<s>
Meta-regression	B-General_Concept
is	O
defined	O
to	O
be	O
a	O
meta-analysis	O
that	O
uses	O
regression	O
analysis	O
to	O
combine	O
,	O
compare	O
,	O
and	O
synthesize	O
research	O
findings	O
from	O
multiple	O
studies	O
while	O
adjusting	O
for	O
the	O
effects	O
of	O
available	O
covariates	O
on	O
a	O
response	O
variable	O
.	O
</s>
<s>
A	O
meta-regression	B-General_Concept
analysis	O
aims	O
to	O
reconcile	O
conflicting	O
studies	O
or	O
corroborate	O
consistent	O
ones	O
;	O
a	O
meta-regression	B-General_Concept
analysis	O
is	O
therefore	O
characterized	O
by	O
the	O
collated	O
studies	O
and	O
their	O
corresponding	O
data	O
sets	O
—	O
whether	O
the	O
response	O
variable	O
is	O
study-level	O
(	O
or	O
equivalently	O
aggregate	O
)	O
data	O
or	O
individual	O
participant	O
data	O
(	O
or	O
individual	O
patient	O
data	O
in	O
medicine	O
)	O
.	O
</s>
<s>
A	O
data	O
set	O
is	O
aggregate	O
when	O
it	O
consists	O
of	O
summary	O
statistics	O
such	O
as	O
the	O
sample	O
mean	O
,	O
effect	B-Application
size	I-Application
,	O
or	O
odds	O
ratio	O
.	O
</s>
<s>
A	O
meta-regression	B-General_Concept
can	O
be	O
classified	O
in	O
the	O
same	O
way	O
—	O
meta-regression	B-General_Concept
and	O
network	O
meta-regression	B-General_Concept
—	O
depending	O
on	O
the	O
number	O
of	O
distinct	O
treatments	O
in	O
the	O
regression	O
analysis	O
.	O
</s>
<s>
Meta-analysis	O
(	O
and	O
meta-regression	B-General_Concept
)	O
is	O
often	O
placed	O
at	O
the	O
top	O
of	O
the	O
evidence	O
hierarchy	O
provided	O
that	O
the	O
analysis	O
consists	O
of	O
individual	O
participant	O
data	O
of	O
randomized	O
controlled	O
clinical	O
trials	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
plays	O
a	O
critical	O
role	O
in	O
accounting	O
for	O
covariate	O
effects	O
,	O
especially	O
in	O
the	O
presence	O
of	O
categorical	O
variables	O
that	O
can	O
be	O
used	O
for	O
subgroup	O
analysis	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
covers	O
a	O
large	O
class	O
of	O
models	O
which	O
can	O
differ	O
depending	O
on	O
the	O
characterization	O
of	O
the	O
data	O
at	O
one	O
's	O
disposal	O
.	O
</s>
<s>
There	O
is	O
generally	O
no	O
one-size-fits-all	O
description	O
for	O
meta-regression	B-General_Concept
models	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
sample	O
proportion	O
p̂tk	O
can	O
be	O
logit-transformed	O
or	O
arcsine-transformed	B-General_Concept
prior	O
to	O
meta-regression	B-General_Concept
modeling	O
,	O
i.e.	O
,	O
ytk	O
logit( p̂tk	O
)	O
or	O
ytk	O
arcsin( p̂tk	O
)	O
.	O
</s>
<s>
Likewise	O
,	O
Fisher	B-Algorithm
's	I-Algorithm
z-transformation	I-Algorithm
can	O
be	O
used	O
for	O
sample	O
correlations	O
,	O
i.e.	O
,	O
ytk	O
arctanh(rtk )	O
.	O
</s>
<s>
Note	O
that	O
if	O
a	O
meta-regression	B-General_Concept
is	O
study-level	O
,	O
as	O
opposed	O
to	O
arm-level	O
,	O
there	O
is	O
no	O
subscript	O
t	O
indicating	O
the	O
treatment	O
assigned	O
for	O
the	O
corresponding	O
arm	O
.	O
</s>
<s>
This	O
ultimately	O
translates	O
to	O
a	O
choice	O
between	O
fixed-effect	O
meta-regression	B-General_Concept
and	O
random-effect	O
(	O
rigorously	O
speaking	O
,	O
mixed-effect	O
)	O
meta-regression	B-General_Concept
.	O
</s>
<s>
Fixed-effect	O
meta-regression	B-General_Concept
