Identifiability and estimation of causal effects in randomized trials with noncompliance and completely nonignorable missing data

Summary .  In this article, we first study parameter identifiability in randomized clinical trials with noncompliance and missing outcomes. We show that under certain conditions the parameters of interest are identifiable even under different types of completely nonignorable missing data: that is, the missing mechanism depends on the outcome. We then derive their maximum likelihood and moment estimators and evaluate their finite-sample properties in simulation studies in terms of bias, efficiency, and robustness. Our sensitivity analysis shows that the assumed nonignorable missing-data model has an important impact on the estimated complier average causal effect (CACE) parameter. Our new method provides some new and useful alternative nonignorable missing-data models over the existing latent ignorable model, which guarantees parameter identifiability, for estimating the CACE in a randomized clinical trial with noncompliance and missing data.     

Adjusting for Nonignorable Missingness When Estimating Generalized Additive Models

Generalized additive models (GAMs) have been widely used for flexible modeling of various types of outcomes. When the outcome in a GAM is subject to missing, practical analyses often assume that missingness is missing at random (MAR). This assumption can be of suspicion when the missingness is not by design. Evaluating the potential effects of alternative nonignorable missing data mechanism on the MAR inference from a GAM can be important but often challenging due to the complicatedness of alternative nonignorable models. We apply the index approach to local sensitivity (Troxel, Ma, and Heitjan 2004 (2004). Statistica Sinica 14 , 1221–1237) to evaluate the potential changes of the GAM estimates in the neighborhood of the MAR model. The approach avoids fitting any complicated nonignorable GAM. Only MAR estimates are required to calculate the resulting sensitivity index and adjust the GAM estimates to account for nonignorable missingness. Thus the proposed approach is considerably simpler to conduct, as compared with the alternative methods. The simulation study shows that the index provides valid assessment of the local sensitivity of the GAM estimates to nonignorable missingness. We then illustrate the method using a rheumatoid arthritis clinical trial data set.     

Reparameterizing the pattern mixture model for sensitivity analyses under informative dropout

Pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout. For measured responses, it is typical to model the complete data as a mixture of multivariate normal distributions, where mixing is done over the dropout distribution. Fully parameterized pattern mixture models are not identified by incomplete data; Little (1993, Journal of the American Statistical Association 88, 125-134) has characterized several identifying restrictions that can be used for model fitting. We propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance, allows consideration of a wide range of nonignorable missing-data mechanisms, and has intuitive appeal for eliciting plausible missing-data mechanisms. The parameterization makes clear an advantage of pattern mixture models over parametric selection models, namely that the missing-data mechanism can be varied without affecting the marginal distribution of the observed data. To illustrate the utility of the new parameterization, we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly. Dropout occurs at a high rate and is potentially informative. We undertake a detailed sensitivity analysis to understand the impact of missing-data assumptions on the inference about the effects of growth hormone on muscle strength.     

Fitting the log-F accelerated failure time model with incomplete covariate data

Data obtained from studies in the health sciences often have incompletely observed covariates as well as censored outcomes. In this paper, we present methods for fitting the log-F accelerated failure time model with incomplete continuous and/or categorical time-independent covariates using the Gibbs sampler. A general location model that allows different covariance structures across cells is specified for the covariates, and ignorable missingness of the covariates is assumed. Techniques that accommodate standard assumptions of ignorable censoring as well as certain types of nonignorable censoring are developed. We compare our approach to traditional complete-case analysis in an application to data obtained from a study of melanoma. The comparison indicates that substantial gains in efficiency are possible with our approach.     

Simultaneous inference for semiparametric nonlinear mixed-effects models with covariate measurement errors and missing responses

Semiparametric nonlinear mixed-effects (NLME) models are flexible for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain interindividual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. We propose two approximate likelihood methods for semiparametric NLME models with covariate measurement errors and nonignorable missing responses. The methods are illustrated in a real data example. Simulation results show that both methods perform well and are much better than the commonly used naive method.     

Marginalized transition shared random effects models for longitudinal binary data with nonignorable dropout

In longitudinal studies investigators frequently have to assess and address potential biases introduced by missing data. New methods are proposed for modeling longitudinal categorical data with nonignorable dropout using marginalized transition models and shared random effects models. Random effects are introduced for both serial dependence of outcomes and nonignorable missingness. Fisher‐scoring and Quasi–Newton algorithms are developed for parameter estimation. Methods are illustrated with a real dataset.     

