Pattern-mixture Approach Research Articles

A pattern mixture model with long short-term memory network for acute kidney injury prediction

Acute kidney disease is a serious complication characterized by poor short- and long-term outcomes in the intensive care unit. Impairment in renal function of the kidney significantly increases the mortality rate. Early detection of acute kidney disease could lead to preventive interventions, therefore deep learning systems can detect it before its symptoms and consequences appear. We developed a novel deep learning architecture like Stacked long short-term memory network with pattern mixture approach for kidney injury prediction. A total of 33,754 patients encountered were retrospectively analyzed from the MIMIC-III database. A selection and pattern mixture model was used for preprocessing the time-series data. We compared the proposed result with conventional algorithms like gradient boosted trees and long short-term memory model. Our model was trained on patient time-series data for different time windows and obtained the highest accuracy of 92.4% for 12 h and 92.6% for 24 h. A novel stacked long short-term memory model outperforms the machine learning model, revealing superior performance in predicting kidney injury 24 h before onset.

Bayesian pattern mixture model under nonignorable nonresponse for binary data

We consider a Bayesian pattern mixture model to estimate the proportion of the finite population with missing data. The pattern mixture approach is a way to model missing data. We describe the Bayesian model considering two cases for the parameter of a prior distribution. To fit the model, we use Markov chain Monte Carlo methods. We use the Gibbs sampler with grid method to get the samples of the parameters. We use the National Crime Survey data summarized by Stasny (1991) to estimate the proportion of the finite population. When considering two cases of the parameter of a prior distribution, we saw that the inference for the parameter was not sensitive in our proposed model.

A pattern-mixture model approach for handling missing continuous outcome data in longitudinal cluster randomized trials.

We extend the pattern-mixture approach to handle missing continuous outcome data in longitudinal cluster randomized trials, which randomize groups of individuals to treatment arms, rather than the individuals themselves. Individuals who drop out at the same time point are grouped into the same dropout pattern. We approach extrapolation of the pattern-mixture model by applying multilevel multiple imputation, which imputes missing values while appropriately accounting for the hierarchical data structure found in cluster randomized trials. To assess parameters of interest under various missing data assumptions, imputed values are multiplied by a sensitivity parameter, k, which increases or decreases imputed values. Using simulated data, we show that estimates of parameters of interest can vary widely under differing missing data assumptions. We conduct a sensitivity analysis using real data from a cluster randomized trial by increasing k until the treatment effect inference changes. By performing a sensitivity analysis for missing data, researchers can assess whether certain missing data assumptions are reasonable for their cluster randomized trial.

The use of multiple imputation (MI) in cluster randomised trials with suspected missing not at random (MNAR) outcome

Introduction: The HELP trial of a healthy lifestyle and eating programme for obese pregnant women resulted in a final response rate of 70%. More women in the intervention arm than the control arm were lost to follow-up, leading the trial team to suspect a MNAR mechanism for missing outcome data. Methods: Missing-ness in the primary outcome (BMI) was explored in relation to all baseline demographic and post-randomisation variables using logistic regression. An imputation model was developed with cluster (study site) included as a factor together with significant predictors of missing outcome, variables in the primary analysis model, variables used to balance the randomisation and the outcome. The number of imputations performed was equal to the proportion of missing data. Sensitivity analyses using two approaches were performed on the pooled primary analysis to examine the change in effect for plausible departures from missing at random (MAR) towards MNAR. MI was carried out in STATA v13.1, REALCOM-IMPUTE and SPSS v20 for comparison. Results: Opinions were gathered from the study team to gauge the extent to which they thought BMI data would differ in those who dropped out prior to revealing the results of the trial. The team found this difficult to estimate in order to facilitate the pattern mixture approach to sensitivity analysis. The re-weighting approach to sensitivity analysis was a suitable alternative in this study. Discussion: The pitfalls, challenges and practical considerations of using MI and sensitivity analyses in cluster trials with MAR or MNAR will be discussed.

