A Marginal Model for Analyzing Discrete Outcomes From Longitudinal Surveys With Outcomes Subject to Multiple-Cause Nonresponse

Estimation of finite population duration distributions from longitudinal survey panels with intermittent followup

We consider survival or duration times associated with spells (sojourns in some state) or events experienced by individuals in a population over a specified time period. Duration distributions can be estimated from data recorded during followup of panel members in longitudinal surveys, but adjustments for the sample design, population structure and losses to followup are typically required. We provided weighted Kaplan-Meier estimates that allow for these features and, in particular, adjust for dependent loss to followup through the use of inverse probability of censoring weights.

Semiparametric regression models for repeated measures of mortal cohorts with non-monotone missing outcomes and time-dependent covariates

We propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non-response to estimate regression parameters interpreted as conditioned on being alive. Our proposed method accommodates outcomes and time-dependent covariates that are missing not at random with non-monotone missingness patterns via inverse-probability weighting. Missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse-probability-weighted estimating equation. Thus, we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates. The approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition, inflammation, and age.

Joint modeling of missing data due to non-participation and death in longitudinal aging studies

Specific age-related hypotheses are tested in population-based longitudinal studies. At specific time intervals, both the outcomes of interest and the time-varying covariates are measured. When participants are approached for follow-up, some participants do not provide data. Investigations may show that many have died before the time of follow-up whereas others refused to participate. Some of these non-participants do not provide data at later follow-ups. Few statistical methods for missing data distinguish between 'non-participation' and 'death' among study participants. The augmented inverse probability-weighted estimators are most commonly used in marginal structure models when data are missing at random. Treating non-participation and death as the same, however, may lead to biased estimates and invalid inferences. To overcome this limitation, a multiple inverse probability-weighted approach is presented to account for two types of missing data, non-participation and death, when using a marginal mean model. Under certain conditions, the multiple weighted estimators are consistent and asymptotically normal. Simulation studies will be used to study the finite sample efficiency of the multiple weighted estimators. The proposed method will be applied to study the risk factors associated with the cognitive decline among the aging adults, using data from the Chicago Health and Aging Project (CHAP).

A mixed effects Markov model for repeated binary outcomes with non-ignorable dropout

In many areas of research, repeated binary measures often represent a two-state stochastic process, where individuals can transition among two states. In a behavioural or physical disability setting, individuals can flow from susceptible or subthreshold state, to an infectious or symptomatic state, and back to a subthreshold state. Quite often the transition among the states happens in continuous time but is observed at discrete, irregularly spaced timepoints which may be unique to each individual. Methods for analyses of such data are typically based on the Markov assumption. Cook (Biometrics 1999; 55:915-920) introduced a conditional Markov model that accommodates the subject-to-subject variation in the model parameters with random effects. We extend this model by adding a non-ignorable dropout component to the model. Specification of the distribution of the random effects is made to guarantee a closed form expression of the marginal likelihood. This methodology is illustrated by applications to a data set from a parasitic field infection survey, a data set from a cocaine treatment study, and a data set from an aging study. Simulations suggest that the shared parameter model is robust with respect to at least one alternative non-ignorable model.

Modeling adolescent drug-use patterns in cluster-unit trials with multiple sources of correlation using robust latent class regressions

PURPOSE

The purpose of the study is to examine variation in adolescent drug-use patterns by using latent class regression analysis and evaluate the properties of an estimating-equations approach under different cluster-unit trial designs.

METHODS

A set of second-order estimating equations for latent class models under the cluster-unit trial design are proposed. This approach models the correlation within subclusters (drug-use behaviors), but ignores the correlation within clusters (communities). A robust covariance estimator is proposed that accounts for within-cluster correlation. Performance of this approach is addressed through a Monte Carlo simulation study, and practical implications are illustrated by using data from the National Evaluation of the Enforcing Underage Drinking Laws Randomized Community Trial.

