Journal of Statistical Research

GUIDANCE FOR PRACTITIONERS ON THE CHOICES OF SOFTWARE IMPLEMENTATION FOR FRAILTY MODELS: SIMULATIONS AND AN APPLICATION IN DETERMINING THE BIRTH INTERVAL DYNAMICS

2000-03-09T01:34:31+06:00

In clustered survival analysis applications, researchers frequently fit frailty models using
parametric and nonparametric approaches to obtain the estimates for the parameters associated
with the survival model covariates and heterogeneity (frailty). Availability of the offthe-
shelve implementations and freely available R software packages makes it convenient
for the practitioners to fit these complicated models easily. Even though there has been a
couple of studies assessing the stability of the older packages (e.g., survival, coxme)
under a variety of scenarios, some of the newer implementations (e.g., frailtySurv,
JM and parfm) have not gone through similar rigorous assessment. It is worth evaluating
these new software implementations, and comparing them with the older packages. In
the current work, via simulations, we will examine the estimates from all of these popularly
used software implementations under a variety of scenarios when the corresponding
assumptions related to the baseline hazard and frailty distributions are misspecified. Additionally,
true heterogeneity parameter, censoring patterns and number of clusters were
varied in the simulations to assess respective impacts on the estimates. From these simulations,
we observed that when there is a large number of clusters and mild censoring,
Cox PH frailty models fitted using a newer semiparametric estimation technique (from the
frailtySurv package) produced regression and heterogeneity parameter estimates that
were associated with unusually large bias and variability. On the other hand, when the true
heterogeneity parameter is substantially large, the Cox PH frailty models fitted using the
coxme package were often producing highly variable estimates of the heterogeneity parameter.
The simulation findings then guided our choice of appropriate frailty model in the
context of determining the birth interval dynamics in Bangladesh.

THE NON-STATIONARY BIVARIATE INAR UNDER AN UNCONSTRAINED INTER CORRELATION STRUCTURE

2000-03-09T01:35:44+06:00

It is commonly observed in medical and financial studies that large volume of time series
of count data are collected for several variates. The modelling of such time series and
the estimation of parameters under such processes are rather challenging since these high
dimensional time series are influenced by time-varying covariates that eventually render
the data non-stationary. This paper considers the modelling of a bivariate integer-valued
autoregressive (BINAR(1)) process where the innovation terms are distributed under nonstationary
Poisson moments. Since the full and conditional likelihood approaches are cumbersome
in this situation, a Generalized Quasi-likelihood (GQL) approach is proposed to
estimate the regression effects while the serial and time-dependent cross correlation effects
are handled by method of moments. This new technique is assessed over several simulation
experiments and the results demonstrate that GQL yields consistent estimates and is
computationally stable since few non-convergent simulations are reported.

ESTIMATION OF DENSITY AND DISTRIBUTION FUNCTIONS OF A BURR X DISTRIBUTION

2000-03-09T01:37:37+06:00

Burr type X distribution is one of the members of the Burr family which was originally
derived by Burr (1942) and can be used quite effectively in modelling strength data and
also general lifetime data. In this article, we consider efficient estimation of the probability
density function (PDF) and cumulative distribution function (CDF) of Burr X distribution.
Eight different estimation methods namely maximum likelihood estimation,
uniformly minimum variance unbiased estimation, least square estimation, weighted least
square estimation, percentile estimation, maximum product estimation, Crem´er-von-Mises
estimation and Anderson-Darling estimation are considered. Analytic expressions for bias
and mean squared error are derived. Monte Carlo simulations are performed to compare
the performances of the proposed methods of estimation for both small and large samples.
Finally, a real data set has been analyzed for illustrative purposes.

A GENERALIZED LINEAR MODEL FOR MULTIVARIATE CORRELATED BINARY RESPONSE DATA ON MOBILITY INDEX

2000-03-09T01:38:35+06:00

Dependence in multivariate binary outcomes in longitudinal data is a challenging and an
important issue to address. Numerous studies have been performed to test the dependence
in binary responses either using conditional or marginal probability models. Since the conditional
and marginal approach provide inadequate or misleading results, the joint models
based on both are implemented for bivariate correlated binary responses. In the current
paper, we consider a joint modeling approach and a generalized linear model (GLM) for
tri-variate correlated binary responses. The link function of the GLM is used to test the
dependence of response variables. The mobility index with two categories, no difficulty
and difficulty, over the duration of three waves of Health and Retirement Survey (HRS)
is chosen as the binary response variable. Initial analysis with Marshall-Olkin correlation
coefficients and logistic regression coefficients provide moderate correlation in mobility
indices implying dependence in the response variables. We also found statistically significant
dependence among the response variables using the joint modeling approach. The
mobility at current wave not only depends on the previous mobility status, but also depends
on covariates such as age, gender, and race.

THE RECURRENCE RELATIONS OF ORDER STATISTICS MOMENTS FOR POWER LOMAX DISTRIBUTION

2000-03-09T01:40:02+06:00

The power Lomax distribution due to Rady et al. (2016) is an alternative to and provides
better fits for bladder cancer data (Lee and Wang, 2003) than the Lomax, exponential Lomax,
Weibull Lomax, extended Poisson Lomax and beta Lomax distributions. Exact explicit
expressions as well as recurrence relations for the single and double (product) moments
have been derived from the power Lomax distribution. These recurrence relations
enable computation of the mean, variance, skewness and kurtosis of all order statistics for
all sample sizes in a simple and efficient manner. By using these relation, the mean, variance,
skewness and kurtosis of order statistics for sample sizes up to 5 for various values of
shape and scale parameters are tabulated. Finally, remission times (in months) of bladder
cancer patients have been analyzed to show how the proposed relations work in practice.

VARIANTS OF DOUBLE ROBUST ESTIMATORS FOR TWO-STAGE DYNAMIC TREATMENT REGIMES

2000-03-09T01:41:12+06:00

Certain conditions and illnesses may necessitate multiple stages of treatment and thus require
unique study designs to compare the efficacy of these interventions. Such studies are
characterized by two or more stages of treatment punctuated by decision points where intermediate
outcomes inform the choice for the next stage of treatment. The algorithm that
dictates what treatments to take based on intermediate outcomes is referred to as a dynamic
regime. This paper describes an efficient method of building double robust estimators of
the treatment effect of different regimes. A double robust estimator utilizes both modeling
of the outcome and weighting based on the modeled probability of receiving treatment in
such a way that the resulting estimator is a consistent estimate of the desired population
parameter under the condition that at least one of those models is correct. This new and
more efficient double robust estimator is compared to another double robust estimator as
well as classical regression and inverse probability weighted estimators. The methods are
applied to estimate the regime effects in the STAR*D anti-depression treatment trial.