The negative predictive value is the true-negative test results divided by all patients with negative results. This is also referred to as the  predictive value of a negative test. 

negative predictive value =

= (d / (c + d))



• d =  true negatives

• (c + d) = sum of ( false negatives and true negatives) = all negative test results


If the prevalence of disease in a study is similar to that in the population [prevalence in the population = (a + c) / (a + b + c + d)], then the probability of disease with a negative result is (c / (c + d)), or (1 - NPV).

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