This means that you have incomplete data backwards in time: you only observe life histories backwards from now to the previous event. In survival analysis this is called "current status data". Not only is there incomplete data but also biasing - you are more likely to see individuals in longer rather than in shorter unions. There is a huge literature on the subject.

Thank you fot your support and indications. If you can provide me some starting references I will continue to study on them. What does it means I have to look at "individuals in longer rather than in shorter union"?

I didn't say you *have* to look at individuals in longer rather than shorter union. What I mean is that when you sample at a fixed time point and look at a sampled person's current state, the duration of those states will be length biased. You are more likely to pick someone while they are in a long duration than when in a short duration state. For current status data, try Google "current status data"! This gives many references to recent work mainly in biostatistics. You can also Google "current status data demography" for literature in your field.