1 for the year of adoption and the 2 subsequent
years but before t; L2st = 1
for all years after the second year after adoption but before t. For all other states, L1st and
L2st = 0 for all years. We defined
L3st and L4st similarly
for indirect reforms. Lst was defined
as the 4-element vector containing L1st,
The second set of models allowed the effect of law reforms to vary in
high vs low managed care environments. As discussed in previous work by one
of us (D.P.K.), reductions in liability that reduce defensive practices in
a conventional tort and insurance environment may be either more or less beneficial
in an environment that is influenced by managed care or may even be socially
harmful.11 In these models, we defined ln(λst) = αs + θt + βPst + Wstγ
+ Rstρ + Mstδ + Lstφ + Mst*Lstϕ,
where ϕ is the differential effect of reforms in high managed care environments.
The third set of models decomposed the effect of reforms into 2 parts:
the part caused by the movement of existing physicians between states and
the part caused by the entry of new and the retirement of existing physicians.
Identifying how much of the net effect of reforms is due to moves vs entries
and retirements is important because the welfare consequences to the country
as a whole of aggregate changes in supply (through entries and retirements)
are different from the consequences of reallocation of physicians across states.
To do this, we defined a “moving” physician between year t and year t +1 as one who was
in active practice in t and t +1 but in different states. We defined an “entering” physician
as one who was in active practice in t +1 but not
in t (including immigrating physicians); we defined
a “retiring” physician as one who was in active practice in t but not in t +1 (including emigrating
We used data from 4 sources. First, we used data from the American Medical
Association Physician MasterFile on the number of physicians involved in direct
patient care. The Physician MasterFile represents the most comprehensive data
available on physician supply for the years of our study.12 Second,
we used data on malpractice laws and state political characteristics from
Kessler and McClellan,5 updated through 2001. Third, we used data
on the number of residency programs and the number of residents per capita
in each state for each year from 1985-2001 from the National Graduate Medical
Education Census. Fourth, we used data on state managed care enrollment from
InterStudy Publications. Enrollment rates per capita were calculated by dividing
the number of enrollees (exclusive of preferred provider organization members
and supplementary Medicare enrollees) by the population.
Table 2 previews our basic differences-in-differences
analysis by reporting unadjusted 1985-2001 percentage changes in the number
of physicians from states adopting and not adopting reforms during our study
period. Column 5 of Table 2 presents
the percentage change in physician supply in states with direct reforms only
compared with nonadopting states; column 6 presents the change in supply in
states with indirect reforms only compared with nonadopting states; and column
7 presents the change in supply in states with direct and indirect reforms
compared with nonadopting states. Column 5 of the first row of Table 2 shows our basic result: physician supply increased more
rapidly, by 8.2%, in states adopting direct reforms only vs no reforms.
Trends in physician supply differed by specialty. On an unadjusted basis,
states with direct reforms only vs no reforms showed less-than-average differential
increases in the supply of physicians in the 5 high-malpractice-premium specialties
(with surgeons reporting no differential increase at all), although states
with direct and indirect reforms showed greater-than-average differential
increases in the supply of 2 of the 5 high-premium specialties, anesthesiology
(12.3%) and radiology (11.1%). In contrast, overall physician supply increased
3.4% less rapidly in states with indirect reforms only.
Malpractice reform increased growth more in the supply of physicians
with 20 or more years of experience (as measured by years since completion
of medical school) than growth in the supply of physicians overall. The supply
of experienced physicians in states adopting direct reforms only increased
by 87.8% from 1985-2001 compared to an increase in supply of 69.1% in nonadopting
states, a difference of 18.7%. This result persisted for all of the high-malpractice-pressure
specialties. The number of nongroup physicians shrank during the period. The
unadjusted differences-in-differences effect of direct reforms on nongroup
physicians was slightly smaller than the effect on all physicians.
These simple comparisons do not account for differences in trends in
population, states’ market and political characteristics, and differences
in malpractice law that predate the start of our study period. We explore
the importance of these factors in the regression analysis that follows.
Table 3 presents estimates of
the effects of direct and indirect reforms on state/year counts of the number
of physicians, holding all else constant, from our basic econometric model.
