# 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.

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