Assessing model fit in joint models of longitudinal and survival data with applications to cancer clinical trials

Joint models for longitudinal and survival data now have a long history of being used in clinical trials or other studies in which the goal is to assess a treatment effect while accounting for longitudinal assessments such as patient-reported outcomes or tumor response. Compared to using survival data alone, the joint modeling of survival and longitudinal data allows for estimation of direct and indirect treatment effects, thereby resulting in improved efficacy assessment. Although global fit indices such as AIC or BIC can be used to rank joint models, these measures do not provide separate assessments of each component of the joint model. In this paper, we develop a novel decomposition of AIC and BIC (i.e., AIC = AICLong + AICSurv|Long and BIC = BICLong + BICSurv|Long) that allows us to assess the fit of each component of the joint model and in particular to assess the fit of the longitudinal component of the model and the survival component separately. Based on this decomposition, we then propose ΔAICSurv and ΔBICSurv to determine the importance and contribution of the longitudinal data to the model fit of the survival data. Moreover, this decomposition, along with ΔAICSurv and ΔBICSurv, is also quite useful in comparing, for example, trajectory-based joint models and shared parameter joint models and deciding which type of model best fits the survival data. We examine a detailed case study in mesothelioma to apply our proposed methodology along with an extensive set of simulation studies.

Bayesian design of superiority clinical trials for recurrent events data with applications to bleeding and transfusion events in myelodyplastic syndrome

In many biomedical studies, patients may experience the same type of recurrent event repeatedly over time, such as bleeding, multiple infections and disease. In this article, we propose a Bayesian design to a pivotal clinical trial in which lower risk myelodysplastic syndromes (MDS) patients are treated with MDS disease modifying therapies. One of the key study objectives is to demonstrate the investigational product (treatment) effect on reduction of platelet transfusion and bleeding events while receiving MDS therapies. In this context, we propose a new Bayesian approach for the design of superiority clinical trials using recurrent events frailty regression models. Historical recurrent events data from an already completed phase 2 trial are incorporated into the Bayesian design via the partial borrowing power prior of Ibrahim et al. (2012, Biometrics 68, 578-586). An efficient Gibbs sampling algorithm, a predictive data generation algorithm, and a simulation-based algorithm are developed for sampling from the fitting posterior distribution, generating the predictive recurrent events data, and computing various design quantities such as the type I error rate and power, respectively. An extensive simulation study is conducted to compare the proposed method to the existing frequentist methods and to investigate various operating characteristics of the proposed design.

A note on the relationships between multiple imputation, maximum likelihood and fully Bayesian methods for missing responses in linear regression models

Multiple Imputation, Maximum Likelihood and Fully Bayesian methods are the three most commonly used model-based approaches in missing data problems. Although it is easy to show that when the responses are missing at random (MAR), the complete case analysis is unbiased and efficient, the aforementioned methods are still commonly used in practice for this setting. To examine the performance of and relationships between these three methods in this setting, we derive and investigate small sample and asymptotic expressions of the estimates and standard errors, and fully examine how these estimates are related for the three approaches in the linear regression model when the responses are MAR. We show that when the responses are MAR in the linear model, the estimates of the regression coefficients using these three methods are asymptotically equivalent to the complete case estimates under general conditions. One simulation and a real data set from a liver cancer clinical trial are given to compare the properties of these methods when the responses are MAR.

Mechanisms of chromosomal instability in melanoma

A systems biology approach was applied to investigate the mechanisms of chromosomal instability in melanoma cell lines. Chromosomal instability was quantified using array comparative genomic hybridization to identify somatic copy number alterations (deletions and duplications). Primary human melanocytes displayed an average of 8.5 alterations per cell primarily representing known polymorphisms. Melanoma cell lines displayed 25 to 131 alterations per cell, with an average of 68, indicative of chromosomal instability. Copy number alterations included approximately equal numbers of deletions and duplications with greater numbers of hemizygous (-1,+1) alterations than homozygous (-2,+2). Melanoma oncogenes, such as BRAF and MITF, and tumor suppressor genes, such as CDKN2A/B and PTEN, were included in these alterations. Duplications and deletions were functional as there were significant correlations between DNA copy number and mRNA expression for these genes. Spectral karyotype analysis of three lines confirmed extensive chromosomal instability with polyploidy, aneuploidy, deletions, duplications, and chromosome rearrangements. Bioinformatic analysis identified a signature of gene expression that was correlated with chromosomal instability but this signature provided no clues to the mechanisms of instability. The signature failed to generate a significant (P = 0.105) prediction of melanoma progression in a separate dataset. Chromosomal instability was not correlated with elements of DNA damage response (DDR) such as radiosensitivity, nucleotide excision repair, expression of the DDR biomarkers γH2AX and P-CHEK2, nor G1 or G2 checkpoint function. Chromosomal instability in melanoma cell lines appears to influence gene function but it is not simply explained by alterations in the system of DDR.