All models underlying the results in Table 3 and
subsequent tables are based on a sample of size 800 (50 states × 16
years; 1985-2001, except 1990). States adopting direct reforms during the
study period experienced statistically significantly greater increases in
the supply of physicians than states that did not. In particular, physician
supply in direct-reform states expanded by approximately 2.4% more during
the study period than did supply in nonreform states, all else being held
constant (SE, 0.24%). Supply in indirect reform states, in contrast, contracted
by a smaller amount in absolute value (approximately 1.29%; SE, 0.24%). A
1% increase in managed care enrollment per capita led to a 0.13% decrease
in physician supply (SE, 0.01%). The effect of direct reforms on the supply
of nongroup physicians was substantially larger than the effect on all physicians
(approximately 3.9% compared with 2.4%).
Does malpractice climate have a greater effect on nongroup physicians
because they can transition out of nongroup status or because physicians who
are not in groups are more likely to move or retire (and not be replaced by
physicians entering practice)? To distinguish between these possibilities,
we reestimated the model underlying Table 3 but
limited the universe of physicians to those who were in the sample and in
the same state for all of the study years, thereby excluding all moves, entries,
and retirements. By using the number of nongroup physicians in every state/year
as the dependent variable, we found that direct reforms increased growth in
physician supply by a smaller amount, leading us to conclude that the differential
responsiveness of the supply of nongroup physicians was the result of nongroup
becoming group physicians in nonreform states (data not shown).
Table 3 reports 3 other key findings.
First, direct reforms had a similar effect on the supply of less vs more experienced
physicians. Second, the net effect of indirect reforms on physician supply
masked 2 competing effects: a negative effect on the supply of less experienced
physicians and a positive effect on the supply of more experienced physicians.
Third, the effect of managed care is larger for less experienced physicians.
Table 4 presents estimates of
the effects of reforms on the supply of nongroup physicians in 5 “high-risk”
specialties. We restricted the analysis to nongroup physicians to isolate
the effect of specialty. The proportion of physicians employed in a group
vs nongroup setting differs by specialty and may affect the incidence of malpractice
pressure. Thus, differences by specialty in the effects of malpractice pressure
on the supply of group and nongroup physicians together may represent a combination
of the effect of specialty and differences by specialty in the proportion
of physicians employed in a group setting. The point estimates of direct reforms
for 3 of the 5 high-premium specialties exceeded the average effect of reforms
for all nongroup physicians. For example, direct reforms led to increased
growth in the supply of emergency medicine physicians of approximately 11.5%,
almost 3 times the magnitude of the average nongroup effect of 3.9%. Effects
for anesthesiology and radiology were also larger than the average effect,
although the effect for radiology was statistically significant only at the
10% level (P = .10). The effect of direct reforms
on the supply of surgeons was smaller than the average effect and statistically
nonsignificant (P = .15).
Table 5 presents estimates of
the long-run vs short-run effects of reforms and shows that reforms take time
to reach their equilibrium impact. The magnitude of the effect of direct reforms
long after their adoption is always greater than the magnitude of their effect
soon after adoption, which is consistent with the estimates representing causal
effects of law reforms rather than differences in trends in unobserved characteristics
of states. For example, states adopting direct reforms experienced small and
nonsignificant immediate changes in physician supply but approximately 3.3%
greater growth in physician supply 3 or more years after adoption of reforms
compared with states that did not. The group/nongroup and less experienced/more
experienced effects of direct reforms followed the same pattern, with significantly
greater magnitudes 3 or more years after adoption than within 2 years of adoption.
Table 6 presents estimates of
the effect of reforms and managed care enrollment on physician supply, allowing
the effect of reforms to vary in high- and low-managed care environments. Table 6 shows that direct reforms had a statistically
significantly greater effect on physician supply in high care vs low managed
care states (P<.001). High levels of managed care
either increase the level of malpractice pressure that physicians bear or
increase the disutility of a given amount of malpractice pressure. The opposite
was true of indirect reforms for physicians in aggregate and for less experienced
Table 7 presents estimates of
the effect of reforms and managed care enrollment on physician supply, decomposing
changes in supply into 1 of 2 types: retirements or entries and moves. Table 7 shows that virtually all the effect of
direct reforms was due to increased entry and decreased retirement of physicians
in reforming states rather than the movement of existing physicians from nonreforming
to reforming states. The positive effect of direct reforms on entry (ie, on
less experienced physicians) was smaller in magnitude than the negative effect
of direct reforms on retirements (ie, on more experienced physicians). The
positive effect of indirect reforms on the supply of physicians through moves
was counterbalanced by a substantial negative effect of indirect reforms on
entry, which is consistent with the results in Table 3; indirect reforms are more highly valued by physicians who
have been in practice compared with those who have not.
We estimated several alternative models (not included in the tables)
to further investigate how malpractice liability affects physician supply.
