Page 289 - Contributed Paper Session (CPS) - Volume 7

CPS2102 Iris Reinhard
The β and γ are fixed effects for the covariates xij and zij, respectively, and ai
and bi are random effects generating the within-subject correlation and the
between-subject heterogeneity. It is assumed that

where

Simulation study
In a simulation study the performance of the two-part model is evaluated
in terms of type I error and the mean squared error (MSE) of the estimates.
The data generation process is thereby based on the distribution
characteristics of an empirical data set coming from a controlled prospective
intervention
study which is investigating the cost-effectiveness of an intervention to
reduce compulsory admission into inpatient psychiatric treatment. So it is
possible to deduce more generalized conclusions for health services research.
Thereby a mixture distribution framework involving a two-step process is
applied. To generate the covariates, random samples from a bivariate normal
distribution with different values of correlation (e.g. ρx1x2=-0.2 or ρx1x2=0) are
drawn. We employ six repeated measurements and manipulate the sample
size at four levels: sparse (N=50), small (N=100), medium (N=200) and large
(N=500). The true model incorporates two fixed effects for each component
(two covariates): βk (Normal), γs (Binary); k,s=1,2, as well as two random effects,
each scalar quantities, one for each component (for the binary part bi / for the
normal part ai), correlated or uncorrelated (ρab=-0.4 or ρab=0). For each
scenario 5000 replications are conducted. The nominal α is set to 0.05.
The performance of the mixed two-part model is evaluated under the null
hypothesis H0: βk=0 resp. γs=0, for estimating the significance level and under
the H1 for estimating the parameters. Criteria are (i) the type I error and (ii)
the mean squared error (MSE) of the estimates. As a control model to examine
the consequences of ignoring zero modified data the classical linear mixed
model is used.
The programming environment for the implementation of the two-part
model is SAS 9.4, where the procedure NLMIXED is employed (see e.g. Liu et
al., 2010, Tooze et al., 2002). This procedure directly maximizes an approximate
integrated likelihood. Here an adaptive Gaussian quadrature approximation is
chosen. As an optimization algorithm to carry out the maximization, a
Newton-Raphson optimization is applied which combines a line-search
algorithm with ridging. This technique uses the gradient and the Hessian
matrix.

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