RESULTS

The example shows that the proposed method provides useful information about the heterogeneous nature of drug use by identifying two subtypes of adolescent problem drinkers. A Monte Carlo simulation study supports the proposed estimation method by suggesting that the latent class model parameters were unbiased for 30 or more clusters. Consistent with other studies of generalized estimating equation (GEE) estimators, the robust covariance estimator tended to underestimate the true variance of regression parameters, but the degree of inflation in the test size was relatively small for 70 clusters and only slightly inflated for 30 clusters.

CONCLUSIONS

The proposed model for studying adolescent drug use provides an alternative to standard diagnostic criteria, focusing on the nature of the drug-use profile, rather than relying on univariate symptom counts. The second-order GEE-type estimation procedure provided a computationally feasible approach that performed well for a moderate number of clusters and was consistent with prior studies of GEE under the generalized linear model framework.

The use of weights to account for non-response and drop-out

BACKGROUND

Empirical studies in psychiatric research and other fields often show substantially high refusal and drop-out rates. Non-participation and drop-out may introduce a bias whose magnitude depends on how strongly its determinants are related to the respective parameter of interest.

METHODS

When most information is missing, the standard approach is to estimate each respondent's probability of participating and assign each respondent a weight that is inversely proportional to this probability. This paper contains a review of the major ideas and principles regarding the computation of statistical weights and the analysis of weighted data.

RESULTS

A short software review for weighted data is provided and the use of statistical weights is illustrated through data from the EDSP (Early Developmental Stages of Psychopathology) Study. The results show that disregarding different sampling and response probabilities can have a major impact on estimated odds ratios.

CONCLUSIONS

The benefit of using statistical weights in reducing sampling bias should be balanced against increased variances in the weighted parameter estimates.

Performance of weighted estimating equations for longitudinal binary data with drop-outs missing at random

The generalized estimating equations (GEE) approach is commonly used to model incomplete longitudinal binary data. When drop-outs are missing at random through dependence on observed responses (MAR), GEE may give biased parameter estimates in the model for the marginal means. A weighted estimating equations approach gives consistent estimation under MAR when the drop-out mechanism is correctly specified. In this approach, observations or person-visits are weighted inversely proportional to their probability of being observed. Using a simulation study, we compare the performance of unweighted and weighted GEE in models for time-specific means of a repeated binary response with MAR drop-outs. Weighted GEE resulted in smaller finite sample bias than GEE. However, when the drop-out model was misspecified, weighted GEE sometimes performed worse than GEE. Weighted GEE with observation-level weights gave more efficient estimates than a weighted GEE procedure with cluster-level weights.

Mixed effects logistic regression models for multiple longitudinal binary functional limitation responses with informative drop-out and confounding by baseline outcomes

In the context of analyzing multiple functional limitation responses collected longitudinally from the Longitudinal Study of Aging (LSOA), we investigate the heterogeneity of these outcomes with respect to their associations with previous functional status and other risk factors in the presence of informative drop-out and confounding by baseline outcomes. We accommodate the longitudinal nature of the multiple outcomes with a unique extension of the nested random effects logistic model with an autoregressive structure to include drop-out and baseline outcome components with shared random effects. Estimation of fixed effects and variance components is by maximum likelihood with numerical integration. This shared parameter selection model assumes that drop-out is conditionally independent of the multiple functional limitation outcomes given the underlying random effect representing an individual's trajectory of functional status across time. Whereas it is not possible to fully assess the adequacy of this assumption, we assess the robustness of this approach by varying the assumptions underlying the proposed model such as the random effects structure, the drop-out component, and omission of baseline functional outcomes as dependent variables in the model. Heterogeneity among the associations between each functional limitation outcome and a set of risk factors for functional limitation, such as previous functional limitation and physical activity, exists for the LSOA data of interest. Less heterogeneity is observed among the estimates of time-level random effects variance components that are allowed to vary across functional outcomes and time. We also note that. under an autoregressive structure, bias results from omitting the baseline outcome component linked to the follow-up outcome component by subject-level random effects.