We develop a Bayesian nonparametric model for a longitudinal response in the presence of nonignorable missing data. Our general approach is to first specify a working model that flexibly models the missingness and full outcome processes jointly. We specify a Dirichlet process mixture of missing at random (MAR) models as a prior on the joint distribution of the working model. This aspect of the model governs the fit of the observed data by modeling the observed data distribution as the marginalization over the missing data in the working model. We then separately specify the conditional distribution of the missing data given the observed data and dropout. This approach allows us to identify the distribution of the missing data using identifying restrictions as a starting point. We propose a framework for introducing sensitivity parameters, allowing us to vary the untestable assumptions about the missing data mechanism smoothly. Informative priors on the space of missing data assumptions can be specified to combine inferences under many different assumptions into a final inference and accurately characterize uncertainty. These methods are motivated by, and applied to, data from a clinical trial assessing the efficacy of a new treatment for acute Schizophrenia.
Dirichlet process mixture; Identifiability; Identifying restrictions; Sensitivity analysis
To evaluate the effects and costs of three doses of behavioral weight-loss treatment delivered via Cooperative Extension Offices in rural communities.
Design and Methods
Obese adults (N=612) were randomly assigned to low, moderate or high doses of behavioral treatment (i.e., 16, 32 or 48 sessions over two years) or to a control condition that received nutrition education without instruction in behavior modification strategies.
Two-year mean reductions in initial body weight were 2.9% (95% Credible Interval=1.7–4.3), 3.5% (2.0–4.8), 6.7% (5.3–7.9), and 6.8% (5.5–8.1) for the control, low, moderate, and high-dose conditions, respectively. The moderate-dose treatment produced weight losses similar to the high-dose condition and significantly larger than the low-dose and control conditions (posterior probability > .996). The percentages of participants who achieved weight reductions ≥ 5% at two years were significantly higher in the moderate-dose (58%) and high-dose (58%) conditions compared with low-dose (43%) and control (40%) conditions (posterior probability > .996). Cost-effectiveness analyses favored the moderate-dose treatment over all other conditions.
A moderate dose of behavioral treatment produced two-year weight reductions comparable to high-dose treatment but at a lower cost. These findings have important policy implications for the dissemination of weight-loss interventions into communities with limited resources.
ClinicalTrials.gov number, NCT00912652.
Behavior Therapy; Cost effectiveness; Weight Management Programs; Treatment Outcomes; Dissemination
To evaluate the effects of corticosteroids on the lower extremity muscles in boys with Duchenne muscular dystrophy (DMD) using MRI and magnetic resonance spectroscopy (MRS).
Transverse relaxation time (T2) and fat fraction were measured by MRI/MRS in lower extremity muscles of 15 boys with DMD (age 5.0–6.9 years) taking corticosteroids and 15 corticosteroid-naive boys. Subsequently, fat fraction was measured in a subset of these boys at 1 year. Finally, MRI/MRS data were collected from 16 corticosteroid-naive boys with DMD (age 5–8.9 years) at baseline, 3 months, and 6 months. Five boys were treated with corticosteroids after baseline and the remaining 11 served as corticosteroid-naive controls.
Cross-sectional comparisons demonstrated lower muscle T2 and less intramuscular (IM) fat deposition in boys with DMD on corticosteroids, suggesting reduced inflammation/damage and fat infiltration with treatment. Boys on corticosteroids demonstrated less increase in IM fat infiltration at 1 year. Finally, T2 by MRI/MRS detected effects of corticosteroids on leg muscles as early as 3 months after drug initiation.
These results demonstrate the ability of MRI/MRS to detect therapeutic effects of corticosteroids in reducing inflammatory processes in skeletal muscles of boys with DMD. Our work highlights the potential of MRI/MRS as a biomarker in evaluating therapeutic interventions in DMD.
