Chapter 3-6. Study Designs
There are three primary study designs in epidemiologic research:
cohort study (which include clinical trials)
case-control study
cross-sectional study
Cohort Study (Rothman, 2002, p.57)
In epidemiology, a cohort is defined as:
a designated group of individuals who are followed over a period of time.
A cohort study involves measuring the occurrence of disease within one or more cohorts.
Typically, a cohort comprises persons with a common characteristic, such as an exposure to a
risk factor, which we refer to as the exposed and unexposed cohort.
When measurements are taken on the subjects at multiple time points, the cohort study is often
called a longitudinal study (Rothman and Greenland, 1998, p.422). The repeated measurements
are usually for both exposures and outcomes.
_____________________
Source: Stoddard GJ. Biostatistics and Epidemiology Using Stata: A Course Manual [unpublished manuscript] University of Utah
School of Medicine, 2010.
Chapter 3-6 (revised 16 May 2010)
p. 1
Diagrammatically,
Cohort Study
D
D
E
follow-up
D
D
E
where
E = exposed cohort, E = unexposed cohort
D = disease occurred, D = disease not occurred
Data layout,
Cohort Study
Data Layout for Incidence Proportions
(Stata’s csi command)
Exposed
Not Exposed
Disease
a
b
Not Disease
c
d
N1
N0
or
Data Layout for Incidence Rates
(Stata’s iri command)
Exposed
Not Exposed
Disease Cases
a
b
Person-Time
N1
N0
or
Life Table (survival analysis)
Chapter 3-6 (revised 16 May 2010)
p. 2
Experiments (Rothman, 2002, p.60)
Experiments are cohort studies, although not all cohort studies are experiments.
In epidemiology, an experiment is a study in which the incidence rate or the risk of disease in two
or more cohorts is compared, after assigning the exposure to the people who comprise the
cohorts.
Diagrammatically,
Experiment
D
D
E
follow-up
E
D
D

assigned by investigator
The data layouts are similar to the general cohort study described above.
In an experiment, the reason for the exposure assignment is solely to suit the objectives of the
study.
If people receive their exposure assignment based on considerations other than the study
protocol, it is not a true experiment.
Chapter 3-6 (revised 16 May 2010)
p. 3
Clinical Trials (Rothman, 2002, p.60)
Epidemiologic experiments are most frequently conducted in a clinical setting, with the aim of
evaluating which treatment for a disease is better.
Such studies are known as clinical trials.
(The word trial is used as a synonym for experiment).
All study subjects have been diagnosed with a specific disease, but that disease is not the disease
event that is being studied.
Rather, it is some consequence of that disease, such as death or spread of a cancer, that becomes
the “disease” event studied in a clinical trial.
The aim of a clinical trial is to evaluate the incidence rate of disease complications (or
improvements) in the cohorts assigned to the different treatment groups.
In most trials, treatments are assigned by randomization, using random number assignment.
Randomization tends to produce comparability between the cohorts with respect to factors that
might affect the rate of complications (helps to satisfy the “otherwise comparable” assumption).
Diagrammatically,
Clinical Trial
C
C
E
follow-up
C
C
D
E

assigned by investigator
where
C
= complication or no improvement,
C = no complication or improvement
Chapter 3-6 (revised 16 May 2010)
p. 4
Prospective Cohort Studies (Rothman, 2002, p.70)
A prospective cohort study is one in which the exposure information is recorded at the beginning
of the follow-up and the period of time at risk for disease occurs during the conduct of the study.
This is always the case with experiments and with many non-experimental cohort studies.
Retrospective Cohort Studies (Rothman, 2002, p.70)
In a retrospective cohort study (also known as historical cohort studies), the cohorts are
identified from recorded information and the time during which they are at risk for disease
(follow-up period) occurred before the beginning of the study.
Because a retrospective cohort study must rely on existing records, important information may be
missing or otherwise unavailable.
Nevertheless, when a retrospective cohort study is feasible, it offers the advantage of providing
information that is usually much less costly than that from a prospective cohort study, and it may
produce results much sooner because there is no need to wait for the disease to occur.
Chapter 3-6 (revised 16 May 2010)
p. 5
Case-Control Studies
In a cohort study, we:
1) Define the exposed and unexposed cohorts
2) Determine the number of people in these cohorts. These N’s are used as the
denominators for the risk or part of the person-time for incidence rates.
3) Observe the number of cases occurring in each cohort during the follow-up period.