Multiple imputation for model checking: completed-data plots with missing and latent data

In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset--corresponding to the observed data and imputed unobserved data--using standard procedures for complete-data inference. Here, we extend this approach to model checking by demonstrating the advantages of the use of completed-data model diagnostics on imputed completed datasets. The approach is set in the theoretical framework of Bayesian posterior predictive checks (but, as with missing-data imputation, our methods of missing-data model checking can also be interpreted as "predictive inference" in a non-Bayesian context). We consider the graphical diagnostics within this framework. Advantages of the completed-data approach include: (1) One can often check model fit in terms of quantities that are of key substantive interest in a natural way, which is not always possible using observed data alone. (2) In problems with missing data, checks may be devised that do not require to model the missingness or inclusion mechanism; the latter is useful for the analysis of ignorable but unknown data collection mechanisms, such as are often assumed in the analysis of sample surveys and observational studies. (3) In many problems with latent data, it is possible to check qualitative features of the model (for example, independence of two variables) that can be naturally formalized with the help of the latent data. We illustrate with several applied examples.     

Nonignorable Models for Intermittently Missing Categorical Longitudinal Responses

Summary A class of nonignorable models is presented for handling nonmonotone missingness in categorical longitudinal responses. This class of models includes the traditional selection models and shared parameter models. This allows us to perform a broader than usual sensitivity analysis. In particular, instead of considering variations to a chosen nonignorable model, we study sensitivity between different missing data frameworks. An appealing feature of the developed class is that parameters with a marginal interpretation are obtained, while algebraically simple models are considered. Specifically, marginalized mixed‐effects models ( Heagerty, 1999 , Biometrics 55, 688–698) are used for the longitudinal process that model separately the marginal mean and the correlation structure. For the correlation structure, random effects are introduced and their distribution is modeled either parametrically or non‐parametrically to avoid potential misspecifications.     

An extended general location model for causal inferences from data subject to noncompliance and missing values

Noncompliance is a common problem in experiments involving randomized assignment of treatments, and standard analyses based on intention-to-treat or treatment received have limitations. An attractive alternative is to estimate the Complier-Average Causal Effect (CACE), which is the average treatment effect for the subpopulation of subjects who would comply under either treatment (Angrist, Imbens, and Rubin, 1996, Journal of American Statistical Association 91, 444-472). We propose an extended general location model to estimate the CACE from data with noncompliance and missing data in the outcome and in baseline covariates. Models for both continuous and categorical outcomes and ignorable and latent ignorable (Frangakis and Rubin, 1999, Biometrika 86, 365-379) missing-data mechanisms are developed. Inferences for the models are based on the EM algorithm and Bayesian MCMC methods. We present results from simulations that investigate sensitivity to model assumptions and the influence of missing-data mechanism. We also apply the method to the data from a job search intervention for unemployed workers.     

Generalized additive selection models for the analysis of studies with potentially nonignorable missing outcome data

Rotnitzky, Robins, and Scharfstein (1998, Journal of the American Statistical Association 93, 1321-1339) developed a methodology for conducting sensitivity analysis of studies in which longitudinal outcome data are subject to potentially nonignorable missingness. In their approach, they specify a class of fully parametric selection models, indexed by a non- or weakly identified selection bias function that indicates the degree to which missingness depends on potentially unobservable outcomes. Estimation of the parameters of interest proceeds by varying the selection bias function over a range considered plausible by subject-matter experts. In this article, we focus on cross-sectional, univariate outcome data and extend their approach to a class of semiparametric selection models, using generalized additive restrictions. We propose a backfitting algorithm to estimate the parameters of the generalized additive selection model. For estimation of the mean outcome, we propose three types of estimating functions: simple inverse weighted, doubly robust, and orthogonal. We present the results of a data analysis and a simulation study.     

含不可忽略缺失数据非线性再生散度模型参数的Bayes估计

给出协变量带有不可忽略缺失数据的非线性再生散度模型的Bayes方法,缺失数据机制由Logistic回归模型来确定.Gibbs抽样技术和Metropolis-Hastings算法(简称MH算法)用来得到模型参数、缺失数据机制中回归系数的联合Bayes估计,并用实例加以说明.     

