{"id":125665,"date":"2020-04-06T16:20:43","date_gmt":"2020-04-06T10:50:43","guid":{"rendered":"https:\/\/analyticstraining.com\/?p=15959"},"modified":"2022-11-22T16:48:20","modified_gmt":"2022-11-22T11:18:20","slug":"model-thinking-covid-19-a-brief-discussion-on-confusion-matrix","status":"publish","type":"post","link":"https:\/\/www.jigsawacademy.com\/model-thinking-covid-19-a-brief-discussion-on-confusion-matrix\/","title":{"rendered":"Model Thinking: COVID-19 – A brief discussion on Confusion Matrix"},"content":{"rendered":"

A brief discussion on Confusion Matrix – <\/b>As the COVID-19 pandemic continues to ravage the world, India has done remarkably well. Even as global infections have crossed 1.2 million, India\u2019s number at around 4,000 seem model, given we are home to one-sixth of the world\u2019s population. In per capita terms, only 3 in a million people in India are infected by COVID-19, vs 156 in a million people globally (as of 5<\/span>th<\/span> April 2020).<\/span><\/p>\n

A number of reasons have been suggested including a smaller number of tests<\/a>, BCG vaccine usage in India<\/a>, Indian strain being less virulent<\/a> and Indians being more resistant to infections.<\/span><\/p>\n

In this context, I seek to use the confusion matrix (also called error matrix and matching matrix in unsupervised learning) to discuss the impact of higher testing. <\/span><\/p>\n

Students of my Quantitative Methods class would be familiar with the chart below.  The confusion matrix tends to confuse a lot of the students. Its implications are underappreciated by many practitioners of statistics.<\/span><\/p>\n

\"\"<\/a>In brief, for any test, in medicine or otherwise, the results may have some error. These are classified as:<\/strong><\/h5>\n

1. True Positive:<\/strong> A true positive is the correct affirmation of the presence of a condition<\/span><\/p>\n

For example, concluding a pregnant lady is pregnant would be \u201cTrue Positive\u201d<\/span><\/p>\n

2. False Negative:<\/strong> A false negative <\/span>is an error in which a test result improperly indicates no presence of a condition (the result is <\/span>negative<\/span><\/i>), when in reality, the condition is present.<\/span><\/p>\n

For example, concluding a pregnant lady is not pregnant would be \u201cFalse Negative\u201d<\/span><\/p>\n

3. False Positive:<\/strong> A false positive is the error in affirmation of the presence of a condition<\/span><\/p>\n

For example, concluding a man is pregnant would be \u201cFalse Positive\u201d<\/span><\/p>\n

4. True Negative:<\/strong> A true negative is the correct affirmation that the condition is not present <\/span><\/p>\n

For example, concluding a man is not pregnant would be \u201cTrue Negative\u201d<\/span><\/p>\n

For any tests, some error will occur. Some infected people will be assumed to be uninfected (false negatives) and some uninfected people will show up being infected (false positives). What are the true positive rates (also called sensitivity) for the COVID-19 tests? We don\u2019t know yet. <\/span><\/p>\n

Let’s assume (this is hypothetical and not meant to be a forecast), that: <\/strong><\/h5>\n