The bicuspid aortic valve (AV) is the most common cardiac congenital anomaly and has been found to be a significant risk factor for developing calcific AV disease. However, the mechanisms of disease development remain unclear. In this study we quantified the structure of human normal and bicuspid leaflets in the early disease stage. From these individual leaflet maps average fiber structure maps were generated using a novel spline based technique. Interestingly, we found statistically different and consistent regional structures between the normal and bicuspid valves. The regularity in the observed microstructure was a surprising finding, especially for the pathological BAV leaflets and is an essential cornerstone of any predictive mathematical models of valve disease. In contrast, we determined that isolated valve interstitial cells from BAV leaflets show the same in vitro calcification pathways as those from the normal AV leaflets. This result suggests the VICs are not intrinsically different when isolated, and that external features, such as abnormal microstructure and altered flow may be the primary contributors in the accelerated calcification experienced by BAV patients.
Microstructure; Aortic stenosis; Calcific aortic valve disease; Early disease stage; Fiber structure; Valve interstitial cells
Accumulating evidence suggests that both dietary restriction and exercise (DR + E) should be incorporated in weight loss interventions to treat obese, older adults. However, more information is needed on the effects to lower extremity tissue composition—an important consideration for preserving mobility in older adults.
Twenty-seven sedentary women (body mass index: 36.3±5.4kg/m2; age: 63.6±5.6 yrs) were randomly assigned to 6 months of DR + E or a health education control group. Thigh and calf muscle, subcutaneous adipose tissue (SAT), and intermuscular adipose tissue (IMAT) size were determined using magnetic resonance imaging. Physical function was measured using a long-distance corridor walk and knee extension strength.
Compared with control, DR + E significantly reduced body mass (-6.6±3.7kg vs control: -0.05±3.5kg; p < .01). Thigh and calf muscle volumes responded similarly between groups. Within the DR + E group, adipose tissue was reduced more in the thigh than in the calf (p < .04). Knee extension strength was unaltered by DR + E, but a trend toward increased walking speed was observed in the DR + E group (p = .09). Post hoc analyses showed that reductions in SAT and IMAT within the calf, but not the thigh, were associated with faster walking speed achieved with DR + E (SAT: r = -0.62; p = .01; IMAT: r = -0.62; p = .01).
DR + E preserved lower extremity muscle size and function and reduced regional lower extremity adipose tissue. Although the magnitude of reduction in adipose tissue was greater in the thigh than the calf region, post hoc analyses demonstrated that reductions in calf SAT and IMAT were associated with positive adaptations in physical function.
Body composition; Weight loss; Obesity; Aging; Disability.
CMS currently uses ICD-9-CM codes to determine whether an inpatient fall-related injury may warrant reduction in hospital payment. The purpose of our study was to compare falls and fall-related injuries identified by a fall evaluator or hospital incident report with injuries identified by discharge ICD-9-CM codes for the same set of inpatient episodes of care.
Prospective, descriptive study.
Sixteen adult general medical and surgical units in an urban, major teaching hospital.
All adult patients who sustained a fall with injury during a five-year period (380 falls with injury).
Falls identified by a fall evaluator or hospital incident report were classified according to their injury severity. Discharge abstracts provided diagnoses codes (ICD-9-CM) for the discharge, including fall-related injury codes.
The majority of inpatient falls with injury (n=343; 90.2 %) resulted in temporary harm to the patient; the remaining 37 falls (9.8 %) resulted in more serious harm. We found that 16 of the 37 falls with injury extending hospitalization or resulting in death, or less than one-half, were identified using the CMS-targeted injury code ranges combined with the present on admission (POA) indicators. Among the 21 falls with injury that were not identified, nine (42.9 %) lacked documentation of any injury and seven (33.3 %) identified other injuries outside the CMS-targeted injury code ranges.
The CMS-targeted ICD-9-CM codes used to identify fall-related injuries in claims data do not always detect the most serious falls.
