Additive Hazards Models with Latent Treatment Effectiveness Lag Time

In many clinical trials to evaluate treatment efficacy, it is believed that there may exist latent treatment effectiveness lag times after which medical procedure or chemical compound would be in full effect. In this article, semiparametric regression models are proposed and studied to estimate the treatment effect accounting for such latent lag times. The new models take advantage of the invariance property of the additive hazards model in marginalizing over random effects, so parameters in the models are easy to be estimated and interpreted, while the flexibility without specifying baseline hazard function is kept. Monte Carlo simulation studies demonstrate the appropriateness of the proposed semiparametric estimation procedure. Data collected in the actual randomized clinical trial, which evaluates the effectiveness of biodegradable carmustine polymers for treatment of recurrent brain tumors, are analyzed.

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Optimal and Robust Designs of Step-stress Accelerated Life Testing Experiments for Proportional Hazards Models

Accelerated life testing (ALT) is widely used to obtain reliability information about a product within a limited time frame. The Cox s proportional hazards (PH) model is often utilized for reliability prediction. My master thesis research focuses on designing accelerated life testing experiments for reliability estimation. We consider multiple step-stress ALT plans with censoring. The optimal stress levels and times of changing the stress levels are investigated. We discuss the optimal designs under three optimality criteria. They are D-, A- and Q-optimal designs. We note that the classical designs are optimal only if the model assumed is correct. Due to the nature of prediction made from ALT experimental data, attained under the stress levels higher than the normal condition, extrapolation is encountered. In such case, the assumed model cannot be tested. Therefore, for possible imprecision in the assumed PH model, the method of construction for robust designs is also explored.

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Presence of alternative lengthening of telomeres mechanism in patients with glioblastoma identifies a less aggressive tumor type with longer survival.

Patients with glioblastoma (GBM) have variable clinical courses, but the factors that underlie this heterogeneity are not understood. To determine whether the presence of the telomerase-independent alternative lengthening of telomeres (ALTs) mechanism is a significant prognostic factor for survival, we performed a retrospective analysis of 573 GBM patients. The presence of ALT was identified in paraffin sections using a combination of immunofluorescence for promyelocytic leukemia body and telomere fluorescence in situ hybridization. Alternative lengthening of telomere was present in 15% of the GBM patients. Patients with ALT had longer survival that was independent of age, surgery, and other treatments. Mutations in isocitrate dehydrogenase (IDH1mut) 1 frequently accompanied ALT, and in the presence of both molecular events, there was significantly longer overall survival. These data suggest that most ALT+ tumors may be less aggressive proneural GBMs, and the better prognosis may relate to the set of genetic changes associated with this tumor subtype. Despite improved overall survival of patients treated with the addition of chemotherapy to radiotherapy and surgery, ALT and chemotherapy independently provided a survival advantage, but these factors were not found to be additive. These results suggest a critical need for developing new therapies to target these specific GBM subtypes.

Gene-lifestyle interaction and type 2 diabetes: the EPIC interact case-cohort study.

BACKGROUND Understanding of the genetic basis of type 2 diabetes (T2D) has progressed rapidly, but the interactions between common genetic variants and lifestyle risk factors have not been systematically investigated in studies with adequate statistical power. Therefore, we aimed to quantify the combined effects of genetic and lifestyle factors on risk of T2D in order to inform strategies for prevention. METHODS AND FINDINGS The InterAct study includes 12,403 incident T2D cases and a representative sub-cohort of 16,154 individuals from a cohort of 340,234 European participants with 3.99 million person-years of follow-up. We studied the combined effects of an additive genetic T2D risk score and modifiable and non-modifiable risk factors using Prentice-weighted Cox regression and random effects meta-analysis methods. The effect of the genetic score was significantly greater in younger individuals (p for interaction  = 1.20×10-4). Relative genetic risk (per standard deviation [4.4 risk alleles]) was also larger in participants who were leaner, both in terms of body mass index (p for interaction  = 1.50×10-3) and waist circumference (p for interaction  = 7.49×10-9). Examination of absolute risks by strata showed the importance of obesity for T2D risk. The 10-y cumulative incidence of T2D rose from 0.25% to 0.89% across extreme quartiles of the genetic score in normal weight individuals, compared to 4.22% to 7.99% in obese individuals. We detected no significant interactions between the genetic score and sex, diabetes family history, physical activity, or dietary habits assessed by a Mediterranean diet score. CONCLUSIONS The relative effect of a T2D genetic risk score is greater in younger and leaner participants. However, this sub-group is at low absolute risk and would not be a logical target for preventive interventions. The high absolute risk associated with obesity at any level of genetic risk highlights the importance of universal rather than targeted approaches to lifestyle intervention.