4) Calculate the risk (cases/N) or incidence rate (cases/PT) for each cohort.
Cohort Study
D
D
E
follow-up
D
D
E
where
E = exposed cohort, E = unexposed cohort
D = disease occurred, D = disease not occurred
With cohort studies, you have to follow a large sample of subjects in order to measure the risk or
rate of disease. This is because you start with healthy subjects, and only a small number of them
develop the disease.
Because of this, we generally measure the entire cohort. With just a sample, perhaps your study
will end with no disease cases at all.
To avoid the need for a large study, with the cost and effort of a follow-up period, the casecontrol study design is frequently used.
The case-control study only requires a relatively small sample, without the need for a follow-up
period.
If properly carried out, a case-control study mirrors what would be learned in a cohort study.
Chapter 3-6 (revised 16 May 2010)
p. 6
In a case-control study, we:
1) Identify the cases that have occurred
2) Select a control group of non-cases
3) For both the case and control groups, we retrospectively uncover if the subject was
exposed or unexposed.
4) We estimate the risk ratio or incidence rate ratio from the odds ratio (but we cannot
estimate the incidence proportions or incidence rates, themselves—see box below).
Case-Control Study
E
E
D
E
D
E
where
E = exposure, E = no exposure
D = disease cases, D = non-case controls
Case-Control Study
Data Layout for case-control study
Exposed
Not Exposed
Disease
a
b
(cases)
Not Disease
c
d
(controls)
row totals
Ncases
Ncontrols
where the sample sizes are the row totals.
In contrast,
Cohort Study
Data Layout for cohort study
Exposed
Disease
a
(cases)
Not Disease
c
(controls)
column totals
Nexp
Not Exposed
b
d
Nnot exp
where the sample sizes are the column totals.
Chapter 3-6 (revised 16 May 2010)
p. 7
Prospective and Retrospective Case-Control Studies
Case-control studies, like cohort studies, can also be either prospective or retrospective.
In a retrospective case-control study, cases have already occurred when the study begins; there is
no waiting for new cases to occur.
In a prospective case-control study, the investigator must wait, just as in a prospective cohort
study, for new cases to occur.
Cross-Sectional Studies
A cross-section study simply collects a snapshot of the exposure-disease prevalence relationship.
The only total that is fixed is the total sample size. The row and column totals are random.
There is no fixed exposure cohort and no fixed number of cases. A survey sample is a crosssectional study.
Cross-Sectional Study
Data Layout for cross-sectional study
Exposed
Not Exposed
Disease
a
b
(cases)
Not Disease
c
d
(controls)
column totals
nexp
nnot exp
row totals
ndis
nnot dis
where the sample sizes, both row and column totals, are shown in lowercase to denote they are
observed, or random, rather than fixed by the study.
For this study design, the prevalence is estimated using the incidence proportion formula,
prevalence among exposed = a / nexp
prevalence among not exposed = b/ nnot exp
Chapter 3-6 (revised 16 May 2010)
p. 8
Why incidence proportions and incidence rates cannot be estimated with a case-control
study
In the cohort study data layout
Data Layout for Cohort Study
Exposure
Disease
Exposed
Unexposed
Totals*
cases
a
b
n1
noncases
c
d
n0
Totals*
N1
N0
*The uppercase Ns (sample sizes) are fixed by the researcher,
and the lowercase Ns are observed.
we know the number-at-risk (the column totals, or sample sizes) so we can estimate the incidence
proportion by
incidence proportion = disease cases / persons at risk
Similarly, we will know the time-at-risk for these persons, so we can estimate the incidence rate
by
incidence rate = disease cases / person-time
In the case-control study, however,
Data Layout for Case-Control Study
Exposure
Disease
Exposed
Unexposed
Totals*
cases
a
b
N1
noncases
c
d
N0
Totals*
n1
n0
*The uppercase Ns (sample sizes) are fixed by the researcher,
and the lowercase Ns are observed.
we cannot form a meaningful incidence proportion and incidence rate estimates because our
column totals (n1 and n0) are simply observed. These column totals do not represent the number
at risk. Also the sum a + b, and so the number of cases relative to n1 and n0, is going to be
artifically high. For example, suppose that half of the sample are cases, whereas in the
population the incidence of disease is only 1%. There is no possible way to assign the N1 cases
into cells a and b for which both the Exposed and Unexposed columns could correctly estimate
the population incidence.