Inpatient falls; fall-related injuries; ICD-9-CM codes; hospital-acquired conditions
In longitudinal clinical trials, if a subject drops out due to death, certain responses, such as those measuring quality of life (QOL), will not be defined after the time of death. Thus, standard missing data analyses, e.g., under ignorable dropout, are problematic because these approaches implicitly ‘impute’ values of the response after death. In this paper we define a new survivors average causal effect for a bivariate response in a longitudinal quality of life study that had a high dropout rate with the dropout often due to death (or tumor progression). We show how principal stratification, with a few sensitivity parameters, can be used to draw causal inferences about the joint distribution of these two ordinal quality of life measures.
Duchenne muscular dystrophy (DMD) is an X-linked recessive disorder that results in functional deficits. However, these functional declines are often not able to be quantified in clinical trials for DMD until after age 7. In this study, we hypothesized that 1H2O T2 derived using 1H-MRS and MRI-T2 will be sensitive to muscle involvement at a young age (5–7 years) consistent with increased inflammation and muscle damage in a large cohort of DMD subjects compared to controls.
MR data were acquired from 123 boys with DMD (ages 5–14 years; mean 8.6 SD 2.2 years) and 31 healthy controls (age 9.7 SD 2.3 years) using 3-Tesla MRI instruments at three institutions (University of Florida, Oregon Health & Science University, and Children’s Hospital of Philadelphia). T2-weighted multi-slice spin echo (SE) axial images and single voxel 1H-MRS were acquired from the lower leg and thigh to measure lipid fraction and 1H2O T2.
MRI-T2, 1H2O T2, and lipid fraction were greater (p<0.05) in DMD compared to controls. In the youngest age group, DMD values were different (p<0.05) than controls for the soleus MRI-T2, 1H2O T2 and lipid fraction and vastus lateralis MRI-T2 and 1H2O T2. In the boys with DMD, MRI-T2 and lipid fraction were greater (p<0.05) in the oldest age group (11–14 years) than the youngest age group (5–6.9 years), while 1H2O T2 was lower in the oldest age group compared to the young age group.
Overall, MR measures of T2 and lipid fraction revealed differences between DMD and Controls. Furthermore, MRI-T2 was greater in the older age group compared to the young age group, which was associated with higher lipid fractions. Overall, MR measures of T2 and lipid fraction show excellent sensitivity to DMD disease pathologies and potential therapeutic interventions in DMD, even in the younger boys.
Random effects models are commonly used to analyze longitudinal categorical data. Marginalized random effects models are a class of models that permit direct estimation of marginal mean parameters and characterize serial correlation for longitudinal categorical data via random effects (Heagerty, 1999). Marginally specified logistic-normal models for longitudinal binary data. Biometrics
55, 688–698; Lee and Daniels, 2008. Marginalized models for longitudinal ordinal data with application to quality of life studies. Statistics in Medicine
27, 4359–4380). In this paper, we propose a Kronecker product (KP) covariance structure to capture the correlation between processes at a given time and the correlation within a process over time (serial correlation) for bivariate longitudinal ordinal data. For the latter, we consider a more general class of models than standard (first-order) autoregressive correlation models, by re-parameterizing the correlation matrix using partial autocorrelations (Daniels and Pourahmadi, 2009). Modeling covariance matrices via partial autocorrelations. Journal of Multivariate Analysis
100, 2352–2363). We assess the reasonableness of the KP structure with a score test. A maximum marginal likelihood estimation method is proposed utilizing a quasi-Newton algorithm with quasi-Monte Carlo integration of the random effects. We examine the effects of demographic factors on metabolic syndrome and C-reactive protein using the proposed models.