Combined Healthy Lifestyle Is Inversely Associated with Psychological Disorders among Adults

Background and Aims

Joint association of lifestyle-related factors and mental health has been less studied in earlier studies, especially in Middle Eastern countries. This study aimed to examine how combinations of several lifestyle-related factors related to depression and anxiety in a large group of middle-age Iranian population.

Methods

In a cross-sectional study on 3363 Iranian adults, a healthy lifestyle score was constructed by the use of data from dietary intakes, physical activity, smoking status, psychological distress and obesity. A dish-based 106-item semi-quantitative validated food frequency questionnaire (FFQ), General Practice Physical Activity Questionnaire (GPPAQ), General Health Questionnaire (GHQ) and other pre-tested questionnaires were used to assess the components of healthy lifestyle score. The Hospital Anxiety and Depression Scale (HADS) was applied to screen for anxiety and depression.

Results

After adjustment for potential confounders, we found that individuals with the highest score of healthy lifestyle were 95% less likely to be anxious (OR: 0.05; 95% CI: 0.01–0.27) and 96% less likely to be depressed (OR: 0.04; 95% CI: 0.01–0.15), compared with those with the lowest score. In addition, non-smokers had lower odds of anxiety (OR: 0.64; 95% CI: 0.47–0.88) and depression (OR: 0.62; 95% CI: 0.48–0.81) compared with smokers. Individuals with low levels of psychological distress had expectedly lower odds of anxiety (OR: 0.13; 95% CI: 0.10–0.16) and depression (OR: 0.10; 95% CI: 0.08–0.12) than those with high levels. Individuals with a healthy diet had 29% lower odds of depression (OR: 0.71; 95% CI: 0.59–0.87) than those with a non-healthy diet.

Conclusion

We found evidence indicating that healthy lifestyle score was associated with lower odds of anxiety and depression in this group of Iranian adults. Healthy diet, psychological distress, and smoking status were independent predictors of mental disorders.     

Principal stratification designs to estimate input data missing due to death

We consider studies of cohorts of individuals after a critical event, such as an injury, with the following characteristics. First, the studies are designed to measure "input" variables, which describe the period before the critical event, and to characterize the distribution of the input variables in the cohort. Second, the studies are designed to measure "output" variables, primarily mortality after the critical event, and to characterize the predictive (conditional) distribution of mortality given the input variables in the cohort. Such studies often possess the complication that the input data are missing for those who die shortly after the critical event because the data collection takes place after the event. Standard methods of dealing with the missing inputs, such as imputation or weighting methods based on an assumption of ignorable missingness, are known to be generally invalid when the missingness of inputs is nonignorable, that is, when the distribution of the inputs is different between those who die and those who live. To address this issue, we propose a novel design that obtains and uses information on an additional key variable-a treatment or externally controlled variable, which if set at its "effective" level, could have prevented the death of those who died. We show that the new design can be used to draw valid inferences for the marginal distribution of inputs in the entire cohort, and for the conditional distribution of mortality given the inputs, also in the entire cohort, even under nonignorable missingness. The crucial framework that we use is principal stratification based on the potential outcomes, here mortality under both levels of treatment. We also show using illustrative preliminary injury data that our approach can reveal results that are more reasonable than the results of standard methods, in relatively dramatic ways. Thus, our approach suggests that the routine collection of data on variables that could be used as possible treatments in such studies of inputs and mortality should become common.     

A latent autoregressive model for longitudinal binary data subject to informative missingness

Longitudinal clinical trials often collect long sequences of binary data. Our application is a recent clinical trial in opiate addicts that examined the effect of a new treatment on repeated binary urine tests to assess opiate use over an extended follow-up. The dataset had two sources of missingness: dropout and intermittent missing observations. The primary endpoint of the study was comparing the marginal probability of a positive urine test over follow-up across treatment arms. We present a latent autoregressive model for longitudinal binary data subject to informative missingness. In this model, a Gaussian autoregressive process is shared between the binary response and missing-data processes, thereby inducing informative missingness. Our approach extends the work of others who have developed models that link the various processes through a shared random effect but do not allow for autocorrelation. We discuss parameter estimation using Monte Carlo EM and demonstrate through simulations that incorporating within-subject autocorrelation through a latent autoregressive process can be very important when longitudinal binary data is subject to informative missingness. We illustrate our new methodology using the opiate clinical trial data.     

