Sample-size planning for a Gaussian graphical model

Recommends a sample size for a prospective Gaussian graphical model study, given a prior elicited from a previous one. "DPIR" returns two sizes, one for the graph as a whole and one at the parameterwise level (considering only the off-diagonal elements). "BFDA" returns one per hypothesis: under the null (edge absent) and under the alternative (edge present). "BSDA" returns a single size at which edge selection reaches a target sensitivity or specificity with a given power.

Usage

# S3 method for class 'ggm_elicited'
design(
  params,
  method = c("DPIR", "BFDA", "BSDA"),
  H = 150L,
  J = 20L,
  n = NULL,
  threshold = NULL,
  n_tol = 1L,
  max_n = 5000L,
  target_probability = 0.95,
  rho_quantile = 0.5,
  pow0 = 0.8,
  pow1 = 0.8,
  nsim_bf = 1000L,
  measure = c("sen", "spe"),
  measure_value = 0.8,
  target_pow = 0.8,
  range_lower = 2L,
  control = bsda_control(),
  ...
)

Arguments

params: A ggm_elicited object, as returned by elicit_prior. It also inherits from bgm_elicited.
method: Which planning method to use, "DPIR" (default), "BFDA", or "BSDA". One method runs per call.
H, J: Outer and inner Monte Carlo replication counts. H draws from the prior (default 150), J datasets per draw (default 20).
n: Candidate sample sizes to search over. NULL (default) picks a grid automatically and refines it by bisection.
threshold: DPIR and BFDA only. Target threshold the criterion must reach: the DPIR ratio for "DPIR", the Bayes factor for "BFDA". NULL (default) uses 1.0 for DPIR and 10.0 for BFDA. BSDA uses measure_value instead.
n_tol: Search tolerance, in observation units. The search stops once the bracket reaches this width. Default 1, i.e. exact (increasing this value speeds up the search but may reduce accuracy).
max_n: Largest sample size considered. If the target is not met by max_n, the search stops and reports non-convergence. Default 5000.
target_probability: DPIR only: how often the ratio must reach threshold. Default 0.95.
rho_quantile: BFDA only: which edge to plan around. Edges are ordered by the magnitude of their partial correlation and the one at this quantile is selected. Default 0.5, the median edge. The selected edge is reported with its signed partial correlation.
pow0, pow1: BFDA only: how often the Bayes factor must give decisive evidence for the hypothesis that is true. With BF01 the Bayes factor for edge absence, pow0 targets Pr(BF01 > threshold | H0), correctly excluding the edge, and pow1 targets Pr(BF01 < 1/threshold | H1), correctly detecting the edge. Both default to 0.8.
nsim_bf: BFDA only: number of Monte Carlo samples to estimate the Bayes factor for sparse graphs. Default 1000. Ignored for dense graphs, where the Bayes factor is available in closed form.
measure, measure_value, target_pow: BSDA only: the measure to plan for ("sen" or "spe"), the target value of that measure, and the target power to achieve it. Defaults are "sen", 0.8, and 0.8.
range_lower: BSDA only: the lower bound of the sample size search range. Default 2.
control: BSDA only: a list of control parameters, as returned by bsda_control. Default bsda_control().
...: Ignored, present for consistency with the generic design().

Value

A ggm_design object, which also inherits from bgm_design. Its results component contains the recommended sizes: n_star_global and n_star_pw for "DPIR"; n_star_power_h0 and n_star_power_h1 for "BFDA", each with a convergence flag, and a single n_star with a confidence interval (ci_lo, ci_hi) for "BSDA". For DPIR and BFDA, a sample size not reached within the search is NA with a FALSE convergence flag. For BSDA, identified is FALSE when the fit could not be established (too few non-saturated grid points), and converged is FALSE when the search stopped at max_iter without stabilizing. print and summary methods are available.

Details

Each method targets a criterion at a required frequency, but the criterion and the arguments differ:

DPIR: Targets a data-to-prior information ratio. Uses threshold (the ratio to surpass, default is 1) and target_probability (how often, default is 0.95).
BFDA: Targets a Bayes factor at a representative edge. Uses threshold (the Bayes factor value to surpass, default is 10), pow0/pow1 (the target power under each hypothesis), and rho_quantile (which edge to plan around).
BSDA: Targets a selection criterion (sensitivity or specificity) at a given power. Uses measure ("sen" or "spe"), measure_value (the level to reach, default 0.8), target_pow (the target power, default 0.8), range_lower (the smallest n searched), and control (sampler and fit settings; see bsda_control). Requires posterior inclusion probabilities, supplied as pip to ggm_parameters, and a sparse graph.

Arguments not required by a method are ignored.

Under BFDA the edge is tested with H0 : "the edge is absent" against H1 : "the edge is present", and the Bayes factor reported throughout is BF01, the Bayes factor for absence: BF01 > threshold excludes the edge, BF01 < 1/threshold detects it. This is the reciprocal of the inclusion Bayes factor BF10.

Under BSDA the search proceeds in two stages: a coarse exploration locates the region where the target power is met, then repeatedly fits a probit model to the power curve, inverts it for n*, and narrows the grid, until the recommendation stabilizes. Because the recommendation comes from a fitted curve rather than a direct threshold crossing, it carries a confidence interval, and it can fail in two ways: identified = FALSE (the fit could not be established) or converged = FALSE (the loop hit max_iter without stabilizing).

Cost grows with H * J and with the width of the search: the criterion is evaluated by simulation at every candidate n.

Usage

Arguments

Value

Details

See also