Variance estimation in reference based sensitivity analysis for longitudinal trials with protocol deviation

The statistical analysis of longitudinal randomised clinical trials is frequently complicated by the occurrence of protocol deviations, which result in incomplete data sets for analysis. Analysis and inference then rest on inherently untestable assumptions about the distribution of the unobserved data. It is therefore important to perform sensitivity analysis to explore the robustness of conclusions from the primary analysis to a range of contextually plausible assumptions about the missing data. Carpenter, Roger and Kenward (2013) propose a novel pattern-mixture approach for contextually relevant sensitivity analysis of a longitudinal trial. Their proposal uses multiple imputation to impute post-deviation data by reference to patients in other trial arms. This flexible approach avoids the need for users to specify explicitly the distribution of the post-deviation data. The primary analysis model is retained in the sensitivity analysis allowing direct assessment of the impact of alternative sampling behaviour on the primary analysis conclusions. Reference based sensitivity analysis uses Rubin’s multiple imputation variance rules. However it is unclear precisely what Rubin’s variance formula is estimating when there is a mismatch between the imputation and analysis models. We present theoretical and simulation results that show, in this context, Rubin’s rules approximately preserve the fraction of missing information across a range of sensitivity analysis assumptions. This provides a solid justification for their practical use. We also present a new Stata command “mimix” that conducts reference based multiple imputation for sensitivity analysis of clinical trials with protocol deviation. Authors’ details MRC Clinical Trials Unit at UCL, London, UK. London School of Hygiene and Tropical Medicine, London, UK.

Pattern mixture models for the analysis of repeated attempt designs.

It is not uncommon in follow-up studies to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful or not provides useful information for the purposes of assessing the missing at random (MAR) assumption and facilitating missing not at random (MNAR) modeling. This is because measurements from subjects who provide this data after multiple failed attempts may differ from those who provide the measurement after fewer attempts. This type of "continuum of resistance" to providing a measurement has hitherto been modeled in a selection model framework, where the outcome data is modeled jointly with the success or failure of the attempts given these outcomes. Here, we present a pattern mixture approach to model this type of data. We re-analyze the repeated attempt data from a trial that was previously analyzed using a selection model approach. Our pattern mixture model is more flexible and is more transparent in terms of parameter identifiability than the models that have previously been used to model repeated attempt data and allows for sensitivity analysis. We conclude that our approach to modeling this type of data provides a fully viable alternative to the more established selection model.

Bias in longitudinal data analysis with missing data using typical linear mixed-effects modelling and pattern-mixture approach: an analytical illustration.

We analytically derive the fixed-effects estimates in unconditional linear growth curve models by typical linear mixed-effects modelling (TLME) and by a pattern-mixture (PM) approach with random-slope-dependent two-missing-pattern missing not at random (MNAR) longitudinal data. Results showed that when the missingness mechanism is random-slope-dependent MNAR, TLME estimates of both the mean intercept and mean slope are biased because of incorrect weights used in the estimation. More specifically, the estimate of the mean slope is biased towards the mean slope for completers, whereas the estimate of the mean intercept is biased towards the opposite direction as compared to the estimate of the mean slope. We also discuss why the PM approach can provide unbiased fixed-effects estimates for random-coefficients-dependent MNAR data but does not work well for missing at random or outcome-dependent MNAR data. A small simulation study was conducted to illustrate the results and to compare results from TLME and PM. Results from an empirical data analysis showed that the conceptual finding can be generalized to other real conditions even when some assumptions for the analytical derivation cannot be met. Implications from the analytical and empirical results were discussed and sensitivity analysis was suggested for longitudinal data analysis with missing data.

Race-related disparities in 5-year cognitive level and change in untrained ACTIVE participants.

The current study examined a 5-year cognitive change in untrained African American and White participants from the Advanced Cognitive Training in Independent and Vital Elderly (ACTIVE) study. Five-year trajectories of memory, reasoning, visual processing speed/useful field of view, digit-symbol substitution, and vocabulary were investigated. Education, health, gender, age, and retest/practice effects were controlled for, and a missing data pattern mixture approach was used to adjust for dropout effects. After considering age, education, health, and gender, being African American uniquely explained 2% to 7% of the variance in cognitive performance. There were virtually no significant race differences in the rates of change. Race-related results in the current study are consistent with previous research suggesting that social advantage factors such as education have a stronger influence on the level of performance than the rate of change. The small remaining effects of being African American on performance levels likely reflect uncontrolled variation in factors like literacy and financial advantage.

