# Sensitivity and specificity on cases rather than individual days

I have data collected from sensors to detect disease in several individuals. Each individual has a known disease status (labelled Actual in the table below) for each day and a predicted disease status (Predicted in table below) from prediction equations performed on the sensor data. I am trying to calculate sensitivity/specificity from this. Each individual can have more than one disease case, and cases can last for multiple days. The sensor fairly accurate at detecting disease on the first or second day of disease. On some occasions the sensor data is able to predict disease the day before a case is observed.

For example in the table below, a disease day is predicted from the sensor data the day before a disease event occurred. A healthy day is denoted by a 0 and an ill/diseased day by 1. There has to be 3 clear (healthy) days between recorded disease events for it to be classed as a new event, so days 41 and 42 are part of the same event as days 37-39. This should be classed as a true positive as it was able to predict the disease event.

  Day   Actual   Predicted
----- -------- -----------
34        0           0
35        0           0
36        0           1
37        1           0
38        1           0
39        1           0
40        0           0
41        1           0
42        1           0
43        0           0
44        0           0


The issue with the “traditional” way of performing sensitivity and specificity (or at least the way I’ve been doing it) is that it looks at each day individually rather than on a case by case basis. This gives really poor sensitivity results as cases can last for multiple days, when in fact the sensor is able to detect the disease event on the first day of disease.

Is there a way to perform sensitivity/specificity analysis on this data? Or would another test be more suitable?