Propensity score methods in observational studies [Elektronische Ressource] : estimating the marginal odds ratio / vorgelegt von Susanne Stampf

Sujets

• Mathematics

Informations

• Publié par: albert-ludwigs-universitat_freiburg
• Publié le: 01 janvier 2010
• Nombre de lectures: 31
• Langue: Deutsch
• Poids de l'ouvrage: 1 Mo

Extrait

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Propensity score methods in
observational studies - estimating the
marginal odds ratio
Dissertation zur Erlangung des Doktorgrades
der Mathematischen Fakulta¨t
der Albert-Ludwigs-Universita¨t Freiburg im Breisgau
vorgelegt von
Susanne Stampf
August 2010Dekan: Prof. Dr. Kay Ko¨nigsmann
1. Referent: Prof. Dr. Martin Schumacher
Institut fu¨r Medizinische Biometrie
und Medizinische Informatik
Albert-Ludwigs-Universita¨t Freiburg im Breisgau
Stefan-Meier-Str. 26
79104 Freiburg
2. Referent: Prof. Claudia Czado, Ph.D.
Technische Universita¨t Mu¨nchen
Zentrum Mathematik
Lehrstuhl fu¨r Mathematische Statistik
Parkring 13 (Zimmer 2.01.17)
85748 Garching
Datum der Promotion: 30.11.2010iii
Danke
Geho¨rt es doch zum guten Ton,
dass man sagt Dank’ an dieser Stelle,
ganz aufrichtig und nicht schnelle,
denn Undank ist der Welten Lohn!
Dank gebu¨hrt zuerst den Eltern,
sie waren da, wenn ich sie brauchte,
¨so dass manch‘ Arger schnell verrauchte.
Ich danke hier, ich danke gern!
Meiner Schwester sei nun gedankt,
sie versuchte stets, mich zu erheitern,
und zu bewahren vor dem Scheitern.
Dank dir hab ich viel Kraft getankt!
Auch den Großeltern sei Dank gesagt,
denn sie mich jederzeit moralisch unterstu¨tzten
und waren somit große Stu¨tzen
denn Motivation war oft gefragt!
Nun dank’ ich Freunden und Kollegen,
welch’ stets zu helfen wussten,
egal ob’s wollten oder mussten,
sie ließen mich niemals stehen im Regen!
Dem Chef gedankt sei nun von Herzen,
ein Chef, der stets zugegen war
und immer wußte, was geschah,
und wenn nicht, wir konnten dru¨ber scherzen!
Mit diesen Versen mo¨chte ich mich bei allen bedanken, die Anteil an der Entstehung und
Fertigstellung dieser Arbeit haben. Auch wenn es nicht immer so froh und heiter in den ver-
gangenen vier Jahren zugegangen ist, so hab ich doch viel gelernt, nicht nur fu¨r das wissen-
schaftliche Arbeiten, sondern insbesondere fu¨r das Leben.
Susanne StampfSummary
In the last three decades, the methodology of the propensity score has attracted increasing
attention for estimating treatment effects in observational studies. Propensity score methods
are designed to estimate causal marginal effects in contrast to regression techniques offering
the estimation of associational, conditional effects. The propensity score is defined as the pro-
bability of the assignment to a certain treatment given covariates and it can be used to mimic
data situations as in randomized experiments which in turn permits to estimate marginal treat-
ment effects without further covariate adjustments. In studies with binary outcome, the effect
is often described as an odds ratio and the marginal odds ratio is defined as the change
in odds of outcome if everybody versus nobody were treated. To estimate it, the popular
Mantel-Haenszel estimator has been used for stratified data, although it was shown that it is
an inappropriate estimator for the marginal odds ratio. We study recently proposed alterna-
tive estimators for the marginal odds ratio, one stratified for the propensity score, the other
derived from logistic regression. Additionally, we adapt the methodology of the logistic re-
gression based estimator to covariate adjustment by the propensity score. We also derive
corresponding variance estimators applying the Delta-method and parametric bootstrapping.
The applicability of the proposed estimators and their variance estimators will be illustrated
in two data examples. The first example deals with respiratory tract infections in children in
Germany. The aim is to detect the impact of exposure to a certain virus type on the severity
of respiratory tract infections. Heart diseases are of interest in the second data example,
investigating the short-term outcome after coronary bifurcation lesions. The effect of stent
types used in percutaneous catheter intervention to treat bifurcation lesions on the need for
target re-vascularization or the occurrence of death or an myocardial infarction is to ascertain.
Furthermore, simulation studies are carried out to investigate relative bias and coverage pro-
babilities of the marginal odds ratio estimators and the performance of the corresponding
