Envelope of a difference, a percent change or a rate under publication bounds
Source:R/published_bounds.R
chgenv.RdGiven the intervals from pubbnd()
for the current and the
previous cell, the set of differences and percent changes that the
observed counts could have produced is an interval too: its ends are
reached at the ends of the input intervals, because the difference and
the ratio are monotone in each argument. This is interval arithmetic,
not a confidence interval; it says nothing about sampling and everything
about what the release withheld.
Arguments
- now, prev
rmbl_boundsobjects frompubbnd()(or data frames with numericlowerandupper) for the current and the earlier cell, with the same number of rows.- pop, prepop
Optional numeric exposures (for example residents) for a rate envelope of the current and the previous cell; the rate is
per * count / population. DefaultNULL.prepopis used only withpop.- per
Numeric scalar, the rate base when exposures are given; default
1000(per 1,000).
Value
A data frame, one row per cell, with numeric columns
chglo, chgup, pctlo,
pctup (NA where the previous cell could have been
zero); with population also ratelo and
rateup; with prepop as well
preratelo and prerateup.
Details
With current interval \([a_l, a_u]\) and previous interval
\([b_l, b_u]\): the change lies in \([a_l - b_u, a_u - b_l]\) and the
percent change in \([100(a_l / b_u - 1), 100(a_u / b_l - 1)]\). An end of
the percent interval is NA when its denominator could be zero (an
upper bound needs \(b_l > 0\), a lower bound \(b_u > 0\)), since a
change from zero has no percentage. A rate interval is
\([per \cdot a_l / pop, per \cdot a_u / pop]\); the population is taken
as exact.
Errors when now and prev have different numbers of
rows. The populations are not checked; give one per row (or one value).
Examples
now <- pubbnd(c(45, 120), rnd = 5)
prev <- pubbnd(c(40, 100), rnd = 5)
chgenv(now, prev)
#> ╭── Change between published values ─────────────────────────────────────╮
#> │ Cells 2 │
#> │ Certain rises 1 │
#> │ Certain falls 0 │
#> │ │
#> │ cell change change % │
#> │ ---- -------- -------------- │
#> │ 1 [0, 10] [0.00, 26.67] │
#> │ 2 [15, 25] [14.63, 25.64] │
#> │ │
#> │ Each interval holds every change consistent with the two published │
#> │ (rounded or suppressed) values. An interval that spans 0 cannot tell │
#> │ a rise from a fall. │
#> ╰────────────────────────────────────────────────────────────────────────╯
# with rates per 1,000 residents in both years
chgenv(now, prev, pop = c(10000, 20000),
prepop = c(10000, 19000))
#> ╭── Change between published values ─────────────────────────────────────╮
#> │ Cells 2 │
#> │ Certain rises 1 │
#> │ Certain falls 0 │
#> │ │
#> │ cell change change % rate previous rate │
#> │ ---- -------- -------------- -------------- -------------- │
#> │ 1 [0, 10] [0.00, 26.67] [4.250, 4.750] [3.750, 4.250] │
#> │ 2 [15, 25] [14.63, 25.64] [5.875, 6.125] [5.132, 5.395] │
#> │ │
#> │ Each interval holds every change consistent with the two published │
#> │ (rounded or suppressed) values. An interval that spans 0 cannot tell │
#> │ a rise from a fall. │
#> ╰────────────────────────────────────────────────────────────────────────╯
# a suppressed previous cell could have been zero: no upper percentage
chgenv(pubbnd(12), pubbnd("<5"))
#> ╭── Change between published values ─────────────────────────────────────╮
#> │ Cells 1 │
#> │ Certain rises 1 │
#> │ Certain falls 0 │
#> │ │
#> │ cell change change % │
#> │ ---- ------- -------- │
#> │ 1 [8, 12] [200, ] │
#> │ │
#> │ Each interval holds every change consistent with the two published │
#> │ (rounded or suppressed) values. An interval that spans 0 cannot tell │
#> │ a rise from a fall. │
#> ╰────────────────────────────────────────────────────────────────────────╯
# the two sides must line up
try(chgenv(now, prev[1, ]))
#> Error : `now` and `prev` must have the same number of rows