Category : Science and Education
Archive   : EPI_PAK.ZIP
Filename : SCREEN.DOC

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SCREEN
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A Program for Screening Analysis
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Version 1.2, May 26, 1989
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(c) 1988, 1989
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___________________________________________________________________________
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by
Kevin M. Sullivan
Division of Nutrition
Centers for Disease Control
1600 Clifton Road MS A08
Atlanta, GA 30333

This program was developed to calculate certain screening indices
and their confidence intervals. The table setup is:

TRUTH
YES NO
_______________
POS | a | b | M1
SCREEN |_______|_______|
NEG | c | d | M0
_______________|_______
N1 N0 | T

"TRUTH" is the gold standard to which a screening test is compared.
For example, with tuberculosis (TB), "TRUTH" could be whether or not the
individual has chest X-ray evidence of TB. "YES" means they truly have
the disease or outcome of interest, and "NO" means they truly do not
have the disease/outcome of interest. "SCREEN" is whether, after
application of a screening test, you will call the individual positive
(i.e., likely to have the disease) or negative (unlikely to have the
disease). With the TB example, individuals who have a local reaction to
a skin test are classified as "positive" (POS), and individuals with
little or no local reaction are classified as "negative" (NEG).
Within the table presented above each cell is assigned a letter and
the margins are assigned a letter/number combination. Individuals in
cell "a" are considered "true positives", in cell "b" false positives,
in cell "c" false negatives, and in cell "d" true negatives.
Several tests have been developed to measure the performance of a
screening test. SCREEN provides point estimates and confidence
intervals for sensitivity, specificity, predictive value of a positive
test, predictive value of a negative test, correct ratio, likelihood
ratio of a positive test, prevalence odds ratio, and prevalence ratio.
The user can select either 90%, 95%, or 99% confidence intervals. Each
of the parameters estimated are defined below.

SENSITIVITY: The definition of sensitivity is, among the truly
diseased, the proportion who test positive. The formula for the point
estimate is a/N1. A normal approximation to the binomial of the
standard error1 (SE) is:
____
SE = \/pq/n









SCREEN Document, Version 1.2, May 26, 1989, page 2

where
p=numerator/denominator
q=1-p
n=denominator

The normal approximation for computing a 95% confidence is:

p + Z * SE

where
Z = Z value, e.g., for 95% two-sided CI this is 1.96
SE = the standard error calculated above

The normal approximation to the binomial can produce estimates
outside of the 0-100 percent limits. SCREEN will provide the results of
the normal approximation calculations even if the estimates are outside
the limits, although most authors truncate the estimates to the limits.
One suggested criterion for determining when the normal approximation is
inappropriate is when npq<5.1 A more correct approximation for the
confidence interval for a proportion is calculated using the quadratic
method.2 The formula for the lower bound of the quadratic method is:
____________________________
2 | 2
(2np + Z - 1) - Z \| Z - (2 + 1/n) + 4p(nq + 1)
_________________________________________________
2
2(n + Z )

and the upper bound is:
____________________________
2 | 2
(2np + Z + 1) + Z \| Z + (2 - 1/n) + 4p(nq - 1)
_________________________________________________
2
2(n + Z )

Generally the quadratic method estimates confidence limits within
one percent of confidence limits calculated using the exact binomial
method. Intervals calculated by the quadratic method are always
preferable to those calculated by using the normal approximation. If
the data are sparse (e.g., npq<5), then an exact binomial confidence
interval should probably be calculated using PROPCI or other similar
programs for computing exact confidence intervals.3,4 In situations
where npq<5, SCREEN will place an asterisk to the right of the quadratic
confidence limits and place a message on the bottom portion of the
screen warning the user that exact confidence intervals should probably
be calculated.
Please note that the methods for calculating calculating confidence
intervals are the same for sensitivity, specificity, predictive value
(positive or negative), and correct ratio.

SPECIFICITY: Specificity is defined as, among those truly without
disease, the proportion who test negative. The formula for calculation
specificity is d/N0. Formulas for the standard error and confidence
intervals are the same as shown for sensitivity.

PREDICTIVE VALUE OF A POSITIVE TEST (PV+): This screening index is
defined as, among those who test positive, the proportion who are truly
diseased. The formula for the point estimate is a/M1.





SCREEN Document, Version 1.2, May 26, 1989, page 3

PREDICTIVE VALUE OF A NEGATIVE TEST (PV-): Among the individuals who
test negative, the proportion that truly do not have disease. The point
estimate is calculated as d/M0.

CORRECT RATIO: The proportion of individuals who are classified
correctly, i.e., true positives and true negatives divided by everyone
screened. This measure is also referred to as the "accuracy" of a
screening test.5 The formula is (a+d)/T.