Kronecker product; Metabolic syndrome; Partial autocorrelation
Estimation of the covariance structure for irregular sparse longitudinal data has been studied by many authors in recent years but typically using fully parametric specifications. In addition, when data are collected from several groups over time, it is known that assuming the same or completely different covariance matrices over groups can lead to loss of efficiency and/or bias. Nonparametric approaches have been proposed for estimating the covariance matrix for regular univariate longitudinal data by sharing information across the groups under study. For the irregular case, with longitudinal measurements that are bivariate or multivariate, modeling becomes more difficult. In this article, to model bivariate sparse longitudinal data from several groups, we propose a flexible covariance structure via a novel matrix stick-breaking process for the residual covariance structure and a Dirichlet process mixture of normals for the random effects. Simulation studies are performed to investigate the effectiveness of the proposed approach over more traditional approaches. We also analyze a subset of Framingham Heart Study data to examine how the blood pressure trajectories and covariance structures differ for the patients from different BMI groups (high, medium and low) at baseline.
Covariance matrix; DIC; Dirichlet process mixture of normals; MCMC
The purpose of this study was to provide normative data on fall prevalence in US hospitals by unit type and to determine the 27-month secular trend in falls prior to the implementation of the Centers for Medicare and Medicaid Service (CMS) rule which does not reimburse hospitals for care related to injury resulting from hospital falls.
We used data from the National Database of Nursing Quality Indicators (NDNQI) collected between July 1, 2006 and September 30, 2008 to estimate prevalence and secular trends of falls occurring in adult medical, medical-surgical and surgical nursing units. More than 88 million patient days (pd) of observation were contributed from 6,100 medical, surgical, and medical-surgical nursing units in 1,263 hospitals across the United States.
A total of 315,817 falls occurred (rate=3.56 falls/1,000 pd) during the study period, of which 82,332 (26.1%) resulted in an injury (rate=0.93/1,000 pd). Both total fall and injurious fall rates were highest in medical units (fall rate=4.03/1,000 pd; injurious fall rate=1.08/1,000 pd) and lowest in surgery units (fall rate=2.76/1,000 pd; injurious fall rate=0.67/1,000 pd). Falls (0.4% decrease/quarter, p<0.0001) and injurious falls (1% decrease per quarter, p<0.0001) both decreased over the 27-month study.
In this large sample, fall and injurious fall prevalence varied by nursing unit type in US hospitals. Over the 27 month study, there was a small, but statistically significant, decrease in falls (p<0.0001) and injurious falls (p<0.0001).
Accidental falls; epidemiology; hospital units; injuries/epidemiology; databases
In a typical case-control study, exposure information is collected at a single time-point for the cases and controls. However, case-control studies are often embedded in existing cohort studies containing a wealth of longitudinal exposure history on the participants. Recent medical studies have indicated that incorporating past exposure history, or a constructed summary measure of cumulative exposure derived from the past exposure history, when available, may lead to more precise and clinically meaningful estimates of the disease risk. In this paper, we propose a flexible Bayesian semiparametric approach to model the longitudinal exposure profiles of the cases and controls and then use measures of cumulative exposure based on a weighted integral of this trajectory in the final disease risk model. The estimation is done via a joint likelihood. In the construction of the cumulative exposure summary, we introduce an influence function, a smooth function of time to characterize the association pattern of the exposure profile on the disease status with different time windows potentially having differential influence/weights. This enables us to analyze how the present disease status of a subject is influenced by his/her past exposure history conditional on the current ones. The joint likelihood formulation allows us to properly account for uncertainties associated with both stages of the estimation process in an integrated manner. Analysis is carried out in a hierarchical Bayesian framework using Reversible jump Markov chain Monte Carlo (RJMCMC) algorithms. The proposed methodology is motivated by, and applied to a case-control study of prostate cancer where longitudinal biomarker information is available for the cases and controls.
Adaptive knot selection; Exposure trajectory; Influence function; Odds ratio; Regression spline; Risk score diagnostics; Semiparametric modeling
We propose a nonparametric Bayesian approach to estimate the natural direct and indirect effects through a mediator in the setting of a continuous mediator and a binary response. Several conditional independence assumptions are introduced (with corresponding sensitivity parameters) to make these effects identifiable from the observed data. We suggest strategies for eliciting sensitivity parameters and conduct simulations to assess violations to the assumptions. This approach is used to assess mediation in a recent weight management clinical trial.