Impacts of pollution and climate change on ombrotrophic Sphagnum species in the UK: analysis of uncertainties in two empirical niche models

A significant challenge in the prediction of climate change impacts on ecosystems and biodiversity is quantifying the sources of uncertainty that emerge within and between different models. Statistical species niche models have grown in popularity, yet no single best technique has been identified reflecting differing performance in different situations. Our aim was to quantify uncertainties associated with the application of 2 complimentary modelling techniques. Generalised linear mixed models (GLMM) and generalised additive mixed models (GAMM) were used to model the realised niche of ombrotrophic Sphagnum species in British peatlands. These models were then used to predict changes in Sphagnum cover between 2020 and 2050 based on projections of climate change and atmospheric deposition of nitrogen and sulphur. Over 90% of the variation in the GLMM predictions was due to niche model parameter uncertainty, dropping to 14% for the GAMM. After having covaried out other factors, average variation in predicted values of Sphagnum cover across UK peatlands was the next largest source of variation (8% for the GLMM and 86% for the GAMM). The better performance of the GAMM needs to be weighed against its tendency to overfit the training data. While our niche models are only a first approximation, we used them to undertake a preliminary evaluation of the relative importance of climate change and nitrogen and sulphur deposition and the geographic locations of the largest expected changes in Sphagnum cover. Predicted changes in cover were all small (generally <1% in an average 4 m2 unit area) but also highly uncertain. Peatlands expected to be most affected by climate change in combination with atmospheric pollution were Dartmoor, Brecon Beacons and the western Lake District.

On Causal Mediation Analysis with a Survival Outcome

Suppose that having established a marginal total effect of a point exposure on a time-to-event outcome, an investigator wishes to decompose this effect into its direct and indirect pathways, also know as natural direct and indirect effects, mediated by a variable known to occur after the exposure and prior to the outcome. This paper proposes a theory of estimation of natural direct and indirect effects in two important semiparametric models for a failure time outcome. The underlying survival model for the marginal total effect and thus for the direct and indirect effects, can either be a marginal structural Cox proportional hazards model, or a marginal structural additive hazards model. The proposed theory delivers new estimators for mediation analysis in each of these models, with appealing robustness properties. Specifically, in order to guarantee ignorability with respect to the exposure and mediator variables, the approach, which is multiply robust, allows the investigator to use several flexible working models to adjust for confounding by a large number of pre-exposure variables. Multiple robustness is appealing because it only requires a subset of working models to be correct for consistency; furthermore, the analyst need not know which subset of working models is in fact correct to report valid inferences. Finally, a novel semiparametric sensitivity analysis technique is developed for each of these models, to assess the impact on inference, of a violation of the assumption of ignorability of the mediator.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Diabetes genes and risk of prostate cancer in the Atherosclerosis Risk in Communities study

