Quality & Quantity 36: 1–16, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
A Bootstrap Method To Test If Study Dropouts Are
NORBERT SCHMITZ and MATTHIAS FRANZ
Clinic and Institute for Psychosomatic Medicine and Psychotherapy, Heinrich-Heine-University,
Bergische Landstr. 2, H19 D-40605 Dusseldorf, Germany
Abstract. Withdrawing from a longitudinal investigation is a common problem in epidemiological
research. This paper describes a nonparametric method, based on a bootstrap approach, for assessing
whether dropouts are missed at random. The basic idea is to compare scores of dropouts and non-
dropouts at different assessments using a weighted nonparametric test statistic.
A Monte Carlo investigation evaluates the comparative power of the test to violations from
populations normality, using three commonly occurring distributions. The test proposed here is more
powerful than the parametric counterpart under distributions with extreme skews.
The method is applied to a longitudinal community-based study investigating mental disorders.
It is found that dropouts did not differ from the other subjects with respect to two psychological
variables, although chi-square tests gave some other impressions.
Key words: bootstrap, dropouts, longitudinal data, mental disorders, repeated measures, simulation
Missing data is a common problem in longitudinal investigations, occurring at both
the item and the subject level. The term ‘dropout’ is a special case of missing data
describing a subject who prematurely terminates participation in the study. With-
drawing from a study may be due to noncompliance, adverse side effects, lack of
effect or unwillingness to continue participation. In epidemiological cohort studies,
particularly those involving disease incidence and long follow-up periods, the loss
of subjects may be because of migration, death and the disease itself. Attrition of
the study population can lead to distortion of results. It is therefore important to
know if dropouts cause a sample selection bias, threatening the internal or external
validity of results and leading to systematic bias (e.g., Berk, 1983). For example, in
a longitudinal community-based study investigating mental disorders (Schepank,
1987; Franz et al., 1999), 72 out of 600 subjects dropped out in the second wave
four years later and an additional 195 subjects were lost to 10 year follow up.
The question is whether the dropouts are comparable with those who completed
the study with respect to psychological variables. For example, if dropouts are
characterized by a higher level of psychological impairment, we have a selection