The Journal of Bone and Joint Surgery (American) 83:1650-1655 (2001)
© 2001 The Journal of Bone and Joint Surgery, Inc.
Type-II Error Rates (Beta Errors) of Randomized Trials in Orthopaedic Trauma
Heather V. Lochner, MSc,
Mohit Bhandari, MDMSc and
Paul Tornetta, III, MD
Investigation performed at Boston Medical Center, Boston, Massachusetts
Heather V. Lochner, MSc
Paul Tornetta III, MD
Department of Orthopaedic Surgery, Boston Medical Center, 850
Harrison Avenue, Dowling 2 North, Boston, MA 02118. E-mail address
for P. Tornetta III: ptornetta{at}pol.net
Mohit Bhandari, MD, MSc
Department of Clinical Epidemiology and Biostatistics, McMaster
University Health Sciences Centre, 1200 Main Street West, Room 2C12,
Hamilton, ON L8N 3Z5, Canada. E-mail address: bhandari@sympatico.ca
The authors did not receive grants or outside funding in support
of their research or preparation of this manuscript. They did not
receive payments or other benefits or a commitment or agreement
to provide such benefits from a commercial entity. No commercial
entity paid or directed, or agreed to pay or direct, any benefits
to any research fund, foundation, educational institution, or other
charitable or nonprofit organization with which the authors are
affiliated or associated.
Background: Although an investigator may limit
bias through randomization, concealment of patient allocation, and
blinding, the results of randomized trials may be less convincing
when the sample size is not sufficiently large to reveal a true
difference between treatment groups. When the sample size is small, randomized
trials are subject to beta errors (type-II errors)—that
is, the probability of concluding that no difference between treatment
groups exists when, in fact, there is a difference. The purpose
of this study of randomized trials involving fracture care published
between 1968 and 1999 was twofold: (1) to evaluate type-II error
rates and study power (1 - β) for the primary outcomes
and (2) to identify whether investigators clearly identified the
primary and secondary outcomes.
Methods: To be eligible, studies were required to
(1) be published in English, (2) be described as a randomized trial,
(3) involve the care of adult patients with fractures, treated either
operatively or nonoperatively, and (4) contain sufficient outcome
information to enable study power to be calculated. Computer database
searches were performed independently by two investigators to identify
all potentially relevant study titles. Additional strategies to
identify articles included (1) hand searches of selected orthopaedic
journals from 1989 to 1999, (2) searches of the bibliographies of
potentially relevant articles, and (3) review by content experts
to identify missing studies. For each study, a standard power calculation
was performed on the primary and secondary outcomes. For those studies
in which the primary outcome was not explicitly reported, the most
clinically relevant measure was chosen by consensus. Acceptable
study power was agreed a priori to be 80% (type-I
error of £ 0.20).
Results: We identified 620 potentially relevant
citations from MEDLINE, of which only 187 were potentially eligible.
We identified nine more articles with other searches, and application
of the eligibility criteria to the 196 articles eliminated seventy-nine.
Thus, we analyzed 117 studies in which a total of 19,942 patients
with orthopaedic trauma had been randomized. Sample sizes ranged
from ten to 662 patients (mean and standard deviation, 95 79 patients).
The majority (34%) of trials involved the treatment of
hip fractures. The mean overall study power among the 117 trials
was 24.65% (range, 2% to 99%). The type-II
error rate for primary outcomes was 90.52%.
Conclusions: Mean type-II error rates in the orthopaedic
trauma trials that we analyzed exceeded accepted standards. Investigators
can reduce type-II error rates by performing power and sample-size
calculations prior to conducting a trial.
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