A two‐part mixed‐effects pattern‐mixture model to handle zero‐inflation and incompleteness in a longitudinal setting

Two-part regression models are frequently used to analyze longitudinal count data with excess zeros, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual level that affect the observed process. Further, longitudinal studies often suffer from missing values: individuals dropout of the study before its completion, and thus present incomplete data records. In this paper, we propose a finite mixture of hurdle models to face the heterogeneity problem, which is handled by introducing random effects with a discrete distribution; a pattern-mixture approach is specified to deal with non-ignorable missing values. This approach helps us to consider overdispersed counts, while allowing for association between the two parts of the model, and for non-ignorable dropouts. The effectiveness of the proposal is tested through a simulation study. Finally, an application to real data on skin cancer is provided.

Growth modeling with nonignorable dropout: Alternative analyses of the STAR*D antidepressant trial.

This article uses a general latent variable framework to study a series of models for nonignorable missingness due to dropout. Nonignorable missing data modeling acknowledges that missingness may depend not only on covariates and observed outcomes at previous time points as with the standard missing at random assumption, but also on latent variables such as values that would have been observed (missing outcomes), developmental trends (growth factors), and qualitatively different types of development (latent trajectory classes). These alternative predictors of missing data can be explored in a general latent variable framework with the Mplus program. A flexible new model uses an extended pattern-mixture approach where missingness is a function of latent dropout classes in combination with growth mixture modeling. A new selection model not only allows an influence of the outcomes on missingness but allows this influence to vary across classes. Model selection is discussed. The missing data models are applied to longitudinal data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study, the largest antidepressant clinical trial in the United States to date. Despite the importance of this trial, STAR*D growth model analyses using nonignorable missing data techniques have not been explored until now. The STAR*D data are shown to feature distinct trajectory classes, including a low class corresponding to substantial improvement in depression, a minority class with a U-shaped curve corresponding to transient improvement, and a high class corresponding to no improvement. The analyses provide a new way to assess drug efficiency in the presence of dropout.

Vertical modeling: A pattern mixture approach for competing risks modeling

We study an alternative approach for estimation in the competing risks framework, called vertical modeling. It is motivated by a decomposition of the joint distribution of time and cause of failure. The two elements of this decomposition are (1) the time of failure and (2) the cause of failure condition on time of failure. Both elements of the model are based on observable quantities, namely the total hazard and the relative cause-specific hazards. The model can be implemented using the standard software. The relative cause-specific hazards are flexibly estimated using multinomial logistic regression and smoothing splines. We show estimates of cumulative incidences from vertical modeling to be more efficient statistically than those obtained from the standard nonparametric model. We illustrate our methods using data of 8966 leukemia patients from the European Group for Blood and Marrow Transplantation.

The analysis of longitudinal quality of life measures with informative drop-out: a pattern mixture approach

PurposeThe analysis of longitudinal health-related quality of life measures (HRQOL) can be seriously hampered due to informative drop-out. Random effects models assume Missing At Random and do not take into account informative drop-out. We therefore aim to correct the bias due to informative drop-out.MethodsAnalyses of data from a trial comparing standard-dose and high-dose chemotherapy for patients with breast cancer with respect to long-term impact on HRQOL will serve as illustration. The subscale Physical Function (PF) of the SF36 will be used. A pattern mixture approach is proposed to account for informative drop-out. Patterns are defined based on events related to HRQOL, such as death and relapse. The results of this pattern mixture approach are compared to the results of the commonly used random effects model.ResultsThe findings of the pattern mixture approach are well interpretable, and different courses over time in different patterns are distinguished. In terms of estimated differences between standard dose and high dose, the results of both approaches are slightly different, but have no consequences for the clinical evaluation of both doses.ConclusionUnder the assumption that drop-out is at random within the patterns, the pattern mixture approach adjusts the estimates to a certain degree. This approach accounts in a relatively simple way for informative drop-out.

