Exact Likelihood Functions For Common Designs

Constructs the likelihood function implied by the exact sampling model of several common designs, with any nuisance parameters removed by conditioning or profiling rather than by normal approximation. Returns the same object structure as curve_lik().

curve_lik_exact(type = c("prop", "or", "rr", "mean", "var", "corr"),
  x = NULL, n = NULL, a = NULL, b = NULL, c = NULL, d = NULL,
  t1 = NULL, t0 = NULL, data = NULL, steps = 1000, table = TRUE)

Arguments

type

The design:

"prop"

A binomial proportion. Supply x (successes) and n (trials). The likelihood is exact binomial; the parameter is the risk \(p\).

"or"

A 2x2 table odds ratio. Supply cell counts a, b, c, d (exposed cases, exposed non-cases, unexposed cases, unexposed non-cases). The likelihood is the exact conditional (noncentral hypergeometric) likelihood on the log-odds-ratio scale; its maximum is the conditional MLE, which deliberately differs from \(ad/bc\).

"rr"

A rate ratio from two Poisson counts. Supply a (exposed events), t1 (exposed person-time), b (unexposed events), t0 (unexposed person-time). The likelihood is the exact conditional binomial likelihood on the log-rate-ratio scale.

"mean"

A normal mean. Supply the data vector data; the variance is profiled out.

"var"

A normal variance. Supply data; the parameter is \(\sigma^2\).

"corr"

A bivariate-normal correlation. Supply data as a two-column matrix or data frame; the four nuisance parameters are profiled out numerically.

x, n

Successes and trials for type = "prop".

a, b, c, d

Cell counts for type = "or"; for type = "rr", a and b are the two event counts.

t1, t0

Person-time denominators for type = "rr".

data

Data for type = "mean", "var" (numeric vector), or "corr" (two columns).

steps

Number of grid points. Defaults to 1000.

table

Indicates whether or not a table output should be generated. The default is TRUE.

Value

A list with 2 items where the dataframe of values is in the first object, and the table for the values in the second if table = TRUE.

References

Royall R. Statistical Evidence: A Likelihood Paradigm. Chapman & Hall/CRC; 1997.

Cox DR, Hinkley DV. Theoretical Statistics. Chapman & Hall; 1974.

See also

as_curve_lik() curve_lik_glm() curve_support()

Examples

# exact conditional odds-ratio likelihood for a 2x2 table
lik <- curve_lik_exact(type = "or", a = 12, b = 8, c = 5, d = 15)
ggcurve(lik[[1]], type = "l1", nullvalue = 0)