You can't convert them without knowing rates in exposed and unexposed populations separately, but if the case control study used density sampling you can equate the odds ratio with the hazard ratio. If the case control study used cumulative sampling of a "rare" disease, odds ratio would be a close approximation to hazard ratio.
Son dos mediciones diferentes, deberías contar con la tabla 2x2 para hacer ambos calculos por separado, ademas el uso de una u otra medida depende del diseño metodologico de la investigación.
En meta analisis esta es una necesidad ante la ausencia de articulos cientificos, se desarrollo una formula, pero se usa con la condicion de saber que el OR y el HR son muy parecidos.
HR= OR / (1 - p + (p * OR)
Pero esto posiblemente disminuirá la calidad metodológica de la investigación.
Check the work of ( including the books authored by) Dr David Spiegelhalter & Professor Sir David Cox. Links can be found via Google Scholar, Scopus, OrcID, PubMed etc
The odds ratio (OR) is more intuitive, while the hazard ratio (HR) varies over time and has an inherent selection bias. They are different, have different meanings, and there is no formula to convert the HR to OR. If possible, one should report OR or absolute or relative risk than HR.
This is an excellent paper written by Hernan: Article The Hazards of Hazard Ratios