First, we estimated a model that included a separate law variable for states
that adopted both direct and indirect reforms. Adopting both direct and indirect
reforms had a small (<0.01%) and statistically insignificant effect on
supply (P = .99) over and above the independent effects.
Second, we estimated a model that allowed the effect of caps on damages to
differ from the effect of other direct reforms. Caps on damages have a statistically
significantly larger effect than all other direct reforms (3.0% compared with
0.64%; χ21 testing equality of effects = 25.7).
Third, we estimated models that allowed the effect of managed care to be nonlinear
and that were based on a subset of the years in our full analysis. Although
the estimated effect of direct reforms was robust to these specification changes,
the estimated effects of indirect reforms and managed care were not.
In this study, we developed new empirical evidence on the relationship
between malpractice climate and the supply of medical care. We compared trends
in the supply of physicians in states that adopted and did not adopt law reforms
limiting malpractice liability between 1985 and 2001. We found greater growth
in physician supply in states that adopted reforms directly limiting liability
than in states that did not. This basic result accords with other work published
by Hellinger and Encinosa.13 In our study,
physician supply in direct-reform states expanded by 2.4% more during the
study period than did supply in nonreform states, controlling for fixed differences
across states, population, market and political characteristics, and other
differences in malpractice law. Direct reforms have a larger effect on supply
3 or more years after their adoption (3.3%) compared with 2 or fewer years
after adoption (−0.01%).
Our estimates of the effect of malpractice climate on physician supply
were consistent with previous research finding that physicians practice “defensive
medicine,” changes in practice based on fear of litigation that have
little or no medical benefit for patients.5,11,13-16 Defensive
medicine includes declining to supply care that has medical value to reduce
the risk of malpractice liability. It can manifest itself both in across-the-board
decisions by physicians to refrain from performing certain procedures or treating
certain diseases and in case-by-case decisions not to treat particular patients.
Avoidance behaviors of this sort have received significantly less academic
attention than defensive medicine manifested as excessive testing or unnecessary
Malpractice climate is one of many determinants of the physician workforce,
which accounts for its relatively modest impact in our study. Overall supply
and the specialty and geographic distributions of physicians may be modified
at several junctures: initial choice of career or specialty, retraining, relocation,
and retirement. These decisions are influenced by various economic, experiential,
and nonexperiential factors, which themselves are products of individual,
community, and market characteristics, as well as government policies.1,17-23 To
put our estimates in context, Rizzo and Blumenthal24 found
that a 1% increase in physicians’ wages led to a 0.2% to 0.3% increase
in hours worked. Thus, the 3.3% increase in physician supply from direct malpractice
reform is roughly equivalent to the increase in labor supply that would result
from an 11% increase in wages (11 = 3.3/0.3).
Our results illuminate the mechanisms by which malpractice liability
reduces growth in physician supply. Physician characteristics such as practice
structure, specialty, payer mix, and stage of career mediate the relationship
between malpractice climate and supply. In our study, the estimated effect
of direct reforms was greater among physicians who practice in nongroup settings,
which arose out of the movement of physicians into group settings in nonreform
states. This is consistent with the lesser ability of smaller practices to
spread liability insurance costs among many physicians, cushion premium volatility
with high patient volume, or share risk with hospitals or other health care
Malpractice insurance is priced according to location and specialty
rather than individual physician quality or loss experience.25,26 All
else being equal, one therefore would expect greater supply effects in specialties
known to pay the highest malpractice premiums. Our point estimates show that
reforms had a greater-than-average effect on the supply of physicians in 3
of 5 specialties paying the highest malpractice premiums. The effect of reforms
on the supply of obstetrics and gynecology and general surgical practitioners
were smaller than, although not statistically distinguishable from, the average
In our study, direct reforms had a greater effect on retirements and
entries to the profession than on the propensity of physicians to move between
states. This finding supports the argument that the supply effects of direct
reforms will persist, at least to some degree, even if all states adopt reforms.
The positive effects of direct reforms on physician supply are greater
in high- vs low managed care states. The disutility to physicians of managed
care and malpractice pressure together may lead them to alter their careers
more than either factor alone, although we cannot determine what aspect of
the situation is the proverbial “last straw.” Because managed
care enrollment rose throughout the 1980s and 1990s, effects measured in high
managed care states may be a better approximation of future consequences of
malpractice reform than effects in low managed care states.