Chapter 3-6 (revised 16 May 2010)
p. 9
The Odds Ratio
In the cohort study data layout, with fixed column totals for denominators,
Data Layout for Cohort Study (shown with 0-1 scores)
Exposure
Disease
Exposed (1) Unexposed (0) Totals*
cases (1) a (col %)
b (col %)
n1
noncases (0) c
d
n0
Totals*
N1
N0
*The uppercase Ns (sample sizes) are fixed by the researcher,
and the lowercase Ns are observed.
we can define the risk ratio as the ratio of the two column percents
RR 
risk of disease if exp osed
P(D=1|E=1) a / N1


risk of disease if un exp osed P(D=1|E=0) b / N 0
using conditional probability notation, P( . | . ), read as the probability of
what is on the left of the “|” given what is on the right of the “|”. Thus
P(D=1|E=1) represents “the probability of disease given exposure”.
In the case-control study data layout, with fixed row totals for denominators
Data Layout for Case-Control Study (shown with 0-1 scores)
Exposure
Disease
Exposed (1) Unexposed (0)
Totals*
cases (1) a (row %)
b
N1
noncases (0) c (row %)
d
N0
Totals*
n1
n0
*The uppercase Ns (sample sizes) are fixed by the researcher,
and the lowercase Ns are observed.
we can form meaning probabilities of the form P(E|D) and P(E|D) , which are reversed from the
cohort study probabilities of the form P(D|E) and P(D|E) .
Then defining “odds” as the ratio of the probability of some event occurring to not occurring
(such as the odds of heads vs tails on a coin flip),
we define the odds ratio (also called exposure odds ratio) as:
(a / N1 ) a
P(E=1|D=1)/P(E=0|D=1) (b / N1 ) b ad
OR 

 
P(E=1|D=0)/P(E=0|D=0) (c / N 0 ) c bc
(d / N 0 ) d
Chapter 3-6 (revised 16 May 2010)
p. 10
For the cohort study, we have
(a / N1 ) a
P(D=1|E=1)/P(D=0|E=1) (b / N1 ) b ad
OR 

 
P(D=1|E=0)/P(D=0|E=0) (c / N 0 ) c bc
(d / N 0 ) d
which in its final form (ad/bc) is identical to the case-control study.
For the cross-sectional study, there are no fixed totals that can be used as denominators to
calculate a probability (prevalence is not a probability).
Data Layout for Cross-Sectional Study (shown with 0-1 scores)
Exposure
Disease
Exposed (1) Unexposed (0) Totals*
cases (1) a (row %)
b
n1
noncases (0) c (row %)
d
n0
Totals*
n1
n0
*The uppercase Ns (sample sizes) are fixed by the researcher,
and the lowercase Ns are observed.
In the cross-sectional study, however, we can still define the odds ratio in terms of odds only, and
thus require no fixed denominator.
a
Odds(D=1|E=1)/Odds(D=0|E=1) c ad
OR 
 
Odds(D=1|E=0)/Odds(D=0|E=0) b bc
d
which in its final form (ad/bc) is identical to the above two study designs.
We see, then, that the odds ratio in its final form (ad/bc) does not depend on the row or column
totals for any of these three study designs, only the cell counts. The odds ratio is identically
OR = ad/bc for all three study designs.
In the cohort study, with fixed column totals, the column cells, a & c, and b & d, are free to vary
in the way they occur in the population. In the case-control study, with fixed row totals, the row
cells, a & b, and c & d, are free to vary in the way they occur in the population. In the crosssection study, all cells are free to vary in the way they occur in the population. Because of this
freedom to vary the cells proportional to the population frequencies, all three study designs can
correctly measure an association between between exposure and disease.
Chapter 3-6 (revised 16 May 2010)
p. 11
Rare Disease Assumption Rule of Thumb (Rosner, 1995, p. 368)
If the data are collected using a case-control study design, and the disease under study is
rare (disease incidence < .10), then we can estimate the risk ratio by the odds ratio.
Woodward (1999, p.113) adds:
The estimation is only good if both the exposed and unexposed groups have a rare disease
incidence.
(In other words, apply the < .10 rule to both groups.)
Exercise: where does the “< .10” rule-of-thumb come from?
Look at the figure in the Zhang and Yu (1998) article,
ZhangJAMA1998CorrectingOR.pdf, which illustrates how when the incidence of the
outcome is low (<10%), the odds ratio is close to the risk ratio.
