++
Several different approaches can be used to analyze the results
of a cohort study, as described in the following sections.
++
The results of a cohort study can be summarized using the format
shown in Table 8–6. In that table, the letters A–D represent numbers of subjects
in the four possible combinations of exposure and outcome status (in
this instance, death).
++
- A. Exposed persons who
later die
- B. Unexposed persons who later
die
- C. Exposed persons who do not
die
- D. Unexposed persons who do
not die
++
++
The total number of subjects in this study is the sum of A + B + C + D. The
total number of exposed persons is A + C, and the total number of unexposed
persons is B + D.
++
Among exposed persons, the risk (R)
of death is defined as
++
++
As indicated in Chapter 2: Epidemiologic Measures, risk can vary between 0 (no exposed
persons die) and 1 (all exposed persons die). As in all statements
of risk, some time period for the development of the outcome must
be specified. For example, the outcome might be the risk of death
in the first year of life. Among unexposed persons, the risk of
death is defined as
++
++

As indicated in
Chapters 4: Medical Surveillance and
7: Clinical Trials, one approach to contrasting
the risk in two groups is to create a ratio measure. The
risk ratio (
RR)
or relative risk is
++
++
If the exposed and unexposed persons have the same risk of death,
the RR is 1 (ie, the null value). That
is, exposure is not related to the outcome.
++

If the risk among exposed persons is greater than the corresponding
risk among unexposed persons, the
RR is
greater than 1 (ie, hazardous exposure). In contrast, if the risk
among exposed persons is smaller than the corresponding risk among
unexposed persons, the
RR is less than
1 (ie, beneficial exposure).
++
The calculation of risk ratio can be illustrated from the study
of perinatal asphyxia. The data in Table 8–7 relate to
infants who weighed more than 2500 g at birth. Exposure is defined
as an Apgar score of 0–3 at 10 minutes of life, and the
comparison group of less exposed newborns had Apgar scores of 4–6
at 10 minutes. In the actual study, a third group with Apgar scores
of 7–10 was included, but the data are not described here
in detail.
++
++
The risk among exposed newborns is
++
++
That is, about one of three newborns weighing more than 2500
g and having very low Apgar scores at 10 minutes died during the
first year of life. The risk among “less exposed” newborns
is
++
++
In other words, one in eight neonates weighing over 2500 g and
having intermediate Apgar scores at 10 minutes died during the first
year of life.
++
Without any further calculations, it should be obvious that the
neonates with very low 10-minute Apgar scores had a worse prognosis
than those with intermediate 10-minute Apgar scores. Quantification
of the magnitude of this effect is achieved by calculating the risk
ratio
++
++
The RR of 2.8 means that newborns
at this birth weight with very low 10-minute Apgar scores are almost three
times more likely to die in the first year of life than similar-weighing
newborns with intermediate 10-minute Apgar scores. The RR is a measure of the strength of
association between exposure and outcome. The farther the RR is from the null value of 1, the
stronger the association. The strength of association is an important
criterion in evaluating whether an observed association is likely
to represent a cause-and-effect relationship. The RR of 2.8 is consistent with a moderate-to-strong
relationship between the exposure (10-minute Apgar score) and outcome
(infant death).
++
As discussed in Chapter 7: Clinical Trials, a sense of the statistical precision
of this estimated risk ratio can be obtained by calculating confidence intervals around the point
estimate of 2.8. Using the approximation method described in Appendix
B, the 95% confidence interval for the data presented in
Table 8–7 is (1.9, 4.1). That is, at the 95% level of
confidence, the range of RR values
consistent with the observed data falls between 1.9 and 4.1. Thus
the data are consistent with a risk of death in infants with very
low Apgar scores between roughly a doubling and a fourfold increase
(Figure 8–5). As demonstrated in Chapter 7: Clinical Trials, the point estimate
does not lie in the middle of the RR confidence
interval. The asymmetry of this interval derives from the skew of
the range of values of the risk ratio toward the positive direction
(ie, all beneficial effects are compressed into the range 0–1,
whereas hazardous effects range from 1 to positive infinity).
++
++
Since the null value is excluded from this 95% confidence
interval, it can be concluded that the findings are statistically significant. In other
words, these data are not consistent with the null hypothesis of
no association between Apgar scores and infant mortality (at the
prespecified 95% level of confidence). An association as strong
as that observed between Apgar scores and infant mortality, therefore,
cannot be explained by chance alone.
++
As indicated earlier, the argument that the linkage between Apgar
score and death in the first year of life is one of cause
and effect is strengthened if a dose–response relationship
can be demonstrated. A third group of newborns, with Apgar scores
of 7–10, was therefore included in the study. Comparison
of the risk of death in that group with the previous reference group,
which had intermediate Apgar scores of 4–6, yields a risk
ratio of 0.15, with an approximate 95% confidence interval
of (0.11, 0.21). This result means that newborns with a 10-minute
Apgar score of 7–10 have only about one-sixth the risk
of death in the first year of life as newborns with Apgar scores of
4–6. This disparity is statistically significant, and the
very narrow width of the confidence interval indicates a statistically
precise estimate (because it is based on a large number of observations).
++
The dose–response relationship between Apgar score and
the risk ratio of death in the first year of life for newborns weighing
more than 2500 g is shown in Figure 8–6. The reference
group against which others were compared in the preceding calculations
was the group with Apgar scores of 4–6 (ie, the risk ratio
for this group is defined as 1). A clear trend of decreasing risk
ratio with increasing Apgar score is seen, and this trend is unlikely
to have occurred by chance alone. Thus, there is strong evidence
in these data for a dose–response relationship.
++
+++
Attributable
Risk Percent
++
The risk of a specified outcome can be compared with measures
other than a ratio. For example, the risk for one group can be subtracted
from the risk for another group. This measure is termed the risk
difference, or excess risk. Some authors use the term “attributable
risk” for this measure, but that expression is discouraged
here because it may be confused with other expressions. The risk
difference (RD) is defined as
++
++
Using the previously cited data relating 10-minute Apgar scores
(0–3 versus 4–6) to the risk of death in the first
year of life, we calculate the risk difference as
++
++
That is, the risk of death in the first year of life is increased
by 0.219 for newborns who weigh more than 2500 g and have a 10-minute
Apgar score of 0–3, compared with similar-weighing newborns
with a 10-minute Apgar score of 4–6.
++