Bayesian Transformation Models for Multivariate Survival Data

In this paper we propose a general class of gamma frailty transformation models for multivariate survival data. The transformation class includes the commonly used proportional hazards and proportional odds models. The proposed class also includes a family of cure rate models. Under an improper prior for the parameters, we establish propriety of the posterior distribution. A novel Gibbs sampling algorithm is developed for sampling from the observed data posterior distribution. A simulation study is conducted to examine the properties of the proposed methodology. An application to a data set from a cord blood transplantation study is also reported.

Post-diagnosis physical activity and survival after breast cancer diagnosis: the Long Island Breast Cancer Study

Physical activity (PA) is associated with physiological responses thought to beneficially affect survival after breast cancer diagnosis, yet few studies have considered the entire survivorship experience. Effects of post-diagnosis activity on survival were examined in a cohort of 1,423 women diagnosed with in situ or invasive breast cancer in 1996-1997. Subjects were interviewed soon after diagnosis and again after approximately 5 years to assess breast cancer-related factors, including recreational PA before and after diagnosis. Date and cause of death through 2009 were determined from the National Death Index. Adjusted estimates were obtained using proportional hazards regression and a selection model to account for missing data. Survival was improved among women who were highly active after diagnosis (>9.0 MET h/week) compared to inactive women (0 MET h/week) for all-cause [hazard ratio (HR) (95 % credible interval): 0.33 (0.22, 0.48)] and breast cancer-specific mortality [HR: 0.27 (0.15, 0.46)]. The association of PA with overall mortality appeared stronger in the first 2 years after diagnosis [HR: 0.14 (0.03, 0.44)] compared to 2+ years since diagnosis [HR: 0.37 (0.25, 0.55)]. These findings show that post-diagnosis PA is associated with improved survival among women with breast cancer.

Bayesian Sensitivity Analysis of Statistical Models with Missing Data

Methods for handling missing data depend strongly on the mechanism that generated the missing values, such as missing completely at random (MCAR) or missing at random (MAR), as well as other distributional and modeling assumptions at various stages. It is well known that the resulting estimates and tests may be sensitive to these assumptions as well as to outlying observations. In this paper, we introduce various perturbations to modeling assumptions and individual observations, and then develop a formal sensitivity analysis to assess these perturbations in the Bayesian analysis of statistical models with missing data. We develop a geometric framework, called the Bayesian perturbation manifold, to characterize the intrinsic structure of these perturbations. We propose several intrinsic influence measures to perform sensitivity analysis and quantify the effect of various perturbations to statistical models. We use the proposed sensitivity analysis procedure to systematically investigate the tenability of the non-ignorable missing at random (NMAR) assumption. Simulation studies are conducted to evaluate our methods, and a dataset is analyzed to illustrate the use of our diagnostic measures.

Sample size determination in shared frailty models for multivariate time-to-event data

The frailty model is increasingly popular for analyzing multivariate time-to-event data. The most common model is the shared frailty model. Although study design consideration is as important as analysis strategies, sample size determination methodology in studies with multivariate time-to-event data is greatly lacking in the literature. In this article, we develop a sample size determination method for the shared frailty model to investigate the treatment effect on multivariate event times. We analyzed the data using both a parametric model and a piecewise model with unknown baseline hazard, and compare the empirical power with the calculated power. Last, we discuss the formula for testing the treatment effect on recurrent events.

Effect of cytotoxic chemotherapy on markers of molecular age in patients with breast cancer

BACKGROUND

Senescent cells, which express p16 (INK4a) , accumulate with aging and contribute to age-related pathology. To understand whether cytotoxic agents promote molecular aging, we measured expression of p16 (INK4a) and other senescence markers in breast cancer patients treated with adjuvant chemotherapy.