Note: The method of Zhang and Yu has been convincing criticized as unreliable as a method to
correct the ORs to obtain RRs. A better approach is given in Chapter 10.
Chapter 3-6 (revised 16 May 2010)
p. 12
Why OR  RR under rare disease assumption (Woodward, 1999, p.113)
For the cohort study, we have
Disease
cases
noncases
Totals
Exposure
Exposed
Unexposed
a
b
c
d
a+c
b+d
a
RR  a  c
b
bd
If the disease is rare, there will be few disease cases, so a  0 and b  0, making c nearly equal to
a+c and d nearly equal to b+d. That is,
and
ca+c
db+d
Substituting,
a
a
ad
RR  a  c  c 
 OR
b
b bc
bd d
We seen, then, that the OR from the case-control study approximates the RR from the cohort
study when the rare disease assumption is met.
Chapter 3-6 (revised 16 May 2010)
p. 13
Interpreting the Size of Relative Measures of Effect
One of Hill’s “causal criteria” was strength of association. Although Hill did not propose that his
criteria were a checklist for evaluating causation, his criteria have frequently been applied that
way. Rothman (Chapter 2, p.19) points out that strength depends on the prevalence of other
causes and, thus, is not a biologic characteristic. The strength could be the result of confounding
as well. Thus, Rothman, makes no suggestion for interpreting the size of a risk ratio, rate ratio,
or odds ratio
Clinical researchers, unaware of Rothman’s argument, still desire to interpret the size of relative
measures of effect (risk ratio, rate ratio, odds ratio). This might, in part, be due to the wide
acceptance of other rules of thumb for measures of association (e.g., reliability coefficients and
correlation coefficients).
For example, the Pearson correlation coefficient has the range [-1 to 0] or [0 to 1] with perfect
correlation being 1.0 and 0 being no linear association. A rule of thumb for interpreting the size
of the correlation coefficient is found in Hinkle et al (1998, p.120):
Rule of Thumb for Interpreting the Size of a Correlation Coefficient
Size of Correlation
Interpretation
0.90 to 1.00 (-0.90 to -1.00)
Very high correlation
0.70 to 0.90 (-0.70 to -0.90)
High correlation
0.50 to 0.70 (-0.50 to -0.70)
Moderate correlation
0.30 to 0.50 (-0.30 to -0.50)
Low correlation
0.00 to 0.30 ( 0.00 to -0.30)
Little if any correlation
The odds ratio is likewise considered to be a measure of association. The rate ratio and odds
ratio have the range [0 to 1] and [1 to infinity].
Despite that comparisons of strength of associations between exposures is theoretically
unwarranted, Monson (1980, p. 94), while admitting it was theoretically unwarranted, still
suggested a rule of thumb for interpreting rate ratios. He did this to aid researchers and policy
makers in taking action to protect workers from occupational exposures.
Monson’s Rule of Thumb for Interpreting the Rate Ratio
rate ratio
strength of association
0.9 to 1.0 (1.0 to 1.2)
None
0.7 to 0.9 (1.2 to 1.5)
Weak
0.4 to 0.7 (1.5 to 3.0)
Moderate
0.1 to 0.4 (3.0 to 10.0)
Strong
0.0 to 0.1 (>10.0)
Infinite
Chapter 3-6 (revised 16 May 2010)
p. 14
It is problematic to apply this rule of thumb to the risk ratio, however. The risk ratio is the ratio
of two proportions (RR=p1/p2) and its value is constrained by the denominator proportion. For
example, if p2 = 0.5, then the RR can be no larger than 1/0.5 = 2; if p2 = 0.8, then the RR can be
no larger than 1/0.8 = 1.25. The rate ratio and the odds ratio do not have this restriction, which is
one of the reasons why the odds ratio is more popular than the risk ratio (it saves you from
having to explain to the reader that your risk ratios are constrained, making your associations
seem so weak). (Rosner, 1995, p.365)
A rule to thumb for interpreting the odds ratio, however, cannot be proposed. This is because the
value of the odds ratio is so dependent on the underlying disease rate, as shown in the Zhang and
Yu (1998) article. Many researchers, however, have adopted the OR=3.0 cutoff as a guideline
for judging a “strong” effect, similar to Monson’s rule of thumb for the rate ratio (see Taubes,
1995, for some informal examples of epidemiologists using this cutoff).
Chapter 3-6 (revised 16 May 2010)
p. 15
Exercise Look at the Fowler et al (2005) article.