Malpractice reform affects the organization of physician services beyond
simply increasing supply. We found that the differential responsiveness of
the supply of nongroup physicians appears to be the result of nongroup becoming
group physicians in nonreform states. Put another way, liability pressure
is a contributing factor to the increasing corporatism of US medicine. We
also found that indirect reforms increased supply growth of more experienced
physicians but decreased supply growth of less experienced physicians. This
change would occur if more experienced physicians valued indirect reforms
more highly than their less experienced counterparts, and the decline in earnings
or partnership opportunities associated with a greater supply of more experienced
physicians in states with indirect reforms discouraged entry of new graduates.
Further investigation of these effects is needed.
Policy makers should be cautious about the prescriptive implications
of our analysis. The goals of our study were narrowly defined, and our approach
has significant limitations. First, although we controlled for fixed differences
between states, national trends that affected all states, and time-varying
characteristics of states, we were unable to assess the impact of reforms
for states that adopted them before 1986. On one hand, if tort reform that
originated in the malpractice crisis of the 1970s (eg, California’s
Medical Injury Compensation Reform Act) has persistent supply effects, then
our study will understate differences between reform and nonreform states.
On the other hand, supply gains from reforms adopted after the first wave
may be more representative of potential future effects.
Second, we cannot exclude the possibility that the increase in physician
supply we observed in states adopting reforms during our study period was
simply a consequence of those states having more room for growth, because
those states had fewer physicians at baseline. We controlled for differences
in baseline levels of supply but not for differences in baseline growth rates
Third, endogeneity bias may have led us either to understate or overstate
the effect of reforms. If decreases in physician supply lead states to adopt
reforms, endogeneity bias would lead us to understate the effect of reforms.
On the other hand, if increases in physician supply and the adoption of reforms
are both caused by an unobserved factor, such as population preferences for
litigation and medical services, endogeneity bias would lead us to overstate
the effect of reforms.
Fourth, we estimated only the total effect of law reforms on physician
supply. We did not separately identify the effect of malpractice pressure
through which insurance premiums, the frequency of claims or awards, the amount
of awards, and the nonfinancial impact of litigation would require significant
additional econometric assumptions.27 Because
we did not make these assumptions, our results are more robust but less detailed.
Fifth, we estimated the effect of law reforms only on the number of
physicians, not on the total hours worked by physicians. If hours worked per
physician decrease with the number of physicians, then our estimates overstate
the total effect of reforms.
Sixth, we did not assess the impact of malpractice-induced supply changes
on cost, quality, or access. Health policy analysts do not agree on the welfare
implications of having more health care providers.28 Reform-induced
expansions in supply could either decrease or increase health care costs:
competition among health care providers might lead to lower prices and less
wasteful care, or additional physicians might induce demand for their own
services beyond the point at which they are medically necessary. Similarly,
increased supply could lead to higher quality through competition but could
also lead to lower quality if the physicians who exit as a result of malpractice
pressure are disproportionately less skilled. Finally, access to health care
depends on patient characteristics and local distributions of specialists,
as well as on statewide aggregate numbers of providers, and may differ between
acute malpractice crises and noncrisis periods. In one of the few recent studies
of this topic, Dubay et al29 reported that
malpractice pressure results in a small but significant reduction in access
to prenatal care.
Finally, our research does not address the fact that there are tradeoffs
between the potential benefits of direct reforms, such as greater growth in
physician supply, and their potential costs, such as reduced compensation
for medical error.30 Health policy scholars
have proposed alternative ways of improving the overall performance of the
malpractice system.27,31-33 Empirical
investigation of these approaches is an important topic for future research.
Corresponding Author: William M. Sage, MD,
JD, Columbia Law School, 435 W 116th St, New York, NY 10027 (email@example.com).
Author Contributions: Dr Kessler had full access
to all of the data in the study and takes responsibility for the integrity
of the data and the accuracy of the data analysis.
Study concept and design: Kessler, Sage.
Acquisition of data: Kessler.
Analysis and interpretation of data: Kessler,
Drafting of the manuscript: Kessler, Sage.
Critical revision of the manuscript for important
intellectual content: Kessler, Sage, Becker.
Statistical analysis: Kessler, Becker.
Obtained funding: Sage.
Administrative, technical, or material support:
Study supervision: Kessler.
Financial Disclosures: None reported.
Funding/Support: This work was supported by
the Project on Medical Liability in Pennsylvania funded by The Pew Charitable
Trusts (grant 2002-00279).
Role of the Sponsor: The Pew Charitable Trusts
had no role in the design or conduct of the study; analysis and interpretation
of data; or preparation, review, or approval of the manuscript.
Acknowledgment: We thank Columbia student Nathaniel
B. Chase for research assistance.
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