mhbounds
-> s = 2
|
out |
d | ||
|
0 |
1 |
Total | |
|
0 |
518 |
19 |
537 |
|
1 |
58 |
10 |
68 |
|
Total |
576 |
29 |
605 |
Since we have two strata (males and females) in the population we are going to use
the stratum option of mhbounds. Furthermore, we specify that we are interested in the
sensitivity of the results up to a situation where Γ = eγ = 8. Since the data is already
matched, we do not have to run any of the available matching routines in Stata. How-
ever, in order for mhbounds to work we have to define a treatment indicator (treated),
the weight assigned to each individual of both groups (weight) and furthermore identify
the individuals who are within the region of common support (support). To keep the
example simple, we assume equal weights and that all the individuals lie within the
common support region.
. mhbounds out, gamma(1 (1) 8) treated(d) weight(myweight) support(mysupport) s
> tratum(s)
Mantel-Haenszel (1959) bounds for variable out
|
Gamma |
Q_mh+ |
Q_mh- |
p_mh+ |
p_mh- |
|
1 |
4.18665 |
4.18665 |
.000014 |
-.--0-0-00--14 |
|
2 |
1.80445 |
7.05822 |
.035581 |
8.4e-13 |
|
3 |
.515322 |
9.09935 |
.303164 |
0 |
|
4 |
.074087 |
10.7675 |
.470471 |
0 |
|
5 |
.787917 |
12.2124 |
.215372 |
0 |
|
6 |
1.37611 |
13.5046 |
.084394 |
0 |
|
7 |
1.87943 |
14.6841 |
.030093 |
0 |
|
8 |
2.32133 |
15.7759 |
.010134 |
0 |
Gamma : odds of differential assignment due to unobserved factors
Q_mh+ : Mantel-Haenszel statistic (assumption: over-estimation of treatment eff
> ect)
Q_mh- : Mantel-Haenszel statistic (assumption: under-estimation of treatment ef
> fect)
p_mh+ : significance level (assumption: over-estimation of treatment effect)
p_mh- : significance level (assumption: under-estimation of treatment effect)
In a study free of hidden bias, i.e. where Γ = 1, the QMH test-statistic is 4.19 and
would constitute strong evidence that the use of allopurinol causes rash. If we have a
positive (unobserved) selection, in the sense that if those most likely to use the drug, also
have a higher probability to get rash, then the estimated treatment effects overestimate
the true treatment effect. The reported test-statistic QMH is then too high and should
be adjusted downwards. Hence, we will look at Q+mh and p+mh in the Stata output. The
upper bounds on the significance levels for Γ = 1, 2, and 3 are 0.0001, 0.036, and 0.30 (see
also Rosenbaum (2002, p.131)). The study is insensitive to a bias that would double the
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