weightsIMD {weightQuant}

Estimation of observation-specific weights with intermittent missing data

Description

This function provides stabilized weights for incomplete longitudinal data selected by death. The procedure allows intermittent missing data and assumes a missing at random (MAR) mechanism. Weights are defined as the inverse of the probability of being observed. These are obtained by pooled logistic regressions.

Usage

weightsIMD(data, Y, X1, X2, subject, death, time, impute = 0, name = "weight")

Arguments

data

data frame containing the observations and all variables named in Y, X1, X2, subject, death and time arguments.

Y

character indicating the name of the response outcome

X1

character vector indicating the name of the covariates with interaction with the outcome Y in the logistic regressions

X2

character vector indicating the name of the covariates without interaction with the outcome Y in the logistic regressions

subject

character indicating the name of the subject identifier

death

character indicating the time of death variable

time

character indicating the measurement time variable. Time should be 1 for the first (theoretical) visit, 2 for the second (theoretical) visit, etc.

impute

numeric indicating the value to impute if the outcome Y is missing

name

character indicating the name of the weight variable that will be added to the data

Details

Denoting T_i the death time, R_ij the observation indicator for subject i and occasion j, t the time, Y the outcome and X1 and X2 the covariates, we propose weights for intermittent missing data defined as :

w_ij = P(R_ij = 1 | T_i > t_ij, X1_ij, X2_ij) / P(R_ij = 1 | T_i > t_ij, X1_ij, X2_ij, Y_ij-1)

The numerator corresponds to the conditional probability of being observed in the population currently alive under the MCAR assumption.

The denominator is computed by recurrence :

P(R_ij = 1 | T_i > t_ij, X1_ij, X2_ij, Y_ij-1) =

P(R_ij = 1 | T_i > t_ij-1, X1_ij, X2_ij, Y_ij-1, R_ij-1 = 0) * P(R_ij-1 = 0 | T_i > t_ij, X1_ij, X2_ij, Y_ij-1) + P(R_ij = 1 | T_i > t_ij-1, X1_ij, X2_ij, Y_ij-1, R_ij-1 = 1) * P(R_ij-1 = 1 | T_i > t_ij, X1_ij, X2_ij, Y_ij-1)

Under the MAR assumption, the conditional probabilities lambda_ij = P(R_ij = 1 | T_i > t_ij, X1_ij, X2_ij, Y_ij-1, R_ij-1) are obtained from the logistic regression :

logit(lambda_ij) = b_0j + b_1 X1_ij + b_2 X2_ij + b_3 Y_i(j-1) + b_4 X1_ij Y_i(j-1) + b_5 (1-R_ij-1)

Value

A list containing :

data

the data frame with initial data and estimated weights as last column

coef

a list containing the estimates of the logistic regressions. The first element of coef contains the estimates under the MCAR assumption, the second contains the estimates under the MAR assumption.

se

a list containing the standard erros of the estimates contained in coef, in the same order.

Author(s)

Viviane Philipps, Marion Medeville, Anais Rouanet, Helene Jacqmin-Gadda

See Also

weightsMMD

Examples

w_simdata <- weightsIMD(data=simdata,Y="Y",X1="X",X2=NULL,subject="id",
death="death",time="time",impute=20,name="w_imd")$data