College drinking behaviors: Mediational links between parenting styles, impulse control, and alcohol-related outcomes.

Mediational links between parenting styles (authoritative, authoritarian, permissive), impulsiveness (general control), drinking control (specific control), and alcohol use and abuse were tested. A pattern-mixture approach (for modeling non-ignorable missing data) with multiple-group structural equation models with 421 (206 female, 215 male) college students was used. Gender was examined as a potential moderator of parenting styles on control processes related to drinking. Specifically, the parent-child gender match was found to have implications for increased levels of impulsiveness (a significant mediator of parenting effects on drinking control). These findings suggest that a parent with a permissive parenting style who is the same gender as the respondent can directly influence control processes and indirectly influence alcohol use and abuse.

P.3.156 Pattern mixture approach to comparing outcomes - of benefit in guideline development?

Outcomes in RCT's of antipsychotic medications are often examined using last observation carried forward (LOCF) and mixed effect models (MMRM), these ignore meaning of non-completion and thus rely on questionable assumptions. We tested an approach that combines into a single statistic, the drug effect in those who complete trial and proportion of patients in each treatment group who complete trial. This approach offers a conceptually and clinically meaningful endpoint. Composite approach was compared to LOCF (ANCOVA) and MMRM in 59 industry sponsored RCT's. For within study comparisons we computed effect size (z-score) and p values for (a) rates of completion, (b) symptom change for complete cases, which were combined into composite statistic, and (c) symptom change for all cases using last observation forward (LOCF). In the 30 active comparator studies, composite approach detected larger differences in effect size than LOCF (ES=.05) and MMRM (ES=.076). In 10 of the 49 comparisons composite lead to significant differences (p≤.05) where LOCF and MMRM did not. In 3 comparisons LOCF was significant, in 2 MMRM lead to significant differences whereas composite did not. In placebo controlled trials, there was no meaningful difference in effect size between composite and LOCF and MMRM when comparing placebo to active treatment, however composite detected greater differences than other approaches when comparing between active treatments. Composite was more sensitive to effects of experimental treatment vs. active controls (but not placebo) than LOCF and MMRM thereby increasing study power while answering a more relevant question.

Statistical analysis of repeated measurements with informative censoring times.

Incomplete repeated measurement data often arise in medical studies. A problem that has recently drawn much attention in the literature in this situation is that the incompleteness or missingness is informative or related to the underlying variable of interest. In this paper we propose a non-parametric global test for treatment comparison in the presence of informative incompleteness. A semi-parametric regression model is also presented for assessing conditional treatment effects given the drop-out patterns, adopting the idea similar to that behind the pattern-mixture modelling approach and discussed in Shih and Quan. The proposed methods can be easily implemented and are conceptually simple and similar too, but can be applied to more general cases than those given in Yao et al. They are evaluated by numerical studies and applied to data from a clinical trial of adult schizophrenics.

Application of random-effects pattern-mixture models for missing data in longitudinal studies.

Random-effects regression models have become increasingly popular for analysis of longitudinal data. A key advantage of the random-effects approach is that it can be applied when subjects are not measured at the same number of timepoints. In this article we describe use of random-effects pattern-mixture models to further handle and describe the influence of missing data in longitudinal studies. For this approach, subjects are first divided into groups depending on their missing-data pattern and then variables based on these groups are used as model covariates. In this way, researchers are able to examine the effect of missing-data patterns on the outcome (or outcomes) of interest. Furthermore, overall estimates can be obtained by averaging over the missing-data patterns. A psychiatric clinical trials data set is used to illustrate the random-effects pattern-mixture approach to longitudinal data analysis with missing data. Longitudinal studies occupy an important role in psychological and psychiatric research. In these studies the same individuals are repeatedly measured on a number of important variables over a series of timepoints. As an example, a longitudinal design is often used to determine whether a particular therapeutic agent can produce changes in clinical status over the course of an illness. Another application for the longitudinal study is to assess potential indicators of a change, in the subject's clinical status; for example, the assessment of whether drug plasma level measurements indicate clinical outcome. Even in well-controlled situations, missing data invariably occur in longitudinal studies. Subjects can be