LIKELIHOOD RATIO OF A POSITIVE TEST: The likelihood ratio is the
proportion of individuals classified as positive among those who are
truly diseased divided by the proportion of individuals classified as
positive among those who truly do not have disease. For example, a
likelihood ratio of 5 would be interpreted as: Diseased individuals are
5 times more likely to test positive than nondiseased individuals. The
point estimate is calculated by (a/N1)/(b/N0). An alternative and
equivalent formula for this index is: sensitivity/(1-specificity). A
Taylor series approach to estimating the standard error and confidence
intervals is used.5 The standard error of the natural log of the
likelihood ratio is:
_________________
SE(ln(LR)) = \/(c/aN1) + (d/bN0)

where
ln=natural log
LR=likelihood ratio point estimate

and the 95% confidence interval is:
__________
exp{ln(LR) + Z \/SE(ln(LR))}

where
exp=antilog

Please note that the variance estimates for the LR and the next two
parameters (odds ratio and prevalence ratio) are based on the assumption
of a large sample size. If you have sparse data (e.g., cells with
values of three or less), then other more correct procedures for
calculating confidence intervals should be used.
For additional information on the use and interpretation of the LR,
please refer to Sackett.5

ODDS RATIO: The odds ratio is a measure of association between the
screening results and "truth". The odds ratio is the odds of disease
among those who test positive (a/b) divided by the odds of disease among
those who test negative (c/d). For further information on the
interpretation of the odds ratio, consult an epidemiologic text such as
the one by Rothman.6 The point estimate for the odds ratio is (ad)/(bc)
which is equivalent to (a/b)/(c/d). Woolf's method for estimating the
standard error of the natural log of the odds ratio is used and the
formula is:
_____________________
SE(ln(OR)) = \/1/a + 1/b + 1/c + 1/d

where
OR=odds ratio point estimate








SCREEN Document, Version 1.2, May 26, 1989, page 4

The confidence interval is calculated using the formula shown for
the likelihood ratio except to substitute the appropriate values of "OR"
for "LR".

PREVALENCE RATIO: The prevalence ratio is the prevalence of disease
among those who test positive divided by the prevalence of disease among
those who test negative. This measure is basically the same as a risk
ratio, only rather than knowing the risk of disease, the prevalence of
disease is known. For example, a prevalence ratio of 4 would be
interpreted as follows: Individuals with a positive test are 4 times
more likely to be truly diseased than those who test negative. The
formula for the point estimate is (a/M1)/(c/M0). An alternative and
equivalent formula is: PV+/(1-PV-). The standard error is:
_________________
SE(ln(PR)) = \/(b/aM1) + (d/cM0)

where
PR = prevalence ratio point estimate

The confidence interval is calculated using the formula shown for
the likelihood ratio except to substitute the appropriate values of "PR"
for "LR".

DISTRIBUTION CONDITIONS
NON-WARRANTY. SCREEN is provided "as is" and without any warranty
expressed or implied. The user assumes all risks of the use of SCREEN.
SCREEN may not run on your particular hardware/software configuration.
We bear no responsibility for any mishap or economic loss resulting
therefrom the use of this software.
COPYRIGHT CONDITIONS. You may make and distribute copies of SCREEN
provided that there is no material gain involved.
USE AT YOUR OWN RISK. All risk of loss of any kind due to the use
of SCREEN is with you, the user. You are responsible for all mishaps,
even if the program proves to be defective. This program makes certain
assumptions about the data. These assumptions affect the validity of
conclusions made based on the output from this program.




























SCREEN Document, Version 1.2, May 26, 1989, page 5

EXAMPLE

The following example of the output from SCREEN is from the text by
Mausner and Kramer.7


TRUTH
YES NO Prevalence (%)
---------------
POS | 18| 49| 67 26.866
SCREEN |-------|-------|
NEG | 2| 931| 933 0.214
---------------|-------
20 980| 1000 2.000
__NORMAL_APPROXIMATION__ ___QUADRATIC___
PARAMETER Pt. Est. S.E. 95% CI 95% CI
----------------------------------------------------------------------
|SENSITIVITY (%) | 90.000 6.708 ( 76.852, 103.148) ( 66.872, 98.249) *|
|SPECIFICITY (%) | 95.000 0.696 ( 93.635, 96.365) ( 93.394, 96.242) |
|PV+ (%) | 26.866 5.415 ( 16.252, 37.480) ( 17.103, 39.308) |
|PV- (%) | 99.786 0.151 ( 99.489, 100.082) ( 99.139, 99.963) *|
|CORRECT (%) | 94.900 0.696 ( 93.536, 96.264) ( 93.300, 96.143) |
|LIKELIHOOD RATIO| 18.000 0.158 ( 13.208, 24.531) |
|ODDS RATIO |171.000 0.760 ( 38.582, 757.890) |
|PREVALENCE RATIO|125.328 0.735 ( 29.702, 528.820) |
----------------------------------------------------------------------
* May want to compute exact confidence interval.



Please acknowledge SCREEN in any manuscript that uses its
calculations.


REFERENCES

1. Rosner B. Fundamentals of Biostatistics. Duxbury Press, Boston,
1982.

2. Fleiss JL. Statistical Methods for Rates and Proportions, 2nd Ed.
John Wiley & Sons, New York, 1981.

3. Rothman KJ, Boice JD Jr: Epidemiologic analysis with a
programmable calculator. NIH Pub No. 79-1649. Bethesda, MD:
National Institutes of Health, 1979;31-32.

4. Software inventory for epidemiologists continues to grow. The
Epidemiology Monitor, 1988:9;1-4.

5. Sackett DL, Haynes RB, Tugwell P. Clinical Epidemiology: a basic
science for clinical medicine. Little, Brown and Company, Boston,
1985.

6. Rothman KJ. Modern Epidemiology. Little, Brown and Company,
Boston, 1986.

7. Mausner JS, Kramer S. Mausner & Bahn Epidemiology - An
Introductory Text, 2nd Ed. W. B. Saunders Co., Philadelphia, 1985.