variance estimators. Whenever outcome rates or regression based approaches are used,
reasonable performance of the marginal odds ratio estimators can be shown. The variance
estimators also perform well if specific assumptions are fulfilled. In contrast, the stratified
Mantel-Haenszel estimator is substantially biased in some situations due to problems of non-
collapsibility and thus is generally inappropriate for a reliable estimation of the marginal odds
ratio.
vContents
Summary v
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Overview and history of the propensity score 5
2.1 Causation vs. association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The role of observational studies . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 History of the propensity score . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3.1 The propensity score in general . . . . . . . . . . . . . . . . . . . . . . 9
2.3.2 The estimation of the propensity score . . . . . . . . . . . . . . . . . . . 10
2.3.3 The propensity score challenges the odds ratio . . . . . . . . . . . . . . 12
3 The propensity score and related methods 15
3.1 The propensity score . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Stratification by the propensity score . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Matching by the propensity score . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4 Inverse probability weighting by the propensity score . . . . . . . . . . . . . . . 23
3.5 Covariate adjustment by the propensity score . . . . . . . . . . . . . . . . . . . 25
4 A new approach for estimating the marginal odds ratio 29
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Estimators for the marginal odds ratio . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.1 Stratification by the propensity score . . . . . . . . . . . . . . . . . . . . 33
4.2.2 Logistic regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.3 Covariate adjustment by the propensity score . . . . . . . . . . . . . . . 35
4.2.4 Inverse probability weighting by the propensity score . . . . . . . . . . . 36
4.3 Variance estimators for marginal odds ratio estimators . . . . . . . . . . . . . . 36
viiviii CONTENTS
4.3.1 Stratification by the propensity score . . . . . . . . . . . . . . . . . . . . 39
4.3.2 Logistic regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.3 Covariate adjustment by the propensity score . . . . . . . . . . . . . . . 42
4.4 Estimators for the covariance between marginal outcome probabilities . . . . . . 43
4.4.1 Empirical covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4.2 Bootstrap resampling for covariance estimation . . . . . . . . . . . . . . 44
5 Simulation studies investigating properties of marginal odds ratio estimators 49
5.1 Simulation design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.1.1 Generating process for covariates and treatment . . . . . . . . . . . . . 50
5.1.2 Generating process for outcome . . . . . . . . . . . . . . . . . . . . . . 51
5.1.3 Generation of data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Analysis concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Regression based analysis . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.2 Propensity score analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.3 Simulation scheme for covariance estimation . . . . . . . . . . . . . . . 54
5.2.4 Summary of analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.1 Results regarding mean estimates and relative bias . . . . . . . . . . . . 57
5.3.2 Results regarding mean variance estimates and coverage probability . . 66
6 Application to real data examples 81
6.1 Lower respiratory tract infections in infants and children in Germany (PRI.De) . . 81
6.2 Bifurcations Bad Krozingen (BBK) registry: Analysis of short-term outcome
after coronary bifurcation lesions . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7 Discussion 97
A Glossary 103
B Supplemental material regarding the simulation study 107
B.1 Pre-defined parameters in simulation settings . . . . . . . . . . . . . . . . . . . 107
B.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
C Check of balance for covariates in data examples 141
C.1 Lower respiratory tract infections in infants and children in Germany (PRI.De) . . 141
C.2 Bifurcations Bad Krozingen (BBK) registry: Analysis of short-term outcome
after coronary bifurcation lesions . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Bibliography 147Chapter 1
Introductio