Trend in a count series, as a rate ratio per period

Fits a Poisson log-linear trend by iteratively reweighted least squares and reports the multiplicative change per period, which is what a count series' trend actually is. An offset carries the denominator when the exposure varies.

Usage

count_trend(y, x = NULL, offset = NULL, conf_level = 0.95)

Arguments

y

Counts, in period order.

x

Periods. Defaults to the position.

offset

Exposure for each period – a population, a number of admissions, a number of days. The trend is then in the rate rather than in the count.

conf_level

Confidence level for the rate ratio.

Value

A list with rate_ratio (per period), its interval, p_value, the fitted values, the dispersion, and overdispersed.

Details

The dispersion is reported because a Poisson fit assumes it is one. When it is well above one the interval is too narrow, and the quasi-Poisson interval – which scales the standard error by the square root of the dispersion – is returned instead, with overdispersed set.

References

Bilder, C. R. and Loughin, T. M. Analysis of Categorical Data with R, 2nd edn. Chapman and Hall/CRC, on the quasi-likelihood treatment of an overdispersed Poisson fit: the variance is scaled by an estimated dispersion, which widens the interval while leaving the point estimate alone. That is the behaviour reported here through dispersion and overdispersed.

Examples

# A count falling by about 15% a year.
set.seed(3)
y <- stats::rpois(8, lambda = 200 * 0.85^(0:7))
fit <- count_trend(y)
round(fit$rate_ratio, 3)
#> [1] 0.869

# With a varying denominator the trend is in the rate.
count_trend(c(20, 25, 30), offset = c(1000, 1500, 2500))$rate_ratio
#> [1] 0.7708656