BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
There are seven questions at the end of this article. This assignment is worth 80 points.
Place answers in this table:
1.
2.
3.
4.
5.
6.
7.
BIOSTAT Case Study: Tests of Association for Categorical Data
LEARNING OBJECTIVES
At the completion of this Case Study, participants should be able to:
➢ Compare two or more proportions
➢ Calculate and interpret confidence intervals for proportions
➢ Understand the impact of expected values on the choice of statistical test used to
compare proportions
➢ Interpret the results of tests of association
➢ Interpret logistic regression results.
This material was developed by the staff at the Global Tuberculosis Institute (GTBI), one
of four Regional Training and Medical Consultation Centers funded by the Centers for
Disease Control and Prevention. It is published for learning purposes only. Permission to
reprint excerpts from other sources was granted.
Case study author(s) name and position:
Marian R. Passannante, PhD
Associate Professor, University of Medicine & Dentistry of New Jersey, New Jersey
Medical School and School of Public Health
Epidemiologist, NJMS, GTBI
For further information please contact:
New Jersey Medical School Global Tuberculosis Institute (GTBI)
225 Warren Street P.O. Box 1709
Newark, NJ 07101-1709
or by phone at 973-972-0979
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
Suggested Citation: New Jersey Medical School Global Tuberculosis Institute. /Incorporating
Tuberculosis into Public Health Core Curriculum./ 2009: BIOSTATISTICS CASE STUDY 2: Tests of
Association for Categorical Data STUDENT Version 1.0.
Introduction
This exercise is based on the following study. Sections of this document have been reprinted
with permission of the journal.
Factors influencing the successful treatment of infectious pulmonary tuberculosis WS. Chung,*† Y-C. Chang,† M-C. Yang†, * Department of Internal Medicine, Hualien General
Hospital, Hualien, † Institute of Health Care Int J Tuberc Lung Dis 11:59–64 © 2007 The
Union
The abstract states that “(t)his study used a population-based…design. All PTB [pulmonary
TB] patients residing in southern Taiwan recorded in the tuberculosis registry from 1 January
to 30 June 2003 were identified. Each patient’s medical record was requested from treating
hospitals and retrospectively reviewed for 15 months after the date PTB was confirmed.” 1
Following is the methods section of this article1.
METHODS
We carried out a population-based medical record review in southern Taiwan, where
the only chest specialty hospital geared towards specialized thoracic disease care,
mainly for TB, is located. Hospitals and primary practitioners that provided TB care in
the same region can be used as comparative care providers. Study areas include
Chiayi County, Chiayi City, Tainan County and Tainan City. As mandated by law in
Taiwan, all suspected and confirmed TB cases must be reported in a timely manner to
the national computerized registry maintained by the Taiwan Center for Disease
Control (CDC). Reporting of cases has been encouraged and reinforced through the
implementation of a no-notification, no-reimbursement policy and a notification-for-fee
policy since 1997. 7 We requested data on all suspected and confirmed TB patients
residing in the studied areas and recorded in the registry for the period 1 January to
30 June 2003. The study team, including four registered nurses (each with a
minimum of 6 years’ clinical experience), two head nurses (each with a minimum of 12
years’ clinical experience) and one pulmonologist, had undergone a series of training
courses designed to ensure proper validation of data consistency. Site visits were
arranged to review the medical record of each patient, and the 15-month follow-up of
medical records after start of treatment was reviewed.
Health care institutions
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
Health care institutions that had ever reported cases in the study areas included the
chest hospital, two academic medical centers, 11 regional hospitals and 15 district
hospitals and primary practitioners (district hospitals and primary practitioners are
regarded as being at the same level in terms of TB treatment). In Taiwan, institutions
are classified by the government as follows: ‘medical centers’ are health care, training
and research facilities that house over 500 acute-care beds; ‘regional hospitals’ have
no fewer than 250 acute care beds and are staffed by physicians of various specialties
with the purpose of providing health care services to patients and training for
specialists; and ‘district hospitals’ provide primary health care services similar to those
offered by primary practitioners but with the added availability of in-patient care.
Infectious PTB
Infectious PTB is defined as sputum culture-confirmed disease caused by
Mycobacterium tuberculosis, or two sputum smear examinations positive for acid-fast
bacilli (AFB) or one positive sputum examination, radiological signs and a clinician’s
decision to treat.8
Directly observed treatment
For directly observed treatment (DOT), a health worker or other trained person who is
not a family member watches as the patient swallows anti-tuberculosis medicines for
at least the first 2 months of treatment.1 DOT thus shifts the responsibility for cure
from the patient to the health care system. In Taiwan, whether or not the patient is
receiving DOT, TB is treated using WHO-recommended regimens; the initial phase
consists of 2 months of isoniazid (H), ethambutol (E), rifampicin (R) and pyrazinamide
(Z), followed by a 4-month continuation phase consisting of H, E and R
(2HERZ/4HER).9,10
Treatment success
Treatment success is defined as a patient who has been cured or has received a
complete course of treatment. A cured case is defined as a PTB patient who has
finished treatment with a negative bacteriology result during and at the end of
treatment. A case recorded as completed treatment is defined as a PTB patient who
has finished treatment, but who has not met the criteria to be defined as a cure or a
failure.11,12
Ethical consideration
The study was approved by the Taiwan CDC. All staff members involved in the study
signed a statement of agreement to maintain patient confidentiality.
Data analysis
Bivariate analyses with 2 tests were used to compare differences in proportions of
dichotomous and categorical variables, which extracted potential predictors of
successful treatment. We then performed multivariate logistic regression analyses on
the potential predictors with P < 0.10 obtained from bivariate analyses. We
constructed a full model that included all the potential predictors identified through
bivariate analyses and then applied the forward substitution model building procedure
to construct a reduced model in which all the predictors were statistically significant.
