I would like to know if I can include these study designs apart from longitudinal studies in my systematic review which will focus on measuring incidence of a disease.
If you know the person years of the population from which the cases are obtained in a case control study you can determine disease incidence- will this type of study design be classified as a case cohort study?
I think, here the major challenge in this case, to define denominator in a case control study. It is understood that, 1. as a part of systematic review you include only studies which has been completed/ published; 2. case control studies don't have information on denominator; 3. Even, usually it is not possible to count and enroll all the events/ outcomes in the case control study; 4. in most of studies, cases and control come from different places. Hence, given the study design is systematic review, largely case control studies won't be fulfilling the eligibility criteria, rarely you may find such situations in the published literature.
In Cross sectional studies, the finding will be highly biased to determine incidence as primary purpose of such studies won't be identification of new cases and incidence, if it provides such information, would be highly biased especially suffering from recall bias. In case some cross sectional studies are included in the meta-analysis, sensitivity analysis should be done whether study design may have affected to estimates.
Reagarding cross-sectional and classical case control studies, you can not measure the incidence of a disease because by the time of the study already the exposure and outcome occured. But i think it can be estimated with specific type of case control like nested case control.
The proper method of estimating the incidence is selecting candidates free of disease and count those who developed the disease later weather prospectively or retrospectively where a proper records and documentation are available, other than that, the results will be questionable.