METHODS

Blood and clinical information were prospectively obtained from 33 women with stage I to III breast cancer at four time points: before anthracycline-based chemotherapy, immediately after anthracycline-based chemotherapy, 3 months after anthracycline-based chemotherapy, and 12 months after anthracycline-based chemotherapy. Expression of senescence markers p16 (INK4a) and ARF mRNA was determined using TaqMan quantitative reverse-transcription polymerase chain reaction in CD3(+) T lymphocytes, telomere length was determined by Southern analysis, and senescence-associated cytokines were determined by enzyme-linked immunosorbent assay. Findings were independently assessed in a cross-sectional cohort of 176 breast cancer survivors enrolled a median of 3.4 years after treatment; 39% previously received chemotherapy. All statistical tests were two-sided.

RESULTS

In prospectively analyzed patients, expression of p16 (INK4a) and ARF increased immediately after chemotherapy and remained elevated 12 months after treatment. Median increase in log2 p16 (INK4a) was 0.81 (interquartile range = 0.28-1.62; Wilcoxon signed-rank P < .001), or a 75% absolute increase in expression, equivalent to the increase observed over 14.7 years of chronological aging. ARF expression was comparably increased (P < .001). Increased expression of p16 (INK4a) and ARF was associated with dose-dense therapy and hematological toxicity. Expression of two senescence-associated cytokines (VEGFA and MCP1) was durably increased by adjuvant chemotherapy. Telomere length was not affected by chemotherapy. In a cross-sectional cohort, prior chemotherapy exposure was independently associated with a log2-increase in p16 (INK4a) expression of 0.57 (repeated measures model, P < .001), comparable with 10.4 years of chronological aging.

CONCLUSIONS

Adjuvant chemotherapy for breast cancer is gerontogenic, inducing cellular senescence in vivo, thereby accelerating molecular aging of hematopoietic tissues.

Some Statistical Strategies for DAE-seq Data Analysis: Variable Selection and Modeling Dependencies among Observations

In DAE (DNA After Enrichment)-seq experiments, genomic regions related with certain biological processes are enriched/isolated by an assay and are then sequenced on a high-throughput sequencing platform to determine their genomic positions. Statistical analysis of DAE-seq data aims to detect genomic regions with significant aggregations of isolated DNA fragments ("enriched regions") versus all the other regions ("background"). However, many confounding factors may influence DAE-seq signals. In addition, the signals in adjacent genomic regions may exhibit strong correlations, which invalidate the independence assumption employed by many existing methods. To mitigate these issues, we develop a novel Autoregressive Hidden Markov Model (AR-HMM) to account for covariates effects and violations of the independence assumption. We demonstrate that our AR-HMM leads to improved performance in identifying enriched regions in both simulated and real datasets, especially in those in epigenetic datasets with broader regions of DAE-seq signal enrichment. We also introduce a variable selection procedure in the context of the HMM/AR-HMM where the observations are not independent and the mean value of each state-specific emission distribution is modeled by some covariates. We study the theoretical properties of this variable selection procedure and demonstrate its efficacy in simulated and real DAE-seq data. In summary, we develop several practical approaches for DAE-seq data analysis that are also applicable to more general problems in statistics.

Patients' understanding of how genotype variation affects benefits of tamoxifen therapy for breast cancer

BACKGROUND

CYP2D6 is a critical enzyme in the metabolism of tamoxifen and potentially a key determinant in breast cancer outcomes. Our study examined patients' beliefs about how the CYP2D6 genotype would affect their prognoses.

METHODS

Women enrolled in a pharmacogenomic clinical trial and on tamoxifen for prevention or treatment of breast cancer underwent CYP2D6 genotyping (EM = extensive, IM = intermediate, PM = poor metabolizing alleles). The informed consent said that the purpose of the trial was to examine effects of dose adjustment based on genotype, but that clinical benefits were uncertain. Our embedded sub-study surveyed 320 patients prior to receiving their genotypes. We experimentally manipulated 6 vignettes to describe hypothetical tamoxifen treatment (no or yes) and hypothetical genotype (EM, IM or PM). For each vignette, women gave their perceived recurrence risk (RR; 0-100%).

RESULTS

Women believed that genotype would not affect their RR if they did not take tamoxifen (p = 0.06). However, women believed that if prescribed tamoxifen, genotype would affect their RR (22% if EM, 30% if IM and 40% if PM, p < 0.001).

CONCLUSION

Women believed that extensive tamoxifen metabolizers had better prognoses, despite study materials stating uncertainty about any benefit. The rapidly changing nature of genomic science calls for caution when communicating clinical utility.

