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Number Needed to Protect (NNP.xl4) Calculator
(Absolute Risk Production)
Clinical Decision Making Program
Department of Family Medicine, University of Oklahoma Health Sciences Center

Many studies talk about the relative risk or risk ratio of being exposed, versus not
exposed, to an entity such as a chemical or toxin or food or drug.
This is the rate of a bad outcome among those exposed, divided by the rate
among those not exposed. The problem is that equal risk rates will have different
impacts depending on how rare the outcome is.

An example is a statement in Science in 1995: Epidemiologists do not
take a reported risk seriously unless there is a risk ratio of at least 3.

The solution is to produce the absolute risk production (akin to the
absolute risk reduction for treatments) and the Number Needed to Protect (analogue of
the number needed to treat). How many people do we need to protect
in order to prevent one adverse outcome?

To do this we need information on the number of people who have bad outcomes
with and without the exposure.

This spreadsheet will calculate the Number Needed to Protect given raw data,
risk ratio, and odds ratio.

Raw Data Input                Page 2
Risk Ratio Input              Page 3
Odds Ratio Input              Page 4
Case/Control Data             Page 5




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Page 2

If the data come in the form of counts of patients who got, and did not get,
the adverse reaction, in a population based study or randomized controlled trial,
fill those in here and results will appear in the tables below.

                                    Outcome:
                                 Adverse     Good                 Rate

Exposed to risk factor                    300               300            0.500
Not exposed                               700               750            0.483

               No Exposure Exposure             Relative          Absolute       Number needed
                                                Risk                             to
                                                                  Risk Production protect

               NE                E              E/NE              E-NE             1/ARP

                         0.483          0.500            1.036             0.017         58.000


               Adverse        No adverse
               Outcome        Outcome
               a              b           a+b
Exposure                  300         300                   600

               c                 d              c+d
No exposure               700             750              1450

               a+c               b+d            a+b+c+d                            (Other options
                         1000            1050         2050                         below)

Correlation:   Phi Coefficient (or "r")                             r=                     0.016
               (ad-bc)/sqrt[(a+b)(c+d)(a+c)(b+d)]                   r2 =                   0.000

Yule's Q       Q = (ad-bc)/(ad+bc)                                 Q=                      0.034

Standardized increment       SI = (p2-p1)/sqrt(PQ)          SI =                           0.034
              = (a/(a+b) - c/(c+d))/sqrt((a+c)/N)*(b+d)/N))
              where N = a+b+c+d

Rate Ratio     RR =[a/(a+b)]/[c/(c+d)]                             RR =                    1.036

Odds Ratio     OR = ad/bc                                          OR =                    1.071

             L
Log Odds Ratioog OR = log a + log d - log b - log c                Log OR =                0.030

Rate Difference                  RD = a/(a+b) - c/(c+d)

               Disease rate increases from            0.482759
                               to                     0.500000
               due to exposure, for a gain of                      RD =               0.017241




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If the data come in the form of risk ratio, plus the risk for unexposed,
then give that and we will construct the table of counts.

              Reported risk ratio                         1.01
              Reported or est risk
               for the unexposed                            0.5
              Number of people/categ:                     1000


                                    Outcome:
                                 Adverse     Good                 Rate

Exposed to risk factor                  505                495           0.505
Not exposed                             500                500           0.500




              No Exposure Exposure             Relative           Absolute       Number needed
                                               Risk                              to
                                                                  Risk Production protect

              NE                 E             E/NE               E-NE           1/ARP

                         0.500         0.505          1.010              0.005      200.000




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If the data come in the form of odds ratio, plus the odds for unexposed,
then give that and we will construct the table of counts.

              Reported odds ratio                            5
              Reported or est odds
               for the unexposed                             8
              Number of people/categ:                     1000


                                    Outcome:                                                             # adverse for unexposed = (OUE/(1-OUE))*N
                                 Adverse     Good                Rate           Odds                     # good for unexposed = N - (OUE/(1-OUE))*N

Exposed to risk factor                 975.6           24.4             0.976             40             # adverse for exposed = OR*OUE*N/(1 + OR*OUE)
Not exposed                            888.9          111.1             0.889              8             # good for exposed = N - OR*OUE*N/(1 + OR*OUE)




              No Exposure Exposure             Relative          Absolute       Number needed
                                               Risk                             to
                                                                 Risk Production protect

              NE                 E             E/NE              E-NE           1/ARP

                         0.889         0.976          1.098             0.087          11.531




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If the data come in the form of counts of patients who got, and did not get,
the adverse reaction, in a case/control study,
fill those in here and results will appear in the tables below.

Cases:
                                 Adverse outcome
Exposed to risk factor                    30                       Proportion of cases exposed
Not exposed                               20                                  0.6

Controls:
                                 Adverse outcome
Exposed to risk factor                    20                       Proportion of controls exposed
Not exposed                               60                                 0.25

Rate of adverse outcome in the population                    0.5
Total number for the following table                       1000

                                    Outcome:
                                 Adverse     Good                  Rate

Exposed to risk factor                    300               125             0.706
Not exposed                               200               375             0.348

               No Exposure Exposure             Relative           Absolute       Number needed
                                                Risk                              to
                                                                   Risk Production protect

               NE                E              E/NE               E-NE             1/ARP

                         0.348          0.706            2.029              0.358           2.793


               Adverse        No adverse
               Outcome        Outcome
               a              b           a+b
Exposure                  300         125                   425

               c                 d              c+d
No exposure               200             375               575

               a+c               b+d          a+b+c+d                               (Other options
                          500             500       1000                            below)

Correlation:   Phi Coefficient (or "r")                              r=                     0.354
               (ad-bc)/sqrt[(a+b)(c+d)(a+c)(b+d)]                    r2 =                   0.125

Yule's Q       Q = (ad-bc)/(ad+bc)                                  Q=                      0.636

Standardized increment       SI = (p2-p1)/sqrt(PQ)          SI =                            0.716
              = (a/(a+b) - c/(c+d))/sqrt((a+c)/N)*(b+d)/N))
              where N = a+b+c+d

Rate Ratio     RR =[a/(a+b)]/[c/(c+d)]                              RR =                    2.029

Odds Ratio     OR = ad/bc                                           OR =                    4.500

             L
Log Odds Ratioog OR = log a + log d - log b - log c                 Log OR =                0.653

Rate Difference                  RD = a/(a+b) - c/(c+d)

               Disease rate increases from            0.347826
                               to                     0.705882
               due to exposure, for a gain of                       RD =               0.358056




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