samon: Sensitivity Analysis for monotone missing data

In samon: Sensitivity Analysis for Missing Data

Sensitivity Analysis for monotone missing data

Description

Given data from one arm of a repeated measures clinical trial, produces estimates of the expected value of the outcome at the final time-point for a range of sensitivity parameters.

Usage

samon(mat, Npart = 10, InitialSigmaH = 1.0, HighSigmaH = 2.0,
InitialSigmaF = 1.0, HighSigmaF = 2.0, lb = 0, ub = 101, 
zeta1 = 1, zeta2 = 1,NSamples = 0, seed0 = 1, MaxIter = 25,
FAconvg = 1E-7, FRconvg = 1E-7, SAconvg = 1E-7, alphaList= c(0), 
MJackknife = FALSE, SJackknife = FALSE, retIFiM = FALSE, 
retIFiS = FALSE, Tfun= NULL)

Arguments

mat	a matrix with the (i,j) entry representing the outcome value for subject i at time-point j.
Npart	Number of partitions to use when estimating optimal smoothing parameters, sigma H and sigma F.
InitialSigmaH	Initial value when calculating optimal sigma H.
HighSigmaH	Upper bound of search region when calculating optimal sigma H.
InitialSigmaF	Initial value when calculation optimal sigma F.
HighSigmaF	Upper bound of search region when calculating optimal sigma F.
lb	Lower bound for Y.
ub	Upper bound for Y.
zeta1	parameter to cumulative beta.
zeta2	parameter to cumulative beta.
NSamples	Number of parametric bootstrap samples to generate.
seed0	Seed to use.
MaxIter	Maximum iterations to use in optimizer.
FAconvg	Absolute change in function convergence criterion.
FRconvg	Relative change in function convergence criterion.
SAconvg	Step size convergence criterion.
alphaList	a vector of sensitivity parameters
MJackknife	Jackknife main data (logical)
SJackknife	Jackknife bootstrap samples (logical)
retIFiM	return individual IF estimates from main data.
retIFiS	return individual IF estimates from samples.
Tfun	n by 2 matrix with tilting function values.

Details

The matrix mat represents repeated measure outcome data from a single arm or treatment group of a trial. Each row represents the data from a single subject and each column data from a single time-point.

The values in the first column of mat are the baseline values and should not have missing values. Samon creates one-step bias corrected estimates of the mean value of Y at the last time-point for a number of specified sensitivity parameters, alpha.

Samon determines two smoothing parameters, sigma H, which represents smoothing in the "missingness" model and, sigma F, which represents smoothing in the "outcome" model. These smoothing parameters are determined by minimizing loss functions. Minimization is performed using Newton's method. The parameter InitialSigmaH is used as the initial value in the optimization of the missingness model. In a similar vein InitialSigmaF is used as the initial value in the optimization of the outcome model.

A number of stopping criteria are available: MaxIter: the maximum number of iterations to perform FAconvg: stop when abs( fsub(i+1) - f_i ) < FAconvg, where f_i is the loss function value at iteration i. FRconvg: stop when abs( (fsub(i+1) - f_i)/(fsub(i+1) + f_i)) < FRconvg. SAconvg: stop when the absolute step size falls below SAconvg, i.e., abs( xsub(i+1) - x_i ) < SAconvg. HighSigmaH: should the value of sigma H go above this value, then the optimal value of sigma H is set to HighSigmaH. This is useful if larger values of sigma H do not change the missingness model substantially. HighSigmaF: should the value of sigma F go above this value, then the optimal value of sigma F is set to HighSigmaF. This is useful if larger values of sigma F do not change the missingness model substantially.

Using the optimal values for sigma H and sigma F, samon produces estimates of the mean value of the outcome at the last visit, for the set of sensitivity parameters given in the vector alphaList.

If the sensitivity parameters are applied to the cumulative beta function, IB. Four parameters are used to map the values of the outcome, y to the domain of the cumulative beta. r(y) = IB( (y-lb)/(ub-lb), zeta1, zeta2) where zeta1 and zeta2 are the shape parameters.

Alternatively samon may be called with a user specified sensitivity function. This is given as an n by 2 matrix with the first column holding the unique values of the data in mat and the second column the value of the sensitivity function at that value.

Value

samon returns a list which includes the following:

HM	matrix of results from sigma H optimization for the input data mat. Columns are sample, type, return code, iterations, optimal sigma H, and the loss function value at optimal sigma H. The "M" in the name "HM" refers to the main or input matrix mat. In this case the sample and type columns are set to 0.
FM	matrix of results from sigma F optimization for the input data mat. Columns are sample, type, return code, iterations, optimal sigma F, and loss function value at optimal sigma F. The "M" in the name "FM" refers to the main or input matrix mat. In this case the sample and type columns are set to 0.

The return code takes the following values:

1	absolute function convergence was met
2	relative function convergence was met
3	second derivative has become too small
4	maximum iterations reached
5	value reset to HighSigmaH or HighSigmaF
6	loss function smaller at HighSigmaH or HighSigmaF
IFM	matrix with 7 columns containing one-step bias-corrected estimates (sometimes referred to here as IF estimates). Columns are sample, type, alpha, est0, se0, IFEst, IFVar. The columns sample and type take the value 0. IFEst and IFVar are the one-step bias corrected estimates and an estimate of their variance for the original data, mat, at each value of the sensitivity parameters, alpha.

In a similar manner, "HS", "FS", and "IFS" contain results from parametric bootstraps (should NSamples be greater than 0). The first columns in this case contain the sample number, 1, 2, ..., NSamples. In other respects these matrices have the same structure as the corresponding matrix "HM", "FM" and "IFM".

If MJackknife is set to TRUE, then, "HMjk", "FMjk", "IFMjk" are produced, holding the jackknife results for the main data mat. Again the first column "sample" is set to 0, and the second column is termed "Dropped" and gives the observation number dropped to form the jackknife sample.

Finally, if SJackknife is set to TRUE, then, "HSjk", "FSjk", "IFSjk" are produced. These hold the jackknife results for the bootstrap samples.

See Also

The samon_userDoc.pdf file in the Examples subdirectory.

Examples

data("samonPANSS1")

Results1 <- samon(
  mat            = samonPANSS1,
  Npart          =          10, # number of partitions
    
  InitialSigmaH  =        15.0, # initial value
  HighSigmaH     =        50.0, # high value for H
    
  InitialSigmaF  =         8.0, # initial value
  HighSigmaF     =        50.0, # high value for F
    
  lb             =          30, # parameters to
  ub             =         210, # cumulative 
  zeta1          =         4.0, # beta distribution
  zeta2          =         7.0,

  alphaList      =        -1:1 )

samon documentation built on Oct. 26, 2023, 9:06 a.m.