There are a few other notable education performance indices.
The International Association for the Evaluation of Educational Achievement (IEA) publishes the Progress in International Reading Literacy Study. It's cited by The Washington Post as an example of an international test.
PIRLS provides internationally comparative data on how well children read by assessing students’ reading achievement. PIRLS collects considerable background information on how education systems provide educational opportunities to their students, as well as the factors that influence how students use these opportunities.
There's also the Trends in International Mathematics and Science Study which is published also by IEA and it's cited as another example of an international test by The Washington Post and also by Brookings Institute and The Guardian.
TIMSS has been measuring trends in mathematics and science achievement at the fourth and eighth grades since 1995. Conducted every four years at the fourth and eighth grades, TIMSS has a quasi-longitudinal design, with the fourth grade student cohort assessed four years later at the eighth grade.
Wikipedia has some other rankings regarding "education and innovation" but most are mainly about literacy rates.