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This are beautiful graphs @mdmadhusudan
My take on these: Most concerning states are Gujrat & West Bengal, the case fatality is high while case detection rates are static. This means that they have poor surveillance systems. They are not actively looking for cases. 1 of n
Madhya Pradesh has done well in bringing its case fatality while slowly (very slow) in improving detection rates. They can do better of course. That will increase denominator for case fatality and it will improve.

Punjab is the star performer in reducing case fatality.
Bihar is an outlier

For all the states, you can see some correlation between case detection and fatality, but not for Bihar. The concerning thing is deaths are increasing in the last one week, an early sign of undetected hot spots. 3 of n.
What we want to see is a V shape seen in Kerala. It is ideal.
Case detection keeps improving and case fatality keeps decreasing.

All the south Indian states, Haryana & Rajastha are mimicking this v shape from some point of time. Good sign for these states. 4 of n
Delhi is relatively better in tackling case fatality, while MH seems to be increasing. Concerning, may suggest several things.
1. Delayed detection.
2. Late admission
3. Poor access to hospitals
4. Ineffective specialized care
5. Greater % of elderly/comorbidities 5 of n
Caveats:
1. We need to adjust for health system capacity
2. These simple descriptive stats do not account for silent districts (future hot spots)
3. The graphs should be adjusted for quality of surveillance systems
4. Several confounders need to be adjusted. 6 of n
In general, deaths show how good the combined response of surveillance (early reporting ) of curative services are (how well you treated)

Testing shows how good your surveillance system is. If you want to test more, you will detect more cases, and also case fatality falls. n/n
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