salbmCombine: Sensitivity Analysis for Binary Missing Data

In salbm: Sensitivity Analysis for Binary Missing Data

Description

Combines main and bootstrap results.

Usage

salbmCombine(x0, Samps=NULL, div=c(NA,NA))

Arguments

x0	main results from original data.
Samps	list of sample results
div	low and high alpha points

Details

Combines data and produces bootstrap summaries including confidence intervals.

Four types of confidence intervals are calculated after combining the results. Fixing the sensitivity parameter, let E be an estimate for a treatment group and for b=1,2,…,B let E_b be the corresponding estimate for bootstrap b. Let SE be a standard error estimate for E and SE_b be a standard error estimate for E_b. Let q( \{x_i\}, v) be the vth quantile for the collection \{x_i\}.

1. Let q_l = q( \{E_b\}, 0.025 ) and q_u = q( \{E_b\}, 0.975 ). Then a 95% confdence interval for E is given by ( q_l, q_u ). These are refered to as c("lb1","ub1") or type 1 confidence intervals.

2. Let q_s = q( \{\mid E_b - E\mid\}, 0.95 ). Then a 95% confdence interval for E is given by ( E - qs, E + qs ). These are refered to as c("lb2","ub2") or type 2 confidence intervals.

3. Let t_b = ( E_b - E ) / SE_b, eqnq_l = q( {t_b}, 0.025 ) and q_u = q( \{t_b\}, 0.975 ). Let M be the mean of E_b. Then a 95% confdence interval for eqnE is given by ( M - q_u SE, M - q_l SE ) These are refered to as c("lb3","ub3") or type 3 confidence intervals.

4. Let t_b = ( E_b - E ) / SE_b, and q_s = q( \{\mid t_b \mid\}, 0.95 ). Let M be the mean of E_b. Then a 95% confdence interval for E is given by ( M - q_s SE, M + q_s SE ) These are refered to as c("lb4","ub4") or type 4 confidence intervals.

Computing SE

Let D be a dataset with n rows and T a fixed timepoint. Three standard deviations are computed

SD_0 the standard deviation of the data in D at timepoint T when 0 is substituted for missing values in D,

SD_1 the standard deviation of the data in D at timepoint T when 1 is substituted for missing values in D, and

SD_m the standard deviation of the data in D at timepoint T when mean value at time T is substituted for missing values at time T.

A low, mid and high values of alpha are choosen and denoted by a_l, a_0, and a_u respectively. In salbm a_0 = 0. Then a standard error is computed as:

SE = ≤ft\{\Large\begin{array}{ll} \frac{( α - a_l ) SD_0 + ( a_0 - α ) SD_m }{ ( a_0 - a_l ) √{n} }&\normalsize \mbox{\hspace{0.2in} when } \normalsize α < 0 \\[0.15in] \frac{( a_u - α ) SD_1 + ( α - a_0 ) SD_m }{ ( a_u - a_0 ) √{n} }&\normalsize \mbox{\hspace{0.2in} when } \normalsize α ≥ 0 \end{array} \right.

Value

a list with combined results

See Also

salbm

Examples

  data(trt1)
  data(trt2)
  data <- list( trt1 = trt1, trt2 = trt2 )

  ## main run
  x0 <- salbm( data = data , K = 6, ntree = 250, 
               seeds = c(22,18), seeds2 = c(-2,-3),
               alphas = -5:5, NBootstraps=0 )

  ## add Bootstraps
  samp1 <- addSamples(obj=x0, seeds=c(99,12), 
               seeds2 = c(-45,-80), bBS=1,
               NBootstraps=250)
  ## add more Bootstraps
  samp2 <- addSamples(obj=x0, seeds=c(9,2), 
               seeds2 = c(-54,-8), bBS=251,
               NBootstraps=250)

  ## Together
  R <- salbmCombine(x0=x0, Samps=list(samp1,samp2))

salbm documentation built on May 25, 2021, 9:07 a.m.