A Bayesian quantile joint modeling of multivariate longitudinal and time-to-event data.

Linear mixed models are traditionally used for jointly modeling (multivariate) longitudinal outcomes and event-time(s). However, when the outcomes are non-Gaussian a quantile regression model is more appropriate. In addition, in the presence of some time-varying covariates, it might be of interest to see how the effects of different covariates vary from one quantile level (of outcomes) to the other, and consequently how the event-time changes across different quantiles. For such analyses linear quantile mixed models can be used, and an efficient computational algorithm can be developed. We analyze a dataset from the Acute Lymphocytic Leukemia (ALL) maintenance study conducted by Tata Medical Center, Kolkata. In this study, the patients suffering from ALL were treated with two standard drugs (6MP and MTx) for the first two years, and three biomarkers (e.g. lymphocyte count, neutrophil count and platelet count) were longitudinally measured. After treatment the patients were followed nearly for the next three years, and the relapse-time (if any) for each patient was recorded. For this dataset we develop a Bayesian quantile joint model for the three longitudinal biomarkers and time-to-relapse. We consider an Asymmetric Laplace Distribution (ALD) for each outcome, and exploit the mixture representation of the ALD for developing a Gibbs sampler algorithm to estimate the regression coefficients. Our proposed model allows different quantile levels for different biomarkers, but still simultaneously estimates the regression coefficients corresponding to a particular quantile combination. We infer that a higher lymphocyte count accelerates the chance of a relapse while a higher neutrophil count and a higher platelet count (jointly) reduce it. Also, we infer that across (almost) all quantiles 6MP reduces the lymphocyte count, while MTx increases the neutrophil count. Simulation studies are performed to assess the effectiveness of the proposed approach.

A Bayesian joint model for multivariate longitudinal and time-to-event data with application to ALL maintenance studies.

The most common type of cancer diagnosed among children is the Acute Lymphocytic Leukemia (ALL). A study was conducted by Tata Translational Cancer Research Center (TTCRC) Kolkata, in which 236 children (diagnosed as ALL patients) were treated for the first two years (approximately) with two standard drugs (6MP and MTx) and were then followed nearly for the next 3 years. The goal is to identify the longitudinal biomarkers that are associated with time-to-relapse, and also to assess the effectiveness of the drugs. We develop a Bayesian joint model in which a linear mixed model is used to jointly model three biomarkers (i.e. white blood cell count, neutrophil count, and platelet count) and a semi-parametric proportional hazards model is used to model the time-to-relapse. Our proposed joint model can assess the effects of different covariates on the progression of the biomarkers, and the effects of the biomarkers (and the covariates) on time-to-relapse. In addition, the proposed joint model can impute the missing longitudinal biomarkers efficiently. Our analysis shows that the white blood cell (WBC) count is not associated with time-to-relapse, but the neutrophil count and the platelet count are significantly associated with it. We also infer that a lower dose of 6MP and a higher dose of MTx jointly result in a lower relapse probability in the follow-up period. Interestingly, we find that relapse probability is the lowest for the patients classified into the "high-risk" group at presentation. The effectiveness of the proposed joint model is assessed through the extensive simulation studies.

A Bayesian joint model for multivariate longitudinal and time-to-event data with application to ALL maintenance studies.

The most common type of cancer diagnosed among children is the acute lymphocytic leukemia (ALL). A study was conducted by Tata Translational Cancer Research Center (TTCRC) Kolkata, in which 236 children (diagnosed as ALL patients) were treated for the first two years (approximately) with two standard drugs (6MP and MTx) and were then followed nearly for the next three years. The goal is to identify the longitudinal biomarkers that are associated with time-to-relapse, and also to assess the effectiveness of the drugs. We develop a Bayesian joint model in which a linear mixed model is used to jointly model three biomarkers (i.e. white blood cell count, neutrophil count, and platelet count) and a semi-parametric proportional hazards model is used to model the time-to-relapse. Our proposed joint model can assess the effects of different covariates on the progression of the biomarkers, and the effects of the biomarkers (and the covariates) on time-to-relapse. In addition, the proposed joint model can impute the missing longitudinal biomarkers efficiently. Our analysis shows that the white blood cell (WBC) count is not associated with time-to-relapse, but the neutrophil count and the platelet count are significantly associated with it. We also infer that a lower dose of 6MP and a higher dose of MTx jointly result in a lower relapse probability in the follow-up period. Interestingly, we find that relapse probability is the lowest for the patients classified into the "high-risk" group at presentation. The effectiveness of the proposed joint model is assessed through the extensive simulation studies.