Estimating equations with nonignorably missing response data

Troxel, Lipsitz, and Brennan (1997, Biometrics 53, 857-869) considered parameter estimation from survey data with nonignorable nonresponse and proposed weighted estimating equations to remove the biases in the complete-case analysis that ignores missing observations. This paper suggests two alternative modifications for unbiased estimation of regression parameters when a binary outcome is potentially observed at successive time points. The weighting approach of Robins, Rotnitzky, and Zhao (1995, Journal of the American Statistical Association 90, 106-121) is also modified to obtain unbiased estimating functions. The suggested estimating functions are unbiased only when the missingness probability is correctly specified, and misspecification of the missingness model will result in biases in the estimates. Simulation studies are carried out to assess the performance of different methods when the covariate is binary or normal. For the simulation models used, the relative efficiency of the two new methods to the weighting methods is about 3.0 for the slope parameter and about 2.0 for the intercept parameter when the covariate is continuous and the missingness probability is correctly specified. All methods produce substantial biases in the estimates when the missingness model is misspecified or underspecified. Analysis of data from a medical survey illustrates the use and possible differences of these estimating functions.     

Impact of nonignorable coarsening on Bayesian inference

The coarse data model of Heitjan and Rubin (1991) generalizes the missing data model of Rubin (1976) to cover other forms of incompleteness such as censoring and grouping. The model has 2 components: an ideal data model describing the distribution of the quantity of interest and a coarsening mechanism that describes a distribution over degrees of coarsening given the ideal data. The coarsening mechanism is said to be nonignorable when the degree of coarsening depends on an incompletely observed ideal outcome, in which case failure to properly account for it can spoil inferences. A theme in recent research is to measure sensitivity to nonignorability by evaluating the effect of a small departure from ignorability on the maximum likelihood estimate (MLE) of a parameter of the ideal data model. One such construct is the "index of local sensitivity to nonignorability" (ISNI) (Troxel and others, 2004), which is the derivative of the MLE with respect to a nonignorability parameter evaluated at the ignorable model. In this paper, we adapt ISNI to Bayesian modeling by instead defining it as the derivative of the posterior expectation. We propose the application of ISNI as a first step in judging the robustness of a Bayesian analysis to nonignorable coarsening. We derive formulas for a range of models and apply the method to evaluate sensitivity to nonignorable coarsening in 2 real data examples, one involving missing CD4 counts in an HIV trial and the other involving potentially informatively censored relapse times in a leukemia trial.     

A Model for Adjusting for Nonignorable Verification Bias in Estimation of the ROC Curve and Its Area with Likelihood‐Based Approach

Summary In estimation of the ROC curve, when the true disease status is subject to nonignorable missingness, the observed likelihood involves the missing mechanism given by a selection model. In this article, we proposed a likelihood‐based approach to estimate the ROC curve and the area under the ROC curve when the verification bias is nonignorable. We specified a parametric disease model in order to make the nonignorable selection model identifiable. With the estimated verification and disease probabilities, we constructed four types of empirical estimates of the ROC curve and its area based on imputation and reweighting methods. In practice, a reasonably large sample size is required to estimate the nonignorable selection model in our settings. Simulation studies showed that all four estimators of ROC area performed well, and imputation estimators were generally more efficient than the other estimators proposed. We applied the proposed method to a data set from research in Alzheimer's disease.     

Predictors of local malaria outbreaks: an approach to the development of an early warning system in Colombia

Risk factor surveillance is a complementary tool of morbidity and mortality surveillance that improves the likelihood that public health interventions are implemented in a timely fashion. The aim of this study was to identify population predictors of malaria outbreaks in endemic municipalities of Colombia with the goal of developing an early warning system for malaria outbreaks. We conducted a multiple-group, exploratory, ecological study at the municipal level. Each of the 290 municipalities with endemic malaria that we studied was classified according to the presence or absence of outbreaks. The measurement of variables was based on historic registries and logistic regression was performed to analyse the data. Altitude above sea level [odds ratio (OR) 3.65, 95% confidence interval (CI) 1.34-9.98], variability in rainfall (OR 1.85, 95% CI 1.40-2.44) and the proportion of inhabitants over 45 years of age (OR 0.17, 95% CI 0.08-0.38) were factors associated with malaria outbreaks in Colombian municipalities. The results suggest that environmental and demographic factors could have a significant ability to predict malaria outbreaks on the municipal level in Colombia. To advance the development of an early warning system, it will be necessary to adjust and standardise the collection of required data and to evaluate the accuracy of the forecast models.     