We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.
DIC; Bayes Factor; Longitudinal data; MCMC; Model Selection
In the modeling of longitudinal data from several groups, appropriate handling of the dependence structure is of central importance. Standard methods include specifying a single covariance matrix for all groups or independently estimating the covariance matrix for each group without regard to the others, but when these model assumptions are incorrect, these techniques can lead to biased mean effects or loss of efficiency, respectively. Thus, it is desirable to develop methods to simultaneously estimate the covariance matrix for each group that will borrow strength across groups in a way that is ultimately informed by the data. In addition, for several groups with covariance matrices of even medium dimension, it is difficult to manually select a single best parametric model among the huge number of possibilities given by incorporating structural zeros and/or commonality of individual parameters across groups. In this paper we develop a family of nonparametric priors using the matrix stick-breaking process of Dunson et al. (2008) that seeks to accomplish this task by parameterizing the covariance matrices in terms of the parameters of their modified Cholesky decomposition (Pourahmadi, 1999). We establish some theoretic properties of these priors, examine their effectiveness via a simulation study, and illustrate the priors using data from a longitudinal clinical trial.
Bayesian nonparametric inference; Cholesky decomposition; matrix stick-breaking process; simultaneous covariance estimation; sparsity
We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.
Bayesian variable selection; Bias; Dropout; Missing data; Model selection
Although lung transplantation is an accepted therapy for end-stage disease, recipient outcomes continue to be hindered by early primary graft dysfunction (PGD) as well as late rejection and bronchiolitis obliterans syndrome (BOS). We have previously shown that the pro-inflammatory cytokine response following transplantation correlates with the severity of PGD. We hypothesized that lung-transplant recipients with an increased inflammatory response immediately following surgery would also have a greater incidence of unfavorable long-term outcomes including rejection, BOS and ultimately death.
A retrospective study of lung-transplant recipients (n = 19) for whom serial blood sampling of cytokines was performed for 24 h following transplantation between March 2002 and June 2003 at a single institution. Long-term follow-up was examined for rejection, BOS and survival.
Thirteen single and six bilateral lung recipients were examined. Eleven (58%) developed BOS and eight (42%) did not. Subgroup analysis revealed an association between elevated IL-6 concentrations 4 h after reperfusion of the allograft and development of BOS (P = 0.068). The correlation between IL-6 and survival time was found to be significant (corr = −0.46, P = 0.047), indicating that higher IL-6 response had shorter survival following transplantation.
An elevation in interleukin (IL)-6 concentration immediately following lung transplantation is associated with a trend towards development of bronchiolitis obliterans, rejection and significantly decreased survival time. Further studies are warranted to confirm the correlation between the immediate inflammatory response, PGD and BOS. Identification of patients at risk for BOS based on the cytokine response after surgery may allow for early intervention.
Transplantation; Lung transplantation; Lung other; Inflammation
Rural counties in the U.S. have higher rates of obesity, sedentary lifestyle, and associated chronic diseases than non-rural areas, yet the management of obesity in rural communities has received little attention from researchers.
To compare 2 extended-care programs for weight management with an education control group.
Design, Setting, and Participants
234 obese women from rural communities who completed an initial 6-month weight-loss program were randomized to extended-care, delivered via telephone counseling or face-to-face sessions, or to an education control group. Cooperative Extension Service offices in six medically underserved rural counties served as venues for the trial. The study was conducted from June 2003 to May 2007.
The extended-care programs entailed problem-solving counseling delivered in 26 biweekly sessions. Control group participants received 26 biweekly newsletters containing weight-control advice.
Main Outcome Measure
Change in weight from randomization.
Mean weight at study entry was 96.4 kg. Mean weight loss during the initial 6-month intervention was 10.0 kg. One year after randomization, participants in the telephone and face-to-face conditions regained less weight (means ± SE = 1.3 ± 0.7 and 1.2 ± 0.6 kg, respectively) than those in the education control group (3.7 ± 0.6 kg; Ps = 0.02 and 0.03). The beneficial effects of extended-care counseling were mediated by greater adherence to behavioral weight-management strategies, and cost analyses indicated that telephone counseling was less expensive than face-to-face intervention.
