Abstract
In cohort studies the Mantel-Haenszel estimator OR̂
MH
is computed from sample data and is used as a point estimator of relative risk. Test-based
confidence intervals are estimated with the help of the asymptotic chi-squared distributed
MH-statistic χ2
MHS
. The Mantel-exten-sion-chi-squared is used as a test statistic for a dose-response
relationship. Both test statistics – the Mantel-Haenszel-chi as well as the Mantel-extension-chi
– assume homogeneity of risk across strata, which is rarely present. Also an extended
nonparametric statistic, proposed by Terpstra, which is based on the Mann-Whitney-statistics
assumes homogeneity of risk across strata.
We have earlier defined four risk measures RR
k
j
(k = 1,2,...,4) in the population and considered their estimates and the corresponding
asymptotic distributions. In order to overcome the homogeneity assumption we use the
δ-method to get “test-based” confidence intervals. Because the four risk measures
RR
k
j
are presented as functions of four weights gik
we give, consequently, the asymptotic variances of these risk estimators also as
functions of the weights g
ik
in a closed form. Approximations to these variances are given.
For testing a dose-response relationship we propose a new class of χ2(1)-distributed global measures Ĝk and the corresponding global χ2-test. In contrast to the Mantel-extension-chi homogeneity of risk across strata must
not be assumed. These global test statistics are of the Wald type for composite hypotheses.
The Mantel-extension-chi is a special case of the global-chi statistic and it is further
shown that the Mantel-extension-chi can be expressed as a special weighted Terpstra
statistic. Formulas for computing estimators of the global measures are provided.
Three elaborated examples with hypothetical data of varying structure show, that the
Mantel-extension-chi is systematically biased, generally overestimates the dose-response
relation and leads to wrong conclusions, when heterogeneity is present. This is consistent
with our theoretical considerations. In case of heterogeneity, when one wants to test
an association between exposure and effect, or a dose-response relationship, the new
global-χ2-test should be used in cohort studies.
Key-Words
Cohort Studies - Risk Measures - Heterogeneous Strata - Mantel-Haenszel-chi - Global-χ
2-Test - Dose-Response Relation