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
Odds ratios (ORs) and 95% confidence intervals (CIs) of dichotomous and categorical
risk variables on the binary outcome variables were calculated. All analyses were
conducted using SPSS 10.0 software (SPSS Inc, Chicago, IL, USA), and all the tests
were performed at the two-tailed significance level of 0.05.
References that appear in the excerpt from this article:
1 World Health Organization. Tuberculosis Fact Sheet. Geneva,Switzerland: WHO.
http://www.who.int/tb/en/
7 Chiang C Y, Enarson D A, Yang S L, Suo J, Lin T P. The impactof National Health
Insurance on the notification of tuberculosis in Taiwan. Int J Tuberc Lung Dis 2002; 6:
974–979.
8 Migliori G B, Raviglione M C, Schaberg T, et al. Tuberculosis management in Europe. Task
Force of the European Respiratory Society, the World Health Organization and the
International Union Against Tuberculosis and Lung Disease, EuropeRegion. Eur
Respir J 1999; 14: 978–992.
9 National Tuberculosis and Lung Disease Research Institute/World Health Organization
Collaborating Centre for Tuberculosis.Report on the Second Meeting of National TB
Programme managers from Central and Eastern Europe and the former USSR.
Bulletin No 3. Warsaw, Poland: WHO Collaborating Centre for Tuberculosis, 1997: 1–
30.
10 American Thoracic Society/Centers for Disease Control and Prevention/Infectious
Diseases Society of America. Treatment of tuberculosis. Am J Respir Crit Care Med
2003; 167: 603–662.
11 World Health Organization. Global tuberculosis control. WHO Report 1999.
WHO/CDS/CPC/TB/99.259. Geneva, Switzerland: WHO, 1999.
12 Farah M G, Tverdal A, Steen T W, Heldal E, Brantsaeter A B, Bjune G. Treatment outcome
of new culture positive pulmonary tuberculosis in Norway. BMC Public Health 2005; 5:
14.735–739.
Table 1, on the next page, presents the characteristics of the 399 patients eligible for this
study.1
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
Question 1
What type of study design is described in the abstract? (10 pts)
a.
b.
c.
d.
e.
Observational
Case Control
Retrospective
Cross Sectional
a and c
Question 2
What proportion of patients was successfully treated? (10 pts)
Question 3
Calculate a 95% Confidence Interval (CI) for the true population proportion with successful
treatment. Hint: The SE of p is the square root of (pq)/n. (10 pts)
Upper limit CI = _____
Lower Limit CI = _____
Question 4
Which of the following is true with regard to the confidence interval computed in Question 3
above: (10 pts)
a. 95 times out of 100 one would expect a the sample of 399 taken from the same
population to have a proportion of successfully treated patients to be between the
upper and lower limits of the confidence interval computed in Question 2.
b. 95 times out of 100 one would expect a the sample of 399 taken from the same
population to have a proportion of successfully treated patients to be outside the upper
and lower limits of the confidence interval computed in Question 2.
c. 5 times out of 100 one would expect a the sample of 399 taken from the same
population to have a proportion of successfully treated patients to be outside the upper
and lower limits of the confidence interval computed in Question 2.
d. a and c.
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
Question 5 (15 pts)
Using the information from Table 1, construct a 3 x 2 table to test the association between
DOT status and successful treatment.
Observed
DOT
Treatment Success
Yes
No
Total
Yes
250
No
146
Unknown
3
Total
275
124
399
Generate the expected values for the empty cells below. Hint: the expected value for any
cell is the row total x column total divided by the grand (overall) total.
Expected
DOT
Treatment Success Values
Yes
No
Total
Yes
250
No
146
Unknown
Total
3
275
124
399
Question 6
Using the DOT status groups, generate the chi-squared test statistic, by hand, using a
calculator, or using a computer. Include the unknown values, even though there are only 3.
Alpha = 0.05
df = _____ (5 pts)
Critical value = _____ (5 pts)
Chhi-squared test statistic = _____ (5 pts)
Based on comparing the Chi square statistic to the critical value which of the following is
true? (5 pts)
a.
b.
c.
d.
Successful outcome is dependent on DOT status.
Successful outcome is independent of DOT status.
No conclusion can be made.
The Chi square test is invalid because of only 1 degree of freedom.
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
Multiple logistic regression analysis allows us to look at the impact of independent variables
(potential predictor variables) on a dichotomous outcome variable such as successful
treatment completion (yes/no) when controlling for other independent variables. Table 3
presents some of the results of the multiple logistic regression model.1 The outcome is
successful treatment.
Note:
Other footnotes are intentionally excluded from this table.
One way to assess the importance of a potential predictor variable is to examine the odds
ratios (ORs) and associated 95% CIs that are estimated from the logistic regression model.
Question 7 (10 pts)
Which independent variables listed below is (are) positively significantly associated with
successful treatment?
a.
b.
c.
d.
e.
Institutions
Physician
DOT
CXR
a, b, and c.
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
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BIOSTATISTICS CASE STUDY:
Tests of Association for Categorical Data
References
1. Chung,*† Y-C. Chang,† M-C. Yang†, * Department of Internal Medicine, Hualien General
Hospital, Hualien, † Institute of Health Care Int J Tuberc Lung Dis 11:59–64 © 2007 The
Union
2. Dawson, B and Trapp, R Basic &Clinical Biostatistics, 4th edition, Lange Basic Science,
2004 page 152.
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