Extended care delivered either by telephone or face-to-face sessions improved the one-year maintenance of lost weight compared to education alone. Telephone counseling constitutes an effective and cost-efficient option for long-term weight management. Delivering lifestyle interventions via the existing infrastructure of the Cooperative Extension Service represents a viable means of research translation into rural communities with limited access to preventive health services.
ClinicalTrials.gov number, NCT00201006.
A major challenge following successful weight loss is continuing the behaviors required for long-term weight maintenance. This challenge may be exacerbated in rural areas with limited local support resources.
This study describes and compares program costs and cost-effectiveness for 12-month extended care lifestyle maintenance programs following an initial 6-month weight loss program.
A 1-year prospective controlled randomized clinical trial.
The study included 215 female participants age 50 or older from rural areas who completed an initial 6-month lifestyle program for weight loss. The study was conducted from June 1, 2003, to May 31, 2007.
The intervention was delivered through local Cooperative Extension Service offices in rural Florida. Participants were randomly-assigned to a 12-month extended care program using either individual telephone counseling (n=67), group face-to-face counseling (n=74), or a mail/control group (n=74).
Main Outcome Measures
Program delivery costs, weight loss, and self-reported health status were directly assessed through questionnaires and program activity logs. Costs were estimated across a range of enrollment sizes to allow inferences beyond the study sample.
Statistical Analyses Performed
Non-parametric and parametric tests of differences across groups for program outcomes were combined with direct program cost estimates and expected value calculations to determine which scales of operation favored alternative formats for lifestyle maintenance.
Median weight regain during the intervention year was 1.7 kg for participants in the face-to-face format, 2.1 kg for the telephone format, and 3.1 kg for the mail/control format. For a typical group size of 13 participants, the face-to-face format had higher fixed costs, which translated into higher overall program costs ($420 per participant) when compared to individual telephone counseling ($268 per participant) and control ($226 per participant) programs. While the net weight lost after the 12-month maintenance program was higher for the face-to-face and telephone programs compared to the control group, the average cost per expected kilogram of weight lost was higher for the face-to-face program ($47/kg) compared to the other two programs (approximately $33/kg for telephone and control).
Both the scale of operations and local demand for programs are important considerations in selecting a delivery format for lifestyle maintenance. In this study, the telephone format had a lower cost, but similar outcomes compared to the face-to-face format.
Obesity; cost-effectiveness; randomized trial; rural health
Bed alarm systems intended to prevent hospital falls have not been formally evaluated.
To investigate whether an intervention aimed at increasing bed alarm use decreases hospital falls and related events.
Pair-matched, cluster randomized trial over 18 months. Nursing units were allocated by computer-generated randomization on the basis of baseline fall rates. Patients and outcome assessors were blinded to unit assignment; outcome assessors may have become unblinded. (ClinicalTrials.gov registration number: NCT00183053)
16 nursing units in an urban community hospital.
27 672 inpatients in general medical, surgical, and specialty units.
Education, training, and technical support to promote use of a standard bed alarm system (intervention units); bed alarms available but not formally promoted or supported (control units).
Pre–post difference in change in falls per 1000 patient-days (primary end point); number of patients who fell, fall-related injuries, and number of patients restrained (secondary end points).
Prevalence of alarm use was 64.41 days per 1000 patient-days on intervention units and 1.79 days per 1000 patient-days on control units (P = 0.004). There was no difference in change in fall rates per 1000 patient-days (risk ratio, 1.09 [95% CI, 0.85 to 1.53]; difference, 0.41 [CI, −1.05 to 2.47], which corresponds to a greater difference in falls in control vs. intervention units) or in the number of patients who fell, injurious fall rates, or the number of patients physically restrained on intervention units compared with control units.
