Comment on 'Small sample GEE estimation of regression parameters for longitudinal data'.

In longitudinal studies, the generalized estimating equation (GEE) estimator of the parameters of a marginal model is known to be consistent even if the working intra-subject covariance matrix is incorrectly specified. Recently, a small sample correction for the bias of the GEE estimator has been proposed. We show that this correction formula relies on the correct specification of the working intra-subject covariance matrix. We provide a revised formula that is valid under misspecification and develop the R package 'BCgee' to ease the practical use of the formula. Copyright © 2017 John Wiley & Sons, Ltd.

A Bayesian Shrinkage Model for Incomplete Longitudinal Binary Data with Application to the Breast Cancer Prevention Trial.

We consider inference in randomized longitudinal studies with missing data that is generated by skipped clinic visits and loss to follow-up. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and partial ignorability for the intermittent missingness. We posit an exponential tilt model that links non-identifiable distributions and distributions identified under partial ignorability. This exponential tilt model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated by, and applied to, data from the Breast Cancer Prevention Trial.

Prevalence and incidence of depressive disorder: the Baltimore ECA follow-up, 1981-2004.

OBJECTIVE: To describe trends in prevalence and incidence of depressive disorder in a cohort from Eastern Baltimore. METHOD: Twenty-three-year-old longitudinal cohort, the Baltimore Epidemiologic Catchment Area Follow-up. Participants were selected probabilistically from the household population in 1981, and interviewed in 1981, 1993, and 2004. Diagnoses were made via the Diagnostic Interview Schedule according to successive editions of the American Psychiatric Association Diagnostic and Statistical Manual. RESULTS: Older age, lower education, non-White race, and cognitive impairment are independent predictors of attrition due to death and loss of contact, but depressive disorder is not related to attrition. Prevalence rates rise for females between 1981, 1993, and 2004. Incidence rates in the period 1993-2004 are lower than the period 1981-1993, suggesting the rise in prevalence is due to increasing chronicity. CONCLUSION: There has been a rise in the prevalence of depression in the prior quarter century among middle-aged females.

Inference in randomized studies with informative censoring and discrete time-to-event endpoints.

In this article, we present a method for estimating and comparing the treatment-specific distributions of a discrete time-to-event variable from right-censored data. Our method allows for (1) adjustment for informative censoring due to measured prognostic factors for time to event and censoring and (2) quantification of the sensitivity of the inference to residual dependence between time to event and censoring due to unmeasured factors. We develop our approach in the context of a randomized trial for the treatment of chronic schizophrenia. We perform a simulation study to assess the practical performance of our methodology.

Early effects of the healthy steps for young children program.

OBJECTIVE: The Healthy Steps for Young Children Program (HS) incorporates early child development specialists and enhanced developmental services into routine pediatric care. An evaluation of HS is being conducted at 6 randomization and 9 quasi-experimental sites. Services received, satisfaction with services, and parent practices were assessed when infants were aged 2 to 4 months. METHODS: Telephone interviews with mothers were conducted for 2631 intervention (response rate, 89%) and 2265 control (response rate, 87%) families. Analyses were conducted separately for randomization and quasi-experimental sites and adjusted for baseline differences between intervention and control groups. Hierarchical linear models assessed overall adjusted effects, while accounting for within-site correlation of outcomes. RESULTS: Intervention families were considerably more likely than controls to report receiving 4 or more developmental services and home visits and discussing 5 infant development topics. They also were more likely to be satisfied and less likely to be dissatisfied with care from their pediatric provider and were less likely to place babies in the prone sleep position or feed them water. The program did not affect breastfeeding continuation. Differences in the percentage of parents who showed picture books to their infants, fed them cereal, followed routines, and played with them daily were found only at the quasi-experimental sites and may reflect factors unrelated to HS. CONCLUSIONS: Intervention families received more developmental services during the first 2 to 4 months of their child's life and were happier with care received than were control families. Future surveys and medical record reviews will address whether these findings persist and translate into improved language development, better utilization of well-child care, and an effect on costs.

Methods for conducting sensitivity analysis of trials with potentially nonignorable competing causes of censoring.

