In general, the methods of diagnosis in phytopathology are used to classify plants in two groups depending on the presence or absence of the specific pathogen. The results of the analysis permit to elaborate an opinion, which consitiutes the diagnosis. Without a correct diagnosis is not possible an efficient and effective decision making. Moreover, it is necessary to assume that there are no perfect methods free of false positive and/or false negative results.
The results of the analysis of a population can be summarized in the following table, which allows the evaluation of the technique.
Contingency table for the evaluation of a diagnostic method
|
|
|
Sanitary status |
|
|
|
|
|
Disease |
No disease |
|
|
Result of the technique |
Positive |
a |
b |
a+b |
|
Negative |
c |
d |
c+d |
|
|
|
|
a+c |
b+d |
N |
Parameters to evaluate diagnostic methods
The incidence is the new occurrences of disease in a population over a period of time. Formula to calculate incidence is: new cases / population at risk.
There are two indicators of the operational capacity of a technique, sensitivity and specificity, which provide information on the proportion of true positives and true negatives identified by the method. This is the behavior of the method using the squares aligned in the columns of the contingency table. These values are inherent to the technique and they do not vary with the prevalence . A sensitive technique will be used to rule out disease and a specific technique to rule in disease.
In the contingency table the value of sensitivity is a / (a + c) and the value of specificity is d / (b + d).
False positive a negative rates
The false positive rate for a technique is the false
positive results divided by all plants without the disease.
In the contingency table the value of false positive rate is
b / (b + d)
= 1- specificity
The false negative rate for a technique is the false
negative results divided by all plants with the disease. In
the contingency table the value of false negative rate is
c / (a + c)
= 1- sensitivity
Positive and negative predictive values
Sensitivity and specificity do not answer the question that concerns to a technician of a Diagnositc Service. This is how much is the probability that the plant is infected if the test result is positive or not infected if the result is negative. In other words, the behavior of the method using the squares aligned in the rows of the contingency table. These concepts are the predictive values of the method. Therefore, the probability that a method makes an accurate diagnosis is determined calculating the predictive values.
In the contingency table the value of positive predictive value is a / (a + b) and the negative predictive value is d / (c + d). However, predictive values change with prevalence and are not stable parameters.Sensitivity and specificity do not include false positive and false negative rates to calculate their values. Predictive values depend on the prevalence of disease. Do exist parameters free of these influences?.
Likelihood ratios are free of influence of the prevalence and they can be calculated on the basis of the sensitivity and specificity, which are stable for each method. The positive likelihood ratio will be applied in case that the technique diagnoses a sample as positive and the negative likelihood ratio will be applied in case the technique diagnoses a sample as negative. All of them give the likelihood of having disease.
Positive likelihood ratio considers sensitivity and false positives rate that the method diagnoses. In the contingency table it is the division between sensitivity and proportion of false positives [a/(a+c)]/[b/(b+d)]Because the proportion of false positives or [b/(b+d)] is equal to 1-[d/(b+d)] or alternatively 1 - specificity, subsequentlyPositive likelihood ratio = sensitivity/1 - specificity
Negative likelihood ratio considers false negative rate and specificity that the method diagnoses. In the contingency table it is the division between the proportion of false negatives and specificity[c/(a+c)]/[d/(b+d)]Because the proportion of false negatives or [c/(a+c)] is equal to 1-[a/(a+c)] or alternatively 1 - sensitivity, subsequentlyNegative likelihood ratio = 1 - sensitivity/specificity
