After some further discussion and research, there are differences in how epidemiological weeks can be calculated.
EPITOOLS as.week
In public health, reportable diseases are often reported by 'disease
week' (either week of reporting or week of symptom onset). In R, weeks
are numbered from 0 to 53 in the same year. The first day of week 1
starts with either the first Sunday or Monday of the year. Days before
week 1 are numbered as 0s. In contrast to R, the as.week function
generates weeks numbered from 1 to 53. The week before week 1 takes on
the value (52 or 53) from the last week of the previous year. The
as.week functions facilitates working with multiple years and
generating epidemic curves.
MMWR week
Values for MMWR week range from 1 to 53, although most years consist
of 52 weeks. The first day of any MMWR week is Sunday. MMWR week
numbering is sequential beginning with 1 and incrementing with each
week to a maximum of 52 or 53. MMWR week #1 of an MMWR year is the
first week of the year that has at least four days in the calendar
year. For example, if January 1 occurs on a Sunday, Monday, Tuesday or
Wednesday, the calendar week that includes January 1 would be MMWR
week #1. If January 1 occurs on a Thursday, Friday, or Saturday, the
calendar week that includes January 1 would be the last MMWR week of
the previous year (#52 or #53). Because of this rule, December 29, 30,
and 31 could potentially fall into MMWR week #1 of the following MMWR
year.
EPIWEEK for STATA
Each epidemiological week begins on a Sunday and ends on Saturday. And
the first epidemiological week of year ends on the first Saturday of
January, provided that it falls at least four or more days into the
month
ISO (or business) week
An ISO week-numbering year (also called ISO year informally) has 52 or
53 full weeks. That is 364 or 371 days instead of the usual 365 or 366
days. The extra week is referred to here as a leap week, although ISO
8601 does not use this term. Weeks start with Monday. The first week
of a year is the week that contains the first Thursday of the year
Week "u" in SAS
Each epidemiological week begins on a Sunday and ends on Saturday. And
the first epidemiological week of year contains Sunday. Weeks range
from 0 to 53 but do not always count 7 days
dput(DATE_variable)
. – shadow?epicurve.weeks
page a bit, I see that your understanding of the "week" definition does not agree with the 'epitools' author's definition. – IRTFM