The study was conducted at a single site and was slightly underpowered compared with the initial design.
An intervention designed to increase bed alarm use in an urban hospital increased alarm use but had no statistically or clinically significant effect on fall-related events or physical restraint use.
Primary Funding Source
National Institute on Aging.
Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions are one approach to mixture model identification (Little, 1995; Little and Wang, 1996; Thijs et al., 2002; Kenward et al., 2003; Daniels and Hogan, 2008) and are a natural starting point for missing not at random sensitivity analysis (Thijs et al., 2002; Daniels and Hogan, 2008). However, when the pattern specific models are multivariate normal, identifying restrictions corresponding to missing at random may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g. baseline covariates with time-invariant coefficients). In this paper, we explore conditions necessary for identifying restrictions that result in missing at random (MAR) to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. In addition, we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data. We adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches. We also apply the methods to a longitudinal clinical trial. Problems caused by baseline covariates with time-invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.
Missing at random; Non-future dependence; Deviance information criterion
Missing phenotype data can be a major hurdle to mapping quantitative trait loci (QTL). Though in many cases experiments may be designed to minimize the occurrence of missing data, it is often unavoidable in practice; thus, statistical methods to account for missing data are needed. In this paper we describe an approach for conjoining multiple imputation and QTL mapping. Methods are applied to map genes associated with increased breathing effort in mice after lung inflammation due to allergen challenge in developing lines of the Collaborative Cross, a new mouse genetics resource. Missing data poses a particular challenge in this study because the desired phenotype summary to be mapped is a function of incompletely observed dose-response curves. Comparison of the multiple imputation approach to two naive approaches for handling missing data suggest that these simpler methods may yield poor results: ignoring missing data through a complete case analysis may lead to incorrect conclusions, while using a last observation carried forward procedure, which does not account for uncertainty in the imputed values, may lead to anti-conservative inference. The proposed approach is widely applicable to other studies with missing phenotype data.
multiple imputation; missing data; quantitative trait loci
Obese older adults are particularly susceptible to sarcopenia and have a higher prevalence of disability than their peers of normal weight. Interventions to improve body composition in late life are crucial to maintaining independence. The main mechanisms underlying sarcopenia have not been determined conclusively, but chronic inflammation, apoptosis, and impaired mitochondrial function are believed to play important roles. It has yet to be determined whether impaired cellular quality control mechanisms contribute to this process. The objective of this study was to assess the effects of a 6-month weight loss program combined with moderate-intensity exercise on the cellular quality control mechanisms autophagy and ubiquitin-proteasome, as well as on inflammation, apoptosis, and mitochondrial function, in the skeletal muscle of older obese women. The intervention resulted in significant weight loss (8.0 ± 3.9 % vs. 0.4 ± 3.1% of baseline weight, p = 0.002) and improvements in walking speed (reduced time to walk 400 meters, − 20.4 ± 16% vs. − 2.5 ± 12%, p = 0.03). In the intervention group, we observed a three-fold increase in messenger RNA (mRNA) levels of the autophagy regulators LC3B, Atg7, and lysosome-associated membrane protein-2 (LAMP-2) compared to controls. Changes in mRNA levels of FoxO3A and its targets MuRF1, MAFBx, and BNIP3 were on average seven-fold higher in the intervention group compared to controls, but these differences were not statistically significant. Tumor necrosis factor-α (TNF-α) mRNA levels were elevated after the intervention, but we did not detect significant changes in the downstream apoptosis markers caspase 8 and 3. Mitochondrial biogenesis markers (PGC1α and TFAm) were increased by the intervention, but this was not accompanied by significant changes in mitochondrial complex content and activity. In conclusion, although exploratory in nature, this study is among the first to report the stimulation of cellular quality control mechanisms elicited by a weight loss and exercise program in older obese women.
In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this paper, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for non-identifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial.
Principal stratification; QOL; Ordinal data; Sensitivity analysis