samonIM {samon}

samonIM: Sensitivity analysis for monotone missing and intermittent 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

samonIM(mat, Npart = 10, InitialSigmaH = 1.0, 
HighSigmaH = 2.0, InitialSigmaF = 1.0, HighSigmaF = 2.0, 
inmodel = inmodel, NSamples = 0, NIMimpute = 1, lb = 0, 
ub = 101, zeta1 = 1, zeta2 = 1, seed0 = 1, seed1 = 1, 
MaxIter = 25, FAconvg = 1E-7, FRconvg = 1E-7, 
SAconvg = 1E-7, alphaList = c(0), retIFiM  = FALSE, 
retIFiS  = FALSE, retSample = FALSE,
retFMatM = FALSE, retFMatS = 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 calculation optimal sigma F.

NSamples

Number of parametric bootstrap samples to generate.

inmodel

NT by 6 matrix indicating which variables to include in logistic model.

NIMimpute

How many times to fill in intermittent missing data.

lb

Lower bound for Y.

ub

Upper bound for Y.

zeta1

parameter to cumulative beta.

zeta2

parameter to cumulative beta.

seed0

Seed to use for parametric bootstrap sampling

seed1

Seed to use for filling intermittent missing data

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

retIFiM

return individual IF estimates from main data.

retIFiS

return individual IF estimates from sample data.

retSample

return the Sample generated

retFMatM

return the main data with intermittent missing data filled in NIMimpute + 1 times

retFMatS

retrun the sample data with intermittent missing data filled in NIMimpute + 1 times

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 be missing. Samon creates 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 and 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.

The inmodel matrix specifies a set of logistic models used to impute intermittent missing data. This is an NT by 6 matrix of 0s and 1s. Each row represents a time-point. Since intermittent missing data cannot occur at baseline or at the final timepoint, the first and NT'th row of inmodel are 0. The six values on a row indicate the following terms should be included in the model:

1

a value of 1 in this position indicates that the logistic model should include an intercept

2

a value of 1 in this position indicates that the model should contain a term for the previous available outcome

3

a value of 1 in this position indicates that the model should contain a term for the next available outcome

4

a value of 1 in this position indicates that the model should contain a term for the location of the next available outcome

5

a value of 1 in this position indicates that the model should contain a term for the interaction between the next available outcome and the position of the next available outcome

6

a value of 1 in this position indicates that the model should contain a term for the last available outcome before dropout.

For example suppose the data consists of the 8 columns v1-v8 and suppose we wish to model the intermittent missingness at the third time-point, that is, we wish to model when v3 has an intermittent missing value. We might model this as is.na(v3) ~ 1 + v2 + n3 + i3 + i3 * n3 + l3 where n3 refers to the next non-missing value of v after the third time-point. i3 refers to the location of that non-missing value, i3 * n3 and interaction between these and l3 the last available value of v for an individual. Specifically we might calculate n3, i3 and l3 as shown:

v1	v2	v3	v4	v5	v6	v7	v8	v2	n3	i3	l3
10	8	NA	9	32	NA	NA	NA	8	9	1	32
11	4	3	5	4	7	7	NA	4	5	1	7
22	15	NA	NA	NA	6	2	9	15	6	3	9

Note that when considering missing values at the NT - 1 time-point the last three terms in the model are not identifiable.

Fitting as many terms in the intermittent missing model might use an inmodel parameter with a matrix like this:

0	0	0	0	0	0
1	1	1	1	1	1
1	1	1	1	1	1
1	1	1	1	1	1
1	1	1	1	1	1
1	1	1	1	1	1
1	1	1	0	0	0
0	0	0	0	0	0

A simpler model using only the intercept and the previous and next available non-missing value would be specified by

0	0	0	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
0	0	0	0	0	0

This simpler model but restricted to an intercept only model at the second and fourth timepoints can be specified by using:

0	0	0	0	0	0
1	0	0	0	0	0
1	1	1	0	0	0
1	0	0	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
1	1	1	0	0	0
0	0	0	0	0	0

In practice the amount of intermittent missing data at a timepoint may not be large enough to support a logistic model with all six parameters. At each step samonIM will attempt to fit the models indicated by the inmodel matrix and reduce the number of model parameters if collinearity is found among the independent variables.

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

Sample

The generated sample of dimension NSamples by ncol(Mat)

See Also

The samon_userDoc.pdf file in the Examples subdirectory.

Examples

data("VAS1")

# inputation model
NT            <- ncol(VAS1)
inmodel       <- matrix(1,NT,6)
inmodel[1,]   <- 0
inmodel[NT,]  <- 0
inmodel[,4:6] <- 0

Results <- samonIM(
  mat           =    VAS1, # imput matrix
  Npart         =       2, # number of partitions
    
  InitialSigmaH =    25.0, # initial value
  HighSigmaH    =   100.0, # high value for H
    
  InitialSigmaF =     8.0, # initial value
  HighSigmaF    =   100.0, # high value for F
    
  lb            =       0, # parameters for
  ub            =     102, # cumulative 
  zeta1         =     1.2, # beta distribution
  zeta2         =     1.6,

  NSamples      =       0, # no of bootstraps
  NIMimpute     =       2, # no of imputations 
    
  seed0         =     441, # seed for bootstraps
  seed1         =     511, # seed for imputations
  inmodel       = inmodel, # input model
    
  alphaList     =   -1:1 )