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

Variable: identify the variable under study.

Classification variable: select or enter a dichotomous variable indicating diagnosis (0=negative, 1=positive). If diagnosis is coded differently than using the values 0 and 1, you can use the IF function to transform the codes into 0 and 1 values, e.g. IF(RESULT="pos",1,0).

Select: (optionally) a selection criterion 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.

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

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 off disease:

post-test odds = pre-test odds x likelihood ratio

The relation between odds and probability is:

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. [Abstract]

See also

• ROC curves: Introduction
• ROC curve analysis in MedCalc
• Interactive dot diagram
• Plot versus criterion values
• Predictive values
• Comparison of ROC curves