Studies proving duration threshold for correlation between tanning bed use and melanoma?

A lot of dermatological research has demonstrated correlation between tanning bed use and skin cancer, but in cities where vitamin D deficiency is becoming the norm, and perhaps itself a greater carcinogenic risk than skin cancer, some dermatologists have recommended use of tanning beds emitting UVB for very low durations/frequencies (2min, 2x/week). None of the studies I can find indicate the duration threshold or the average duration of the samples used when proving correlation between tanning bed use and melanoma; can any scientists/doctors out there find a study which may assist in determining the duration threshold above which risk for melanoma increases?