According to data released by the Department of Civil Protection, there is less than 1 daily tests per thousand people as of July 24 2020.  
Lack of testing means that many of those who have contracted the virus will not be included in the count.  Increased testing may suggest a major surge in cases, that can actually be attributed to testing.  
Testing is also self selected for the most part, meaning that individuals who do not have the time to get tested or are less concerned about contracting a serious case and thus have less of an incentive to get tested, will not be included in the count.
When attempting to measure the population infection rate, Low testing rate is a negative confounding variable, while the unrandomized nature of the sample is a positive confounding variable.

University of California, Davis

The first case was reported in late January, with new reported deaths peaking at 969 on March 27th, and new reported cases peaking at 6,557 on March 21st. This data has been collected and reported by the Italian Department of Civil Protection.  Northern Italy was hit the hardest by the virus, with The cities of Milan, Bergamo, and Brescia seeing the highest total number of cases. The hardest hit regions saw a rate of over 1 in 100 residents testing positive for the virus.These statistics may be significant underestimates according the the Department of Civil Protection itself, as well as at least one study conducted by the Italian National Institute of Statistics.
An important challenge to accurate data collection was the delayed expansion of testing.   


Attempts at Documentation

Pourhoseingholi, M. A., Baghestani, A. R., & Vahedi, M. (2012). How to control confounding effects by statistical analysis. Gastroenterology and hepatology from bed to bench, 5(2), 79–83.

How to control confounding effects by statistical analysis

Data Confounded by Testing Rate

In Italy, official deaths are attributed to COVID-19 only for patients who test positive in hospitals or a limited number of nursing homes that provide testing.  This means that the Italian National Health Authority could have potentially excluded thousands of deaths could have been excluded from the reported data.  If you compare average death rates with death rates reported in the period of the COVID-19, there is a spike in some regions of over 100% increase.  Although it is believed that many national governments have reported inaccurate data, it is believed that official Italian data suffers some major discrepancies.

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