We consider inference for the treatment-arm mean difference of an outcome that would have been measured at the end of a randomized follow-up study if, during the course of the study, patients had not initiated a nonrandomized therapy or dropped out. We argue that the treatment-arm mean difference is not identified unless unverifiable assumptions are made. We describe identifying assumptions that are tantamount to postulating relationships between the components of a pattern-mixture model but that can also be interpreted as imposing restrictions on the cause-specific censoring probabilities of a selection model. We then argue that, although sufficient for identification, these assumptions are insufficient for inference due to the curse of dimensionality. We propose reducing dimensionality by specifying semiparametric cause-specific selection models. These models are useful for conducting a sensitivity analysis to examine how inference for the treatment-arm mean difference changes as one varies the magnitude of the cause-specific selection bias over a plausible range. We provide methodology for conducting such sensitivity analysis and illustrate our methods with an analysis of data from the AIDS Clinical Trial Group (ACTG) study 002.

The quadratic cumulative odds regression model for scored ordinal outcomes: application to alcohol dependence.

In this paper, we develop new regression models for the analysis of scored ordinal data (i.e. ordinal outcomes where the categories are assigned numeric values). The novel feature of these models is that they enable one to capture and identify nonlinear aspects of the relationship between an ordinal clinical measurement (used for disease diagnosis) and risk factors. These nonlinearities may be useful in generating hypotheses about the risk factor's role in the etiologic process as well as suggesting how to design future studies of the risk factor. We apply our model to study the effects of race, gender, and family history on alcohol dependence among a cohort of lifetime drinkers from the 1992 National Longitudinal Alcohol Epidemiologic Survey.

Assessing the impact of pediatric-based development services on infants, families, and clinicians: challenges to evaluating the Health Steps Program.

BACKGROUND: Begun in 1996, the Healthy Steps for Young Children Program (HS) is a new model of pediatric practice that incorporates child development specialists and enhanced developmental services for families of young children. HS is for all families, not just those at high-risk. It is expected to strengthen parents' knowledge, attitudes, and behaviors in ways that promote child health and development, and in turn, to lead to improved child outcomes, such as improved language development, increased utilization of well child care, and decreased problem behaviors, hospitalizations, and injuries. The HS evaluation is designed to assess whether HS is successful in achieving the desired outcomes, measure the program's costs, and determine the relation of the program's costs to its outcomes. OBJECTIVE: This article is the first report of the HS evaluation. It describes the evaluation design and characteristics of the HS sites and sample for the evaluation. METHODS: The evaluation is following a cohort of children from birth to age 3 at 15 evaluation sites across the country. The sites represent a range of organizational practice settings that include group practices, hospital-based clinics, and health maintenance organization pediatric clinics. The evaluation design relies on 2 comparison strategies. At 6 randomization design sites, 400 children were randomized to the intervention or control group. At 9 quasi-experimental design sites, a comparison location with a similar organizational setting and patient profile has been selected and up to 200 children are being followed at each of these sites. At each site, 2 developmental specialists (or their full-time equivalents) work as a team with 4 to 8 pediatricians and pediatric nurse practitioners. The specialist conducts office visits (jointly or sequentially with the pediatric clinician) and home visits, assesses children's developmental progress, provides referrals and follow-up to resources in the community, organizes and conducts parent discussion groups, coordinates early reading activities, and maintains a telephone information line for questions about child development and behavior. The evaluation relies on many data sources including self-administered provider surveys, key informant interviews, forms completed by parents at office visits, telephone interviews with parents, medical record reviews, data from each site on program costs and health services use, and an ongoing log of family contacts maintained by each developmental specialist. Analyses for this article are based on enrollment data for the Healthy Steps sample and national data on 1997 US live births. The chi2 goodness-of-fit test was used to evaluate whether the distribution of selected demographic variables, insurance, and infant's birth weight for the Healthy Steps sample was similar to the distributions for US births in 1997. In addition, comparisons were made between intervention and comparison families at the randomization and quasi-experimental evaluation sites. The chi2 test of independence was used to evaluate differences in variables across groups. RESULTS: Throughout a 26-month period, 5565 children enrolled in the evaluation, 2963 (53.2%) children in the intervention group and 2602 (46.8%) in the comparison group. More than 10% of mothers in the Healthy Steps sample are teenagers; 18% have 11 years of education or less; 27% have completed college; 18% are black or African-American; slightly >20% are of Hispanic origin; 36% are single; and close to one-third used Medicaid for their prenatal care. Approximately 7% of infants were low birth weight. When compared with national birth data for the United States as a whole, the Healthy Steps sample seems similarly diverse. However, with the exception of maternal age, the distribution of variables was significantly different from the distribution for US births. There are no differences between intervention and comparison families at randomization sites on any of

The use of simulation and bootstrap in information-based group sequential studies.

