Interval-specific likelihood ratios

Command:

Statistics

ROC curves

Interval likelihood ratios

Description

Allows to calculate the likelihood ratios (with 95% CI) for user-defined data intervals.

When test results have a continuous or ordinal outcome then valuable information is lost when the data are dichotomized for the calculation of sensitivity, specificity and likelihood ratios as in ROC curve analysis.

Interval likelihood ratios may be more powerful because they use more information contained in the data.

The likelihood ratio can be used to calculate the post-test probability of disease from the pre-test probability of disease.

Required input

Dialog box for Interval likelihood ratios

Variable: select the variable of interest.
Classification variable: select a dichotomous variable indicating diagnosis (0=negative, 1=positive).
If your data are coded differently, you can use the Define status tool to recode your data.
Filter: (optionally) a filter in order to include only a selected subgroup of cases (e.g. AGE>21, SEX="Male").

Define intervals

After some calculations, a new dialog box is displayed with suggested data intervals which you can modify.

Define intervals for likelihood ratios

You can define up to 12 intervals. For each interval you enter the lower and upper (inclusive) boundaries.

For categorical variables, with few categories, it may suffice to enter only one number to define the "interval" as one single category.

Results

Likelihood ratios - results

For each data interval the program reports the number of positive and negative cases in the interval, and the corresponding Likelihood ratio with 95% Confidence interval.

The likelihood ratio can be used to calculate the post-test odds from the pre-test odds of disease:

$$ post\text{-}test\ odds\ =\ pre\text{-}test\ odds\ \times\ likelihood\ ratio $$

The relation between odds and probability is:

$$ odds = \frac {p}{1-p}\ \text{and} \ p=\frac {odds}{1+odds} $$

Using these equations, you can calculate the post-test probability of disease from the pre-test probability of disease.

If, for example, the pre-test probability of disease is 0.6 then the pre-test odds is 0.6/(1-0.6) = 1.5. For a patient with test result in the interval 50-60, corresponding with a likelihood ratio of 12, the post-test odds are 1.5 x 12 = 18. The post-test probability of disease is 18/(1+18) = 0.95.

Literature

Gardner IA, Greiner M (2006) Receiver-operating characteristic curves and likelihood ratios: improvements over traditional methods for the evaluation and application of veterinary clinical pathology tests. Veterinary Clinical Pathology, 35:8-17.