Bayesian Generalized Low Rank Regression Models for Neuroimaging Phenotypes and Genetic Markers

We propose a Bayesian generalized low rank regression model (GLRR) for the analysis of both high-dimensional responses and covariates. This development is motivated by performing searches for associations between genetic variants and brain imaging phenotypes. GLRR integrates a low rank matrix to approximate the high-dimensional regression coefficient matrix of GLRR and a dynamic factor model to model the high-dimensional covariance matrix of brain imaging phenotypes. Local hypothesis testing is developed to identify significant covariates on high-dimensional responses. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. A simulation study is performed to evaluate the finite sample performance of GLRR and its comparison with several competing approaches. We apply GLRR to investigate the impact of 1,071 SNPs on top 40 genes reported by AlzGene database on the volumes of 93 regions of interest (ROI) obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI).

Flexible stopping boundaries when changing primary endpoints after unblinded interim analyses

It has been widely recognized that interim analyses of accumulating data in a clinical trial can inflate type I error. Different methods, from group sequential boundaries to flexible alpha spending functions, have been developed to control the overall type I error at prespecified level. These methods mainly apply to testing the same endpoint in multiple interim analyses. In this article, we consider a group sequential design with preplanned endpoint switching after unblinded interim analyses. We extend the alpha spending function method to group sequential stopping boundaries when the parameters can be different between interim, or between interim and final analyses.

Bayesian gamma frailty models for survival data with semi-competing risks and treatment switching

Motivated from a colorectal cancer study, we propose a class of frailty semi-competing risks survival models to account for the dependence between disease progression time, survival time, and treatment switching. Properties of the proposed models are examined and an efficient Gibbs sampling algorithm using the collapsed Gibbs technique is developed. A Bayesian procedure for assessing the treatment effect is also proposed. The deviance information criterion (DIC) with an appropriate deviance function and Logarithm of the pseudomarginal likelihood (LPML) are constructed for model comparison. A simulation study is conducted to examine the empirical performance of DIC and LPML and as well as the posterior estimates. The proposed method is further applied to analyze data from a colorectal cancer study.

Bayesian sequential meta-analysis design in evaluating cardiovascular risk in a new antidiabetic drug development program

Recently, the Center for Drug Evaluation and Research at the Food and Drug Administration released a guidance that makes recommendations about how to demonstrate that a new antidiabetic therapy to treat type 2 diabetes is not associated with an unacceptable increase in cardiovascular risk. One of the recommendations from the guidance is that phases II and III trials should be appropriately designed and conducted so that a meta-analysis can be performed. In addition, the guidance implies that a sequential meta-analysis strategy could be adopted. That is, the initial meta-analysis could aim at demonstrating the upper bound of a 95% confidence interval (CI) for the estimated hazard ratio to be < 1.8 for the purpose of enabling a new drug application or a biologics license application. Subsequently after the marketing authorization, a final meta-analysis would need to show the upper bound to be < 1.3. In this context, we develop a new Bayesian sequential meta-analysis approach using survival regression models to assess whether the size of a clinical development program is adequate to evaluate a particular safety endpoint. We propose a Bayesian sample size determination methodology for sequential meta-analysis clinical trial design with a focus on controlling the familywise type I error rate and power. We use the partial borrowing power prior to incorporate the historical survival meta-data into the Bayesian design. We examine various properties of the proposed methodology, and simulation-based computational algorithms are developed to generate predictive data at various interim analyses, sample from the posterior distributions, and compute various quantities such as the power and the type I error in the Bayesian sequential meta-analysis trial design. We apply the proposed methodology to the design of a hypothetical antidiabetic drug development program for evaluating cardiovascular risk.

Development of DNA damage response signaling biomarkers using automated, quantitative image analysis

The DNA damage response (DDR) coordinates DNA repair with cell cycle checkpoints to ameliorate or mitigate the pathological effects of DNA damage. Automated quantitative analysis (AQUA) and Tissue Studio are commercial technologies that use digitized immunofluorescence microscopy images to quantify antigen expression in defined tissue compartments. Because DDR is commonly activated in cancer and may reflect genetic instability within the lesion, a method to quantify DDR in cancer offers potential diagnostic and/or prognostic value. In this study, both AQUA and Tissue Studio algorithms were used to quantify the DDR in radiation-damaged skin fibroblasts, melanoma cell lines, moles, and primary and metastatic melanomas. Digital image analysis results for three markers of DDR (γH2AX, P-ATM, P-Chk2) correlated with immunoblot data for irradiated fibroblasts, whereas only γH2AX and P-Chk2 correlated with immunoblot data in melanoma cell lines. Melanoma cell lines displayed substantial variation in γH2AX and P-Chk2 expression, and P-Chk2 expression was significantly correlated with radioresistance. Moles, primary melanomas, and melanoma metastases in brain, lung and liver displayed substantial variation in γH2AX expression, similar to that observed in melanoma cell lines. Automated digital analysis of immunofluorescent images stained for DDR biomarkers may be useful for predicting tumor response to radiation and chemotherapy.

