Is there a branch of statistics that deals with data for which exact values are not known, but for each individual, we know either a maximum or minimum bound to the value?
I suspect that my problem stems largely from the fact that I am struggling to articulate it in statistical terms, but hopefully an example will help to clarify:
Say there are two connected populations $A$ and $B$ such that, at some point, members of $A$ may "transition" into $B$, but the reverse is not possible. The timing of the transition is variable, but non-random. For example, $A$ could be "individuals without offspring" and $B$ "individuals with at least one offspring". I am interested in the age this progression occurs but I only have cross-sectional data. For any given individual, I can find out if they belong to $A$ or $B$. I also know the age of these individuals. For each individual in population $A$, I know that the age at transition will be GREATER THAN their current age. Likewise, for members of $B$, I know that the age at transition was LESS THAN their current age. But I don't know the exact values.
Say I have some other factor that I want to compare with the age of transition. For example, I want to know whether an individual's subspecies or body size affects the age of first offspring. I definitely have some useful information that should inform those questions: on average, of the individuals in $A$, older individuals will have a later transition. But the information is imperfect, particularly for younger individuals. And vice versa for population $B$.
Are there established methods to deal with this sort of data? I do not necessarily need a full method of how to carry out such an analysis, just some search terms or useful resources to start me off in the right place!
Caveats: I am making the simplifying assumption that transition from $A$ to $B$ is instantaneous. I am also prepared to assume that most individuals will at some point progress to $B$, assuming they live long enough. And I realise that longitutinal data would be very helpful, but assume that it is not available in this case.
Apologies if this is a duplicate, as I said, part of my problem is that I don't know what I should be searching for. For the same reason, please add other tags if appropriate.
Sample dataset: Ssp indicates one of two subspecies, $X$ or $Y$. Offspring indicates either no offspring ($A$) or at least one offspring ($B$)
age ssp offsp
21 Y A
20 Y B
26 X B
33 X B
33 X A
24 X B
34 Y B
22 Y B
10 Y B
20 Y A
44 X B
18 Y A
11 Y B
27 X A
31 X B
14 Y B
41 X B
15 Y A
33 X B
24 X B
11 Y A
28 X A
22 X B
16 Y A
16 Y B
24 Y B
20 Y B
18 X B
21 Y B
16 Y B
24 Y A
39 X B
13 Y A
10 Y B
18 Y A
16 Y A
21 X A
26 X B
11 Y A
40 X B
8 Y A
41 X B
29 X B
53 X B
34 X B
34 X B
15 Y A
40 X B
30 X A
40 X B
Edit: example dataset changed as it wasn't very representative