Activity and toxicity of intramuscular 1000 iu/m2 polyethylene glycol-E. coli L-asparaginase in the UKALL 2003 and UKALL 2011 clinical trials.

In successive UK clinical trials (UKALL 2003, UKALL 2011) for paediatric acute lymphoblastic leukaemia (ALL), polyethylene glycol-conjugated E. coli L-asparaginase (PEG-EcASNase) 1000 iu/m2 was administered intramuscularly with risk-stratified treatment. In induction, patients received two PEG-EcASNase doses, 14 days apart. Post-induction, non-high-risk patients (Regimens A, B) received 1-2 doses in delayed intensification (DI) while high-risk Regimen C patients received 6-10 PEG-EcASNase doses, including two in DI. Trial substudies monitored asparaginase (ASNase) activity, ASNase-related toxicity and ASNase-associated antibodies (total, 1112 patients). Median (interquartile range) trough plasma ASNase activity (14 ± 2 days post dose) following first and second induction doses and first DI dose was respectively 217 iu/l (144-307 iu/l), 265 iu/l (165-401 iu/l) and 292 iu/l (194-386 iu/l); 15% (138/910) samples showed subthreshold ASNase activity (<100 iu/l) at any trough time point. Older age was associated with lower (regression coefficient -9.5; p < 0.0001) and DI time point with higher ASNase activity (regression coefficient 29.9; p < 0.0001). Clinical hypersensitivity was observed in 3.8% (UKALL 2003) and 6% (UKALL 2011) of patients, and in 90% or more in Regimen C. A 7% (10/149) silent inactivation rate was observed in UKALL 2003. PEG-EcASNase schedule in UKALL paediatric trials is associated with low toxicity but wide interpatient variability. Therapeutic drug monitoring potentially permits optimisation through individualised asparaginase dosing.

Statistical models for genetic mapping in polyploids: challenges and opportunities.

Statistical methods for genetic mapping have well been developed for diploid species but are lagging in the more complex polyploids. The genetic mapping of polyploids, where genome number is higher than two, is complicated by uncertainty about the genotype-phenotype correspondence, inconsistent meiotic mechanisms, heterozygous genome structures, and increased allelic (action) and nonallelic (interaction) combinations. According to their meiotic configurations, polyploids can be classified as bivalent polyploids, in which only two chromosomes pair during meiosis at a time, and multivalent polyploids, where multiple chromosomes pair simultaneously. For some polyploids, these two types of pairing occur at the same time, leading to a mixed category. This chapter reviews several challenges due to the complexities of linkage analysis in polyploids and describes statistical models and algorithms that have been developed for linkage mapping based on their distinct meiotic characteristics. We discuss several issues that should be addressed to better understand the genome structure and organization of polyploids and the genetic architecture of complex traits for this unique group of plants.

A statistical model for the identification of genes governing the incidence of cancer with age.

The cancer incidence increases with age. This epidemiological pattern of cancer incidence can be attributed to molecular and cellular processes of individual subjects. Also, the incidence of cancer with ages can be controlled by genes. Here we present a dynamic statistical model for explaining the epidemiological pattern of cancer incidence based on individual genes that regulate cancer formation and progression. We incorporate the mathematical equations of age-specific cancer incidence into a framework for functional mapping aimed at identifying quantitative trait loci (QTLs) for dynamic changes of a complex trait. The mathematical parameters that specify differences in the curve of cancer incidence among QTL genotypes are estimated within the context of maximum likelihood. The model provides testable quantitative hypotheses about the initiation and duration of genetic expression for QTLs involved in cancer progression. Computer simulation was used to examine the statistical behavior of the model. The model can be used as a tool for explaining the epidemiological pattern of cancer incidence.