Function for the Kullback-Leibler Divergence of two normally distributed treatment effects for the same pairwise comparison

The user specify the (posterior) mean and standard error (or posterior standard deviation) of two estimated treatment effects, X and Y, that refer to the same pairwise comparison and are assumed to follow a normal distribution. The function returns the Kullback-Leibler Divergence (KLD) measure of 1) approximating X with Y, 2) approximating Y with X, and 3) their average.

Usage

kld_measure(mean_y, sd_y, mean_x, sd_x)

Arguments

mean_y

A real number that refers to the mean of the estimated treatment effect Y on the scale of the selected effect measure (in logarithmic scale for relative effect measures).

sd_y

A positive integer that refers to the posterior standard deviation or the standard error of the estimated treatment effect Y on the scale of the selected effect measure (in logarithmic scale for relative effect measures).

mean_x

A real number that refers to the mean of the estimated treatment effect X on the scale of the selected effect measure (in logarithmic scale for relative effect measures).

sd_x

A positive integer that refers to the posterior standard deviation or the standard error of the estimated treatment effect X on the scale of the selected effect measure (in logarithmic scale for relative effect measures).

Value

The function return the following numeric results:

kld_sym	The symmetric KLD value as the average of two KLD values .
kld_x_true	The KLD value when approximating X by Y (X is the 'truth').
kld_y_true	The KLD value when approximating Y by X (Y is the 'truth').

References

Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat 1951;22(1):79–86. doi: 10.1214/aoms/1177729694

See also

kld_inconsistency, kld_inconsistency_user, robustness_index, robustness_index_user