Notice that the authors report the odds ratio, instead of risk ratio, even though they have a cohort
study design. This is very common. Logistic regression is the most widely used model for
binary outcomes, and it always provides an odds ratio, rather than a risk ratio, even for cohort
studies. (When the time to the disease outcome is available, Cox regression is also popularly
used in cohort studies.)
Exercise Look at the Cooper et al (2006) article.
1) Notice in the Methods section of the abstract they have a cohort study, and then follow 3
subcohorts composing the study cohort.
2) In Table 2, they show these three cohorts. In their analysis they compare the ACE inhibitor
cohort to the other two cohorts.
3) For statistical comparisons, they use “modified Poisson regression” with a count (not persontime) denominator, and robust standard error. This is one of the models that is used in place of
logistic regression. It permitted them to estimate a risk ratio, instead of an odds ratio, in contrast
to what Fowler (2005) did. Using alternatives to logistic regression, where the alternative
provide risk ratios rather than odds ratios, is becoming more popular.
How to compute a modified Poisson regression model is covered in Chapter 3-11.
Exercise Look at the Lee (2006) article, where two study designs are reported in the same paper.
In the cross-sectional study, they report odds ratios and use multivariable logistic regression to
compute adjusted odds ratios, adjusted for potential confounders (Table 4).
In the longitudinal study (cohort study), they report incidence proportions (which they
downplay), incidence rates, and hazard ratios. The hazard ratios and adjusted hazard ratios come
from time-dependent multivariable Cox regression. (Table 5)
Chapter 3-6 (revised 16 May 2010)
p. 16
Exercise: Calculating the odds ratio in Stata
Start the Stata program and read in the data evans.dta, the same dataset used in Chapter 5.
File
Open
Find the directory where you copied the course CD
Change to the subdirectory datasets & do-files
Single click on evans.dta
Open
use "C:\Documents and Settings\u0032770.SRVR\Desktop\
Biostats & Epi With Stata\datasets & do-files\evans.dta", clear
*
which must be all on one line, or use:
cd "C:\Documents and Settings\u0032770.SRVR\Desktop\”
cd “Biostats & Epi With Stata\datasets & do-files"
use evans.dta, clear
To look at the association between CHD and Smoking using a risk ratio, we use
Statistics
Epidemiology and related
Tables for epidemiologists
Cohort study risk ratio etc.
Main tab: Case variable: chd
Exposed variable: smk
OK
cs chd smk
| smk
|
|
Exposed
Unexposed |
Total
-----------------+------------------------+---------Cases |
54
17 |
71
Noncases |
333
205 |
538
-----------------+------------------------+---------Total |
387
222 |
609
|
|
Risk | .1395349
.0765766 | .1165846
|
|
|
Point estimate
| [95% Conf. Interval]
|------------------------+---------------------Risk difference |
.0629583
| .0138116
.112105
Risk ratio |
1.822161
| 1.083858
3.063382
Attr. frac. ex. |
.4512012
| .0773703
.6735634
Attr. frac. pop |
.3431671
|
+----------------------------------------------chi2(1) =
5.43 Pr>chi2 = 0.0198
This dataset is from a cohort study, so the risk ratio is the correct statistic to use.
Chapter 3-6 (revised 16 May 2010)
p. 17
For illustration, however, we will now compute an odds ratio for smoking-CHD association.
Statistics
Epidemiology and related
Tables for epidemiologists
Case-control odds ratio
Main tab: Case variable: chd
Exposed variable: smk
OK
cc chd smk
Proportion
|
Exposed
Unexposed |
Total
Exposed
-----------------+------------------------+-----------------------Cases |
54
17 |
71
0.7606
Controls |
333
205 |
538
0.6190
-----------------+------------------------+-----------------------Total |
387
222 |
609
0.6355
|
|
|
Point estimate
|
[95% Conf. Interval]
|------------------------+-----------------------Odds ratio |
1.955485
|
1.079872
3.695643 (exact)
Attr. frac. ex. |
.4886179
|
.0739645
.7294111 (exact)
Attr. frac. pop |
.3716249
|
+------------------------------------------------chi2(1) =
5.43 Pr>chi2 = 0.0198
Stata calls this command cc to denote case-control study, a logical choice since only the odds
ratio can be calculated for that study design (not a risk ratio or a rate ratio).
Notice we have RR = 1.82 and OR = 1.96. The OR is always larger than the RR, the inflation
being greater as we move away from the rare disease assumption.