Missing Oral Health-Related Data in the interRAI-HC - Associations with Selected Variables of General Health and the Effect of Multiple Imputation on the Relationship between Oral and General Health

Background

Missing data within the comprehensive geriatric assessment of the interRAI suite of assessment instruments potentially imply the under-detection of conditions that require care as well as the risk of biased statistical results. Impaired oral health in older individuals has to be registered accurately as it causes pain and discomfort and is related to the general health status.

Objective

This study was based on interRAI-Home Care (HC) baseline data from 7590 subjects (mean age 81.2 years, SD 6.9) in Belgium. It was investigated if missingness of the oral health-related items was associated with selected variables of general health. It was also determined if multiple imputation of missing data affected the associations between oral and general health.

Materials and Methods

Multivariable logistic regression was used to determine if the prevalence of missingness in the oral health-related variables was associated with activities of daily life (ADLH), cognitive performance (CPS2) and depression (DRS). Associations between oral health and ADLH, CPS2 and DRS were determined, with missing data treated by 1. the complete-case technique and 2. by multiple imputation, and results were compared.

Results

The individual oral health-related variables had a similar proportion of missing values, ranging from 16.3% to 17.2%. The prevalence of missing data in all oral health-related variables was significantly associated with symptoms of depression (dental prosthesis use OR 1.66, CI 1.41–1.95; damaged teeth OR 1.74, CI 1.48–2.04; chewing problems OR 1.74, CI 1.47–2.05; dry mouth OR 1.65, CI 1.40–1.94). Missingness in damaged teeth (OR 1.27, CI 1.08–1.48), chewing problems (OR 1.22, CI 1.04–1.44) and dry mouth (OR 1.23, CI 1.05–1.44) occurred more frequently in cognitively impaired subjects. ADLH was not associated with the prevalence of missing data. When comparing the complete-case technique with the multiple imputation approach, nearly identical odds ratios characterized the associations between oral and general health.

Conclusion

Cognitively impaired and depressive individuals had a higher risk of missing oral health-related information. Associations between oral health and ADLH, CPS2 and DRS were not influenced by multiple imputation of missing data. Further research should concentrate on the mechanisms that mediate the occurrence of missingness to develop preventative strategies.     

Diabetes-Related Distress,Depression and Distress-Depression among Adults with Type 2 Diabetes Mellitus in Malaysia

Type 2 diabetes mellitus (T2DM) brings about an increasing psychosocial problem in adult patients. Prevalence data on and associated factors of diabetes related distress (DRD) and depression have been lacking in Asia. This study aimed to examine the prevalence of DRD and depression, and their associated factors in Asian adult T2DM patients. This study was conducted in three public health clinics measuring DRD (Diabetes Distress Scale, DDS), and depression (Patient Health Questionnaire, PHQ). Patients who were at least 30 years of age, had T2DM for more than one year, with regular follow-up and recent laboratory results (< 3 months) were consecutively recruited. Associations between DRD, depression and the combination DRD-depression with demographic and clinical characteristics were analysed using generalized linear models. From 752 invited people, 700 participated (mean age 56.9 years, 52.8% female, 52.9% Malay, 79.1% married). Prevalence of DRD and depression were 49.2% and 41.7%, respectively. Distress and depression were correlated, spearman’s r = 0.50. Patients with higher DRD were younger (OR 0.995, 95% CI 0.996 to 0.991), Chinese (OR 1.2, 95% CI 1.04 to 1.29), attending Dengkil health clinic (OR 1.1, 95% CI 1.00 to 1.22) and had higher scores on the PHQ (OR 1.1, 95% CI 1.04 to 1.06). Depression was less likely in the unmarried compared to divorced/separately living and those attending Dengkil health clinic, but more likely in patients with microvascular complications (OR 1.4, 95% CI 1.06 to 1.73) and higher DDS (OR 1.03, 95% CI 1.02 to 1.03). For the combination of DRD and depression, unemployment (OR 4.7, 95% CI 1.02 to 21.20) had positive association, whereas those under medical care at the Salak health clinics (OR 0.28, 95% CI 0.12 to 0.63), and those with a blood pressure > 130/80 mmHg (OR 0.53, 95% CI 0.32 to 0.89) were less likely to experience both DRD and depression. DRD and depression were common and correlated in Asian adults with T2DM at primary care level. Socio-demographic more than clinical characteristics were related to DRD and depression.