Differential expression analysis with global network adjustment

Background

Large-scale chromosomal deletions or other non-specific perturbations of the transcriptome can alter the expression of hundreds or thousands of genes, and it is of biological interest to understand which genes are most profoundly affected. We present a method for predicting a gene’s expression as a function of other genes thereby accounting for the effect of transcriptional regulation that confounds the identification of genes differentially expressed relative to a regulatory network. The challenge in constructing such models is that the number of possible regulator transcripts within a global network is on the order of thousands, and the number of biological samples is typically on the order of 10. Nevertheless, there are large gene expression databases that can be used to construct networks that could be helpful in modeling transcriptional regulation in smaller experiments.

Results

We demonstrate a type of penalized regression model that can be estimated from large gene expression databases, and then applied to smaller experiments. The ridge parameter is selected by minimizing the cross-validation error of the predictions in the independent out-sample. This tends to increase the model stability and leads to a much greater degree of parameter shrinkage, but the resulting biased estimation is mitigated by a second round of regression. Nevertheless, the proposed computationally efficient “over-shrinkage” method outperforms previously used LASSO-based techniques. In two independent datasets, we find that the median proportion of explained variability in expression is approximately 25%, and this results in a substantial increase in the signal-to-noise ratio allowing more powerful inferences on differential gene expression leading to biologically intuitive findings. We also show that a large proportion of gene dependencies are conditional on the biological state, which would be impossible with standard differential expression methods.

Conclusions

By adjusting for the effects of the global network on individual genes, both the sensitivity and reliability of differential expression measures are greatly improved.

Cyclobutane Pyrimidine Dimer Density as a Predictive Biomarker of the Biological Effects of Ultraviolet Radiation in Normal Human Fibroblast

This study compared biological responses of normal human fibroblasts (NHF1) to three sources of ultraviolet radiation (UVR), emitting UVC wavelengths, UVB wavelengths, or a combination of UVA and UVB (solar simulator; emission spectrum, 94.3% UVA and 5.7% UVB). The endpoints measured were cytotoxicity, intra-S checkpoint activation, inhibition of DNA replication and mutagenicity. Results show that the magnitude of each response to the indicated radiation sources was best predicted by the density of DNA cyclobutane pyrimidine dimers (CPD). The density of 6-4 pyrimidine-pyrimidone photoproducts was highest in DNA from UVC-irradiated cells (14% of CPD) as compared to those exposed to UVB (11%) or UVA-UVB (7%). The solar simulator source, under the experimental conditions described here, did not induce the formation of 8-oxo-7,8-dihydroguanine in NHF1 above background levels. Taken together, these results suggest that CPD play a dominant role in DNA damage responses and highlight the importance of using endogenous biomarkers to compare and report biological effects induced by different sources of UVR.

Bayesian spatial transformation models with applications in neuroimaging data

The aim of this article is to develop a class of spatial transformation models (STM) to spatially model the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) and a set of covariates. The proposed STM include a varying Box-Cox transformation model for dealing with the issue of non-Gaussian distributed imaging data and a Gaussian Markov random field model for incorporating spatial smoothness of the imaging data. Posterior computation proceeds via an efficient Markov chain Monte Carlo algorithm. Simulations and real data analysis demonstrate that the STM significantly outperforms the voxel-wise linear model with Gaussian noise in recovering meaningful geometric patterns. Our STM is able to reveal important brain regions with morphological changes in children with attention deficit hyperactivity disorder.

Is activation of the intra-S checkpoint in human fibroblasts an important factor in protection against UV-induced mutagenesis?

The ATR/CHK1-dependent intra-S checkpoint inhibits replicon initiation and replication fork progression in response to DNA damage caused by UV (UV) radiation. It has been proposed that this signaling cascade protects against UV-induced mutations by reducing the probability that damaged DNA will be replicated before it can be repaired. Normal human fibroblasts (NHF) were depleted of ATR or CHK1, or treated with the CHK1 kinase inhibitor TCS2312, and the UV-induced mutation frequency at the HPRT locus was measured. Despite clear evidence of S-phase checkpoint abrogation, neither ATR/CHK1 depletion nor CHK1 inhibition caused an increase in the UV-induced HPRT mutation frequency. These results question the premise that the UV-induced intra-S checkpoint plays a prominent role in protecting against UV-induced mutagenesis.

