Deprecated functions in package Replicate.

Description

The functions listed below are deprecated and will be defunct in the near future. Alternative functions with improved functionality are also mentioned. Help pages for deprecated functions are available at help("<function>-deprecated").

Statistical consistency of original study with replication

Description

Given the original study's effect estimate and its variance, the estimated average true effect size in the replications, and the estimated heterogeneity in the replications, computes estimated probability that the original study would have an effect estimate at least as extreme as the observed value if the original and the replications in fact are statistically consistent. Allows for heterogeneity.

Usage

p_orig(yio, vio, yr, t2, vyr)

Arguments

Details

yr, vyr, and t2 can be estimated through, for example, random-effects meta-analysis or a mixed model fit to the individual subject data. See Mathur & VanderWeele's (under review) Appendix for details of how to specify such models.

References

1. Mathur MB & VanderWeele TJ (under review). New statistical metrics for multisite replication projects.

Examples

# replication estimates (Fisher's z scale) and SEs
# from moral credential example in Mathur and VanderWeele
# (under review)
yir = c(0.303, 0.078, 0.113, -0.055, 0.056, 0.073,
0.263, 0.056, 0.002, -0.106, 0.09, 0.024, 0.069, 0.074,
0.107, 0.01, -0.089, -0.187, 0.265, 0.076, 0.082)

seir = c(0.111, 0.092, 0.156, 0.106, 0.105, 0.057,
0.091, 0.089, 0.081, 0.1, 0.093, 0.086, 0.076,
0.094, 0.065, 0.087, 0.108, 0.114, 0.073, 0.105, 0.04)

# meta-analyze the replications
m = metafor::rma.uni( yi = yir, vi = seir^2, measure = "ZCOR" ) 

p_orig( yio = 0.210, vio = 0.062^2, 
yr = m$b, t2 = m$se.tau2^2,  vyr = m$vb )

Compute prediction interval for replication study given original

Description

Given point estimates and their variances for one or multiple original studies and one or more replication studies, returns a vector stating whether each replication estimate is in its corresponding prediction interval. Assumes no heterogeneity.

Usage

pred_int(yio, vio, yir = NULL, vir, level = 0.95)

Arguments

Examples

# calculate prediction interval for a single replication study
pred_int( yio = 1, vio = .5, yir = 0.6,
vir = .2 )

# calculate prediction intervals for a one-to-one design
pred_int( yio = c(1, 1.3), vio = c(.01, .6),
yir = c(.6, .7), vir = c(.01,.3) )

# no need to pass yir if you only want the intervals
pred_int( yio = c(1, 1.3), vio = c(.01, .6),
vir = c(.01,.3) )

# calculate prediction intervals for a many-to-one design
pred_int( yio = c(1), vio = c(.01), yir = c(.6, .7), vir = c(.01,.3) )

Compute probability of "significance agreement" between replication and original study

Description

Given point estimates and their variances for one or multiple original studies and variances for one or more replication studies, returns a vector of probabilities that the replication estimate is "statistically significant" and in the same direction as the original. Can be computed assuming no heterogeneity or allowing for heterogeneity.

Usage

prob_signif_agree(yio, vio, vir, t2 = 0, null = 0, alpha = 0.05)

Arguments

References

1. Mathur MB & VanderWeele TJ (under review). New statistical metrics for multisite replication projects.

Examples

# replication estimates (Fisher's z scale) and SEs
# from moral credential example in Mathur & VanderWeele
# (under review)
yir = c(0.303, 0.078, 0.113, -0.055, 0.056, 0.073,
0.263, 0.056, 0.002, -0.106, 0.09, 0.024, 0.069, 0.074,
0.107, 0.01, -0.089, -0.187, 0.265, 0.076, 0.082)

seir = c(0.111, 0.092, 0.156, 0.106, 0.105, 0.057,
0.091, 0.089, 0.081, 0.1, 0.093, 0.086, 0.076,
0.094, 0.065, 0.087, 0.108, 0.114, 0.073, 0.105, 0.04)

# how many do we expect to agree?
sum( prob_signif_agree( yio = 0.21, vio = 0.004, vir = seir^2 ) )

Probability of true effect stronger than threshold of scientific importance

Description

This function is now deprecated. You should use MetaUtility::prop_stronger instead, which provides better, more general functionality. The below documentation is temporarily maintained before the stronger_than function is deprecated.

