# Determine the optimum sample size in an analysis of the expected net benefit of sampling

Source:`R/enbs.R`

`enbs_opt.Rd`

The optimum sample size for a given willingness to pay is determined either by a simple search over the supplied ENBS estimates for different sample sizes, or by a regression and interpolation method.

## Arguments

- x
Data frame containing a set of ENBS estimates for different sample sizes, which will be optimised over. Usually this is for a common willingness-to-pay. The required components are

`enbs`

and`n`

.- pcut
Cut-off probability which defines a "near-optimal" sample size. The minimum and maximum sample size for which the ENBS is within

`pcut`

(by default 5%) of its maximum value will be determined.- smooth
If

`TRUE`

, then the maximum ENBS is determined after fitting a nonparametric regression to the data frame`x`

, which estimates and smooths the ENBS for every integer sample size in the range of`x$n`

. The regression is done using the default settings of`gam`

from the mgcv package.If this is

`FALSE`

, then no smoothing or interpolation is done, and the maximum is determined by searching over the values supplied in`x`

.- smooth_df
Basis dimension for the smooth regression. Passed as the

`k`

argument to the`s()`

term in`gam`

. Defaults to 6, or the number of unique sample sizes minus 1 if this is lower. Set to a higher number if you think the smoother does not capture the relation of ENBS to sample size accurately enough.- keep_preds
If

`TRUE`

and`smooth=TRUE`

then the data frame of predictions from the smooth regression model is stored in the`"preds"`

attribute of the result.

## Value

A data frame with one row, and the following columns:

`ind`

: An integer index identifying, e.g. the willingness to pay and other common characteristics of the ENBS estimates (e.g. incident population size, decision time horizon). This is copied from `x$ind`

.

`enbsmax`

: the maximum ENBS

`nmax`

: the sample size at which this maximum is achieved

`nlower`

: the lowest sample size for which the ENBS is within

`pcut`

(default 5%) of its maximum value

`nupper`

: the corresponding highest ENBS