Was the rare disease assumption met?
This time, let’s compute the OR using the odds ratio calculator (cci command).
The cci command uses the same data layout as the csi command.
Stata data layout for odds ratio (cci command)
Exposed
Unexposed
Cases
a
b
Noncases
c
d
Chapter 3-6 (revised 16 May 2010)
p. 18
Statistics
Epidemiology and related
Tables for epidemiologists
Case-control odds ratio calculator
54 17
333 205
OK
cci 54 17 333 205
Proportion
|
Exposed
Unexposed |
Total
Exposed
-----------------+------------------------+-----------------------Cases |
54
17 |
71
0.7606
Controls |
333
205 |
538
0.6190
-----------------+------------------------+-----------------------Total |
387
222 |
609
0.6355
|
|
|
Point estimate
|
[95% Conf. Interval]
|------------------------+-----------------------Odds ratio |
1.955485
|
1.079872
3.695643 (exact)
Attr. frac. ex. |
.4886179
|
.0739645
.7294111 (exact)
Attr. frac. pop |
.3716249
|
+------------------------------------------------chi2(1) =
5.43 Pr>chi2 = 0.0198
which, of course, provides identical output to what was produced before.
Prevalence Statistics in Cross-Sectional Study
In Chapter 5, it was stated that because prevalence is a mixture of incidence rate and disease
duration, it is not as useful for studying the cause of disease. (Rothman, 2002, p.42)
Clarifying further, its drawback in studying the cause of disease is that factors that increase
prevalence may do so not by increasing the occurrence of disease, but by increasing the duration
of the condition. (Rothman, 2002, p.43)
Rothman (2002, p.43-44) gives an example,
“...a factor associated with the prevalence of ventricular septal defect at birth could be a
cause of ventricular septal defect, but it could also be a factor that does not cause the
defect but instead enables embryos that develop the defect to survive until birth.”
However, under the assumption of a steady state and equal disease duration in the exposed and
unexposed groups, the prevalence odds ratio directly estimates the incidence rate ratio. Pearce
(2004, p.1048) povides an eloquent presentation of this relationship.
Exercise. Read the section Measures of effect in prevalence studies in the Pearce article (2004,
p.1048).
Chapter 3-6 (revised 16 May 2010)
p. 19
Exercise. Look at the Moran article (2006).
Pearce (2004) points out, under the assumption of a steady state and equal disease duration in the
exposed and unexposed groups, the prevalence odds ratio directly estimates the incidence rate
ratio.
As interesting as that is, researchers usually do not take that approach, but merely report the
prevalence odds ratios, or “odds ratios”, as correlation coefficients, without discussing the
strength of the effect or implying that they may be estimates of the incidence rate ratio. The
Moran article is a good example of this approach.
References
Cooper WO, Hernandez-Diaz S, Arbogast PG, et al. (2006). Major congenital malformations
after first-trimester exposure to ACE inhibitors. NEJM 354(23):2443-2451.
Fowler VG, Miro JM, Hoen B, et al. (2005) Staphylococcus aureus endocarditis: a consequence
of medical progress. JAMA 293(4):3012-21.
Hinkle DE, Wiersma W, Jurs SG. (1998). Applied Statistics for the Behavioral Sciences, 4th ed.
Boston, Houghton Mifflin Company.
Monson RR. (1980). Occupational Epidemiology. Boca Raton, FL, CRC Press, Inc.
Moran GJ, Krishnadasan A, Gorwitz RJ, et al. (2006). Methicillin-resistant S. auerus infections
among patients in the emergency department. NEJM 355(7):666-674.
Pearce N. (2004). Effect measures in prevalence studies. Environmental Health Perspectives.
112(10):1047-1050.
Rosner B. (1995). Fundamentals of Biostatistics, 4th ed., Belmont CA, Duxbury Press.
Rothman KJ. (2002). Epidemiology: An Introduction. New York, Oxford University Press.
Rothman KJ, Greenland S. (1998). Modern Epidemiology, 2nd ed. Philadelphia, PA,
Lippincott-Raven Publishers.
Taubes G. (1995). Epidemiology faces its limits. Science 269(July 14):164-169.
Woodward M. (1999). Epidemiology: Study Design and Data Analysis. New York, Chapman &
Hall/CRC.
Zhang J, Yu KF. (1998). What’s the relative risk? A method of correcting the odds ratio in
cohort studies of common outcomes. JAMA 280(19):1690-91.
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