Mapping the genetic variation of regional brain volumes as explained by all common SNPs from the ADNI study

Typically twin studies are used to investigate the aggregate effects of genetic and environmental influences on brain phenotypic measures. Although some phenotypic measures are highly heritable in twin studies, SNPs (single nucleotide polymorphisms) identified by genome-wide association studies (GWAS) account for only a small fraction of the heritability of these measures. We mapped the genetic variation (the proportion of phenotypic variance explained by variation among SNPs) of volumes of pre-defined regions across the whole brain, as explained by 512,905 SNPs genotyped on 747 adult participants from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We found that 85% of the variance of intracranial volume (ICV) (p = 0.04) was explained by considering all SNPs simultaneously, and after adjusting for ICV, total grey matter (GM) and white matter (WM) volumes had genetic variation estimates near zero (p = 0.5). We found varying estimates of genetic variation across 93 non-overlapping regions, with asymmetry in estimates between the left and right cerebral hemispheres. Several regions reported in previous studies to be related to Alzheimer's disease progression were estimated to have a large proportion of volumetric variance explained by the SNPs.

Use of historical control data for assessing treatment effects in clinical trials

Clinical trials rarely, if ever, occur in a vacuum. Generally, large amounts of clinical data are available prior to the start of a study, particularly on the current study's control arm. There is obvious appeal in using (i.e., 'borrowing') this information. With historical data providing information on the control arm, more trial resources can be devoted to the novel treatment while retaining accurate estimates of the current control arm parameters. This can result in more accurate point estimates, increased power, and reduced type I error in clinical trials, provided the historical information is sufficiently similar to the current control data. If this assumption of similarity is not satisfied, however, one can acquire increased mean square error of point estimates due to bias and either reduced power or increased type I error depending on the direction of the bias. In this manuscript, we review several methods for historical borrowing, illustrating how key parameters in each method affect borrowing behavior, and then, we compare these methods on the basis of mean square error, power and type I error. We emphasize two main themes. First, we discuss the idea of 'dynamic' (versus 'static') borrowing. Second, we emphasize the decision process involved in determining whether or not to include historical borrowing in terms of the perceived likelihood that the current control arm is sufficiently similar to the historical data. Our goal is to provide a clear review of the key issues involved in historical borrowing and provide a comparison of several methods useful for practitioners.

Change-point models to estimate the limit of detection

In many biological and environmental studies, measured data is subject to a limit of detection. The limit of detection is generally defined as the lowest concentration of analyte that can be differentiated from a blank sample with some certainty. Data falling below the limit of detection is left censored, falling below a level that is easily quantified by a measuring device. A great deal of interest lies in estimating the limit of detection for a particular measurement device. In this paper, we propose a change-point model to estimate the limit of detection by using data from an experiment with known analyte concentrations. Estimation of the limit of detection proceeds by a two-stage maximum likelihood method. Extensions are considered that allow for censored measurements and data from multiple experiments. A simulation study is conducted demonstrating that in some settings the change-point model provides less biased estimates of the limit of detection than conventional methods. The proposed method is then applied to data from an HIV pilot study.

Bayesian modeling and inference for clinical trials with partial retrieved data following dropout

In randomized clinical trials, it is common that patients may stop taking their assigned treatments and then switch to a standard treatment (standard of care available to the patient) but not the treatments under investigation. Although the availability of limited retrieved data on patients who switch to standard treatment, called off-protocol data, could be highly valuable in assessing the associated treatment effect with the experimental therapy, it leads to a complex data structure requiring the development of models that link the information of per-protocol data with the off-protocol data. In this paper, we develop a novel Bayesian method to jointly model longitudinal treatment measurements under various dropout scenarios. Specifically, we propose a multivariate normal mixed-effects model for repeated measurements from the assigned treatments and the standard treatment, a multivariate logistic regression model for those stopping the assigned treatments, logistic regression models for those starting a standard treatment off protocol, and a conditional multivariate logistic regression model for completely withdrawing from the study. We assume that withdrawing from the study is non-ignorable, but intermittent missingness is assumed to be at random. We examine various properties of the proposed model. We develop an efficient Markov chain Monte Carlo sampling algorithm. We analyze in detail via the proposed method a real dataset from a clinical trial.