reflects	O
the	O
belief	O
that	O
the	O
studies	O
involved	O
lack	O
substantial	O
difference	O
.	O
</s>
<s>
An	O
arm-level	O
fixed-effect	O
meta-regression	B-General_Concept
is	O
written	O
as	O
ytk	O
xtkβ	O
+	O
ɛtk	O
.	O
</s>
<s>
The	O
terms	O
random-effect	O
meta-regression	B-General_Concept
and	O
mixed-effect	O
meta-regression	B-General_Concept
are	O
equivalent	O
.	O
</s>
<s>
Mixed-effect	O
meta-regression	B-General_Concept
includes	O
a	O
random-effect	O
term	O
in	O
addition	O
to	O
the	O
fixed	O
effects	O
,	O
suggesting	O
that	O
the	O
studies	O
are	O
heterogeneous	O
.	O
</s>
<s>
Random	O
effects	O
in	O
meta-regression	B-General_Concept
are	O
intended	O
to	O
reflect	O
the	O
noisy	O
treatment	O
effects	O
—	O
unless	O
assumed	O
and	O
modeled	O
otherwise	O
—	O
which	O
implies	O
that	O
the	O
length	O
of	O
the	O
corresponding	O
coefficient	O
vector	O
γk	O
should	O
be	O
the	O
same	O
as	O
the	O
number	O
of	O
treatments	O
included	O
in	O
the	O
study	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
has	O
been	O
employed	O
as	O
a	O
technique	O
to	O
derive	O
improved	O
parameter	O
estimates	O
that	O
are	O
of	O
direct	O
use	O
to	O
policymakers	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
provides	O
a	O
framework	O
for	O
replication	O
and	O
offers	O
a	O
sensitivity	O
analysis	O
for	O
model	O
specification	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
models	O
can	O
be	O
extended	O
for	O
modeling	O
within-study	O
dependence	O
,	O
excess	O
heterogeneity	O
and	O
publication	O
selection	O
.	O
</s>
<s>
These	O
heterogeneity	O
tests	O
also	O
do	O
not	O
conclude	O
that	O
there	O
is	O
no	O
heterogeneity	O
even	O
when	O
they	O
come	O
out	O
insignificant	O
,	O
and	O
some	O
researchers	O
advise	O
to	O
opt	O
for	O
mixed-effect	O
meta-regression	B-General_Concept
at	O
any	O
rate	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
is	O
a	O
statistically	O
rigorous	O
approach	O
to	O
systematic	O
reviews	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
analyses	O
have	O
been	O
seen	O
in	O
studies	O
of	O
price	O
and	O
income	O
elasticities	O
of	O
various	O
commodities	O
and	O
taxes	O
,	O
productivity	O
spillovers	O
on	O
multinational	O
companies	O
,	O
and	O
calculations	O
on	O
the	O
value	O
of	O
a	O
statistical	O
life	O
(	O
VSL	O
)	O
.	O
</s>
<s>
Other	O
recent	O
meta-regression	B-General_Concept
analyses	O
have	O
focused	O
on	O
qualifying	O
elasticities	O
derived	O
from	O
demand	O
functions	O
.	O
</s>
<s>
In	O
energy	O
conservation	O
,	O
meta-regression	B-General_Concept
analysis	O
has	O
been	O
used	O
to	O
evaluate	O
behavioral	O
information	O
strategies	O
in	O
the	O
residential	O
electricity	O
sector	O
.	O
</s>
<s>
In	O
water	O
policy	O
analysis	O
,	O
meta-regression	B-General_Concept
has	O
been	O
used	O
to	O
evaluate	O
cost	O
savings	O
estimates	O
due	O
to	O
privatization	O
of	O
local	O
government	O
services	O
for	O
water	O
distribution	O
and	O
solid	O
waste	O
collection	O
.	O
</s>
<s>
Meta-regression	B-General_Concept
is	O
an	O
increasingly	O
popular	O
tool	O
to	O
evaluate	O
the	O
available	O
evidence	O
in	O
cost-benefit	O
analysis	O
studies	O
of	O
a	O
policy	O
or	O
program	O
spread	O
across	O
multiple	O
studies	O
.	O
</s>
