Sascha O. Becker and Marco Caliendo
and
Q-MH =
|Y1 - ΣS=1 -Es | - 0.5
/∕∑S=ι Var E
(6)
where Es and Var(Es) are the large sample approximations to the expectation and
variance of the number of successful participants when u is binary and for given γ.5
3 Syntax
mhbounds computes Mantel-Haenszel bounds to check sensitivity of estimated average
treatment effects on the treated.
mhbounds outcome if , gamma(numlist) treated(newvar) weight(newvar)
support(newvar) stratum(newvar) stratamat
4 Options
gamma(numlist) is a compulsory option and asks users to specify the values of Γ =
eγ ≥ 1 for which to carry out the sensitivity analysis. Estimates at Γ = 1 (no hidden
bias) are included in the calculations by default.
treated(varname) specifies the name of the user-provided treatment variable; If no
name is provided, mhbounds expects .treated from psmatch or psmatch2.
weight(varname) specifies the name of the user-provided variable containing the fre-
quency with which the observation is used as a match; if no name is provided, mhbounds
expects .weight from psmatch or psmatch2.
support(varname) specifies the name of the user-provided common support variable.
If no name is provided, mhbounds expects .support from psmatch or psmatch2.
stratum(varname) specifies the name of the user-provided variable indicating strata.
Aakvik (2001) notes that the Mantel-Haenszel test can be used to test for no treatment
effect both within different strata of the sample and as a weighted average between
strata. This option is particularly useful when used after stratification matching, using,
e.g. atts.
stratamat, in combination with stratum(varname) keeps in memory not only the
matrix outmat containing the overall/combined test statistics, but also the matrices
5. The large sample approximation of Es+ is the unique root of the following quadratic equa-
tion:
Ε2(eγ
N1s
Ns
1)
'—-
Es[(eγ
1)(N1s + Ys) + Ns] + eγ Ys N1s , with the addition of max(0, Ys +
≤ Es
placing eγ by e1γ
≤ min(Ys , N1s )) to decide which root to use.
is determined by re-
The large sample approximation of the variance is given by: V ar(Es) =
(ɪ +
Es
Ys
-Es
N1s
-Es
Ns
-Ys
I____ V1
N1s+Es√