"cases based on" is correct and can be used in written English.
For example, "A judge will decide the outcome of the cases based on the evidence provided."
At one location they used constructed cases, based on current challenges on the ward.
Cosby is fighting numerous civil cases based on those claims.
Already three cases based on his evidence have been dropped.
We present 3 clinical cases based on 3DP modeling technology.
Internationally, there are very positive cases based on strong guidelines.
Analysts would worry if this suit led to more liability cases based on secondary-smoke inhalation.
Ever since, a wave of court cases based on e-mail has mounted.
Prosecutors tend to be cautious about pursuing criminal cases based on novel legal theories.
In both cases, based on past history, the numbers are clearly favorable for Republicans.
Heatmap and hierarchical clustering of myopia cases based on DNA methylation.
The agency has brought seven cases based on information culled from that project since 2011.
