# Simulation Extrapolation Inverse Probability Weighted Generalized Estimating Equations Implementation of the SIMEX inverse probability weighted GEE method for longitudinal data with missing observations and measurement error in covariates ```r swgee(formula, data = parent.frame(), id, family = family, corstr = "independence", missingmodel, SIMEXvariable, SIMEX.err, repeated = FALSE, repind = NULL, B = 50, lambda = seq(0, 2, 0.5)) ``` ## Arguments - `formula`: specifies the model to be fitted, with the variables coming with data. This argument has the same format as the formula argument in the function `geeglm` from package `geepack`, of the form `response ~ predictors`. See documentation of `geeglm` and `formula` for details. - `data`: an optional data frame in which to interpret the variables occurring in the formula, along with the id variable. - `id`: a vector which identifies the clusters. The length of id should be the same as the number of observations. Data are assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula. - `family`: a family object as the family argument in the function `gee` from package `gee`. Families supported in `swgee` are `gaussian`, `binomial`, `poisson`, `Gamma`, and `quasi`. See documentation of `gee` and `family` for details. - `corstr`: a character string specifying the correlation structure. The following are permitted: `"independence"`, `"fixed"`, `"stat_M_dep"`, `"non_stat_M_dep"`, `"exchangeable"`, `"AR-M"` and `"unstructured"`. - `missingmodel`: specifies the misisng model to be fitted, of the form `O~ predictors`, where O is the missing data indicator. - `SIMEXvariable`: a vector of characters containing the name of the covariates subject to measurement error. - `SIMEX.err`: specifies the covariance matrix of measurement errors in error model. - `repeated`: This is the indicator if there are repeated measurements for the covariates with measurement error. The default value is FALSE. - `repind`: This is the index of the repeated measurement variables for each covariate with measurement error. It has an R list form. If repeated = TRUE, repind must be specified. - `B`: the number of simulated samples for the simulation step. The default is set to be 50. - `lambda`: a vector of lambdas for which the simulation step should be done. ## Details The quadratic extrapolation method is implemented as described in Cook and Stefanski ## Returns - **call**: the function call - **family**: family - **corstr**: correlation structure - **SIMEXvariable**: a vector of characters containing the name of the covariates subject to measurement error - **B**: the number of iterations - **beta**: the coefficients associated with the response process - **alpha**: the coefficients associated with the missing process - **simex.plot**: the estimates for every B and lambda ## References Cook, J.R. and Stefanski, L.A. (1994) Simulation-extrapolation estimation in parametric measurement error models. **Journal of the American Statistical Association**, 89, 1314-1328. Carrol, R.J., Ruppert, D., Stefanski, L.A. and Crainiceanu, C. (2006) Measurement error in nonlinear models: A modern perspective., Second Edition. London: Chapman and Hall. Yi, G. Y. (2008) A simulation-based marginal method for longitudinal data with dropout and mismeasured covariates. **Biostatistics**, 9, 501-512. ## Author(s) Juan Xiong, Grace Y. Yi ## See Also `geeglm` ## Examples ```r require(gee) data(BMI) bmidata <- BMI rho <- 0 sigma1 <- 0.5 sigma2 <- 0.5 sigma <- matrix(0,2,2) sigma[1,1] <- sigma1*sigma1 sigma[1,2] <- rho*sigma1*sigma2 sigma[2,1] <- sigma[1,2] sigma[2,2] <- sigma2*sigma2 set.seed(1000) ##naive method, ignore missingness and measurement error output1 <- gee(bbmi~sbp+chol+age, id = id, data = bmidata, family = binomial(link="logit"), corstr = "independence") ##swgee method ########## output2 <- swgee(bbmi~sbp+chol+age, data = bmidata, id = id, family = binomial(link="logit"),corstr = "independence", missingmodel = O~bbmi+sbp+chol+age, SIMEXvariable = c("sbp","chol"), SIMEX.err = sigma, repeated = FALSE, B = 20, lambda = seq(0, 2, 0.5)) summary(output2) ```

swgee function