Some researchers who apparently like being argued with by parents say they have determined when toilet training should begin: between 24 and 32 months, and when matters more than how. This was published in the Journal of Pediatric Urology and described in Science Daily.
I saw this in Science Daily and went to the report. I saw only the abstract, because I'm not prepared to subscribe to any more journals. If I found the right report, its actual results were that "Initiation of toilet training after 32 months of age was associated with urge incontinence (P=0.02)."
Not being current in pediatric or other urology, I then Googled "urge incontinence" and found that it means "involves a strong, sudden need to urinate. Then the bladder contracts, leading to urine leakage."
I think this means if you wait until the kid is older than 32 months to start toilet training, then you're gonna be doing a lot more laundry while they're growing up.
Now I'm not willing to buy the report to read it, and the P=0.02 means they didn't just ask their friends about their kids but are basing it on data, in a peer-reviewed journal, but I have an inbuilt skepticism that there is a causal relation going on here. I'd really like to see a mechanism.