Usage

stronger_than(q, yr, vyr = NULL, t2, vt2 = NULL, CI.level = 0.95,
  tail)

Arguments

Details

Given the original study's effect estimate and its variance, the estimated average true effect size in the replications, and the estimated heterogeneity in the replications, computes estimated probability that the original study would have an effect estimate at least as extreme as the observed value if the original and the replications in fact are statistically consistent. Allows for heterogeneity.

See Also

Replicate-deprecated

Compute marginal log-likelihood of tau^2

Description

Given point estimates and their variances, returns the marginal restricted log-likelihood of a specified tau^2 per Veroniki AA, et al. (2016), Section 3.11. Useful as a diagnostic for p_orig per Mathur VanderWeele (under review).

Usage

t2_lkl(yi, vi, t2)

Arguments

References

1. Veroniki AA et al. (2016). Methods to estimate the between-study variance and its uncertainty in meta-analysis. Research Synthesis Methods.

2. Mathur MB & VanderWeele TJ (under review). New statistical metrics for multisite replication projects.

Examples

# replication estimates (Fisher's z scale) and SEs
# from moral credential example in Mathur & VanderWeele
# (under review)
yir = c(0.303, 0.078, 0.113, -0.055, 0.056, 0.073,
        0.263, 0.056, 0.002, -0.106, 0.09, 0.024, 0.069, 0.074,
        0.107, 0.01, -0.089, -0.187, 0.265, 0.076, 0.082)

seir = c(0.111, 0.092, 0.156, 0.106, 0.105, 0.057,
         0.091, 0.089, 0.081, 0.1, 0.093, 0.086, 0.076,
         0.094, 0.065, 0.087, 0.108, 0.114, 0.073, 0.105, 0.04)

vir = seir^2

# fit meta-analysis
.m = metafor::rma.uni( yi = yir,
              vi = vir,
              knha = TRUE ) 

# vector and list of tau^2 at which to compute the log-likelihood
t2.vec = seq(0, .m$tau2*10, .001)
t2l = as.list(t2.vec)

# compute the likelihood ratio vs. the MLE for each tau^2 in t2l
temp = lapply( t2l,
               FUN = function(t2) {
                 # log-lkl itself
                 t2_lkl( yi = yir,
                         vi = vir,
                         t2 = t2 )
                 
                 # lkl ratio vs. the MLE
                 exp( t2_lkl( yi = yir,
                              vi = vir,
                              t2 = t2 ) ) / exp( t2_lkl( yi = yir,
                                                         vi = vir,
                                                         t2 = .m$tau2 ) )
               })

# plotting dataframe
dp = data.frame( tau = sqrt(t2.vec),
                 V = t2.vec,
                 lkl = unlist(temp) )

# fn: ratio of the plotted tau^2 vs. the actual MLE (for secondary x-axis)
g = function(x) x / .m$tau2

# breaks for main and secondary x-axes
breaks.x1 = seq( 0, max(dp$V), .005 )
breaks.x2 = seq( 0, max( g(dp$V) ), 1 )

p = ggplot2::ggplot( data = dp,
        ggplot2::aes(x = V, 
            y = lkl ) ) +
  
  ggplot2::geom_vline(xintercept = .m$tau2,
             lty = 2,
             color = "red") +  # the actual MLE
  
  ggplot2::geom_line(lwd = 1.2) +
  ggplot2::theme_classic() +
  ggplot2::xlab( bquote( hat(tau)["*"]^2 ) ) +
  ggplot2::ylab( "Marginal likelihood ratio of " ~ hat(tau)["*"]^2 ~ " vs. " ~ hat(tau)^2 ) +
  ggplot2::scale_x_continuous( limits = c(0, max(breaks.x1)),
                      breaks = breaks.x1,
                      sec.axis = ggplot2::sec_axis( ~ g(.),  
                                           name = bquote( hat(tau)["*"]^2 / hat(tau)^2 ),
                                           breaks=breaks.x2 ) ) +
  ggplot2::scale_y_continuous( limits = c(0,1),
                      breaks = seq(0,1,.1) )
graphics::plot(p)