Another measure of interest is the attributable risk percent
(
ARP), in which the risk difference
is expressed as a percentage of the total risk experienced by the exposed
group:
++
++
For the Apgar score–infant mortality data, the attributable
risk percent is
++
++
In other words, almost two thirds of the total risk of infant
mortality for newborns who weigh more than 2500 g and have 10-minute
Apgar scores of 0–3 is related to an Apgar score below
the 4–6 level. The attributable risk percent typically
is used as an indicator of the public health impact of exposure.
These data suggest that birth asphyxia is a major contributor to—but
not the sole cause of—infant mortality among severely asphyxiated
children.
++
The analyses presented thus far are based on comparisons of risk
estimates across exposure groups. In a cohort study, the measured
outcome may be an incidence (or mortality) rate rather than a risk.
Rate data in a cohort study can be summarized using the format shown
in Table 8–8. The rate ratio is derived as follows
++
++
++
The magnitude of the rate ratio is interpreted in the same manner
as the risk ratio (< 1 = protective effect, 1 = no
effect, > 1 = harmful effect of exposure). The farther
away from the null value, the stronger the association between exposure
and the rate of the outcome. The data collected in the study of
perinatal asphyxia were not presented in a manner that allows calculation
of rate ratios.
++
To illustrate this measure, data are drawn from the Chicago Heart
Association Detection Project in Industry (Dyer et al, 1992). That
investigation involved almost 40,000 men and women at 84 cooperating
companies and institutions in the Chicago area. Subjects were enrolled
between 1967 and 1973, screened for risk factors for cardiovascular
disease, and then followed an average of 14–15 years. For
white males aged 25–39 at entry, the relationship between
baseline serum cholesterol level and subsequent rate of coronary
heart disease (CHD) is shown in Table 8–9. The rate ratio
is
++
++
++
In other words, the mortality rate from CHD among white males
with borderline high cholesterol levels was about 3.5 times higher
than that of white males with lower cholesterol levels. Adjustment
for underlying age differences in the study groups reduced the observed
rate ratio to 3.1. Comparison of mortality from CHD among white
males aged 25–39 with high serum cholesterol levels (>
6.2 mmol/L [> 240 mg/dL]) with
white males of the same age with normal serum cholesterol levels
(< 5.1 mmol/L [< 197 mg/dL])
yielded an age-adjusted rate ratio of 5.1. Thus, a dose–response
relationship was evident between baseline serum cholesterol level
and subsequent CHD mortality.