In this paper, we present an information-based design and monitoring procedure which applies to any type of model for any type of group sequential study provided there is a unique parameter of interest one can estimate efficiently. Simulation techniques are described to handle the design phase of this procedure. Since designs depend on potentially unreliable guesses of nuisance parameters, we propose a bootstrap method that uses the information available at the interim analysis times to generate projections and prediction intervals for the time at which the study will be fully powered. A monitoring board can use this information to decide whether a redesign of the trial is warranted. We also show how to use simulation to redesign studies in progress. We illustrate all of these techniques with data from AIDS Clinical Trial Group Protocol 021.

Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data.

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant rho and assumes that [formula: see text] where g: rho(s) = log(rho-1(s-rho - 1)) for rho > 0, g0(s) = log(-logs), S(t[symbol: see text]Z) is the survival function of the time to event for an individual with q x 1 covariate vector Z, beta is a q x 1 vector of unknown regression parameters, and alpha(t) is some arbitrary increasing function of t. When rho = 0, this model is equivalent to the proportional hazards model and when rho = 1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for beta and exp(alpha(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for beta is semiparametric efficient in the sense that it attains the semiparametric variance bound.

Design of developmental toxicity studies for assessing joint effects of dose and duration.

In the assessment of developmental and reproductive effects, the timing and duration of exposures to chemical compounds or other environmental contaminants are of particular interest, as the gestational cycle is known to have periods of increased sensitivity. The goal of this research is to identify optimal experimental designs for conducting developmental toxicity studies when the effects of both exposure level and duration of exposure are of interest. The elements of the study design considered in this evaluation are the allocation of animals to dose-duration exposure groups and the determination of the most efficient intermediate exposure levels. The optimality of various designs is assessed via the accuracy of the estimated excess risk as well as testing criteria. Simulation studies are conducted to compare these criteria and determine optimal design strategies under various underlying dose-response patterns. Asymptotic results are also derived to lend support to the simulation studies.

Modeling fetal death and malformation in developmental toxicity studies.

We review approaches to dose-response modeling and risk assessment for binary data from developmental toxicity studies. In particular, we focus on jointly modeling fetal death and malformation and use a continuation ratio formulation of the multinomial distribution to provide a model for risk. Generalized estimating equations are used to account for clustering of animals within litters. The fitted model is then used to calculate doses corresponding to a specified level of excess risk. Two methods of arriving at a lower confidence limit or Benchmark dose are illustrated and compared. We also discuss models based on single binary end points and compare our approach to a binary analysis of whether or not the animal was 'affected' (either dead or malformed). The models are illustrated using data from four developmental toxicity studies in EG, DEHP, TGDM, and DYME conducted through the National Toxicology Program.

Statistical model for fetal death, fetal weight, and malformation in developmental toxicity studies.

The purpose of this paper is to present a statistical model for analyzing the joint effects of exposure on fetal death, fetal weight, and malformation in a developmental toxicity study. In addition to allowing for the usual litter effect, the model allows for correlations between different outcomes measured on the same fetus. Fitting the model requires first focusing on non-live outcomes by modeling the probability of fetal death or resorption as a function of dose. Then outcomes among live fetuses are modeled using a two-stage regression approach. The first stage models fetal weight as a function of dose and the second stage models fetal malformation as a function of dose, as well as residuals from the weight model. The regression coefficients from the malformation model have intuitive interpretations in terms of correlations between littermates and between different outcomes measured within the same fetus. Not only does the approach provide a useful way to investigate the relationship between adverse fetal outcomes, it also yields a natural framework for conducting quantitative risk assessment. A procedure is proposed for quantifying overall risk by incorporating the three outcomes in order to estimate safe dose levels and corresponding lower confidence limits. The method is illustrated using data from an experiment in mice conducted through the National Toxicology Program.