Prostate cancer (PrCa) is a leading cause of morbidity and mortality, yet the etiology remains uncertain. Meta-analyses show that PrCa risk is reduced by 16% in men with type 2 diabetes (T2D), but the mechanism is unknown. Recent genome-wide association studies and meta-analyses have found single nucleotide polymorphisms (SNPs) that consistently predict T2D risk. We evaluated associations of incident PrCa with 14 T2D SNPs in the Atherosclerosis Risk in Communities (ARIC) study. From 1987-2000, there were 397 incident PrCa cases ascertained from state or local cancer registries among 6,642 men (1,560 blacks and 5,082 whites) aged 45-64 years at baseline. Genotypes were determined by TaqMan assay. Cox proportional hazards models were used to assess the association between PrCa and increasing number of T2D risk-raising alleles for individual SNPs and for genetic risk scores (GRS) comprised of the number of T2D risk-raising alleles across SNPs. Two-way gene-gene interactions were evaluated with likelihood ratio tests. Using additive genetic models, the T2D risk-raising allele was associated with significantly reduced risk of PrCa for IGF2BP2 rs4402960 (hazard ratio [HR]=0.79; P=0.07 among blacks only), SLC2A2 rs5400 (race-adjusted HR=0.85; P=0.05) and UCP2 rs660339 (race-adjusted HR=0.84; P=0.02), but significantly increased risk of PrCa for CAPN10 rs3792267 (race-adjusted HR=1.20; P=0.05). No other SNPs were associated with PrCa using an additive genetic model. However, at least one copy of the T2D risk-raising allele for TCF7L2 rs7903146 was associated with reduced PrCa risk using a dominant genetic model (race-adjusted HR=0.79; P=0.03). These results imply that the T2D-PrCa association may be partly due to shared genetic variation, but these results should be verified since multiple tests were performed. When the combined, additive effects of these SNPs were tested using a GRS, there was nearly a 10% reduction in risk of PrCa per T2D risk-raising allele (race-adjusted HR=0.92; P=0.02). SNPs in IGF2BP2, KCNJ11 and SLC2A2 were also involved in multiple synergistic gene-gene interactions on a multiplicative scale. In conclusion, it appears that the T2D-PrCa association may be due, in part, to common genetic variation. Further knowledge of T2D gene-PrCa mechanisms may improve understanding of PrCa etiology and may inform PrCa prevention and treatment.^

The Value Of The 2005 International Society Of Urological Pathology (isup) Modified Gleason Grading System As A Predictor Of Biochemical Recurrence After Radical Prostatectomy.

To compare time and risk to biochemical recurrence (BR) after radical prostatectomy of two chronologically different groups of patients using the standard and the modified Gleason system (MGS). Cohort 1 comprised biopsies of 197 patients graded according to the standard Gleason system (SGS) in the period 1997/2004, and cohort 2, 176 biopsies graded according to the modified system in the period 2005/2011. Time to BR was analyzed with the Kaplan-Meier product-limit analysis and prediction of shorter time to recurrence using univariate and multivariate Cox proportional hazards model. Patients in cohort 2 reflected time-related changes: striking increase in clinical stage T1c, systematic use of extended biopsies, and lower percentage of total length of cancer in millimeter in all cores. The MGS used in cohort 2 showed fewer biopsies with Gleason score ≤ 6 and more biopsies of the intermediate Gleason score 7. Time to BR using the Kaplan-Meier curves showed statistical significance using the MGS in cohort 2, but not the SGS in cohort 1. Only the MGS predicted shorter time to BR on univariate analysis and on multivariate analysis was an independent predictor. The results favor that the 2005 International Society of Urological Pathology modified system is a refinement of the Gleason grading and valuable for contemporary clinical practice.

Análise bayesiana do modelo de herança monogênica no melhoramento vegetal: um exemplo com abobrinha

A common breeding strategy is to carry out basic studies to investigate the hypothesis of a single gene controlling the trait (major gene) with or without polygenes of minor effect. In this study we used Bayesian inference to fit genetic additive-dominance models of inheritance to plant breeding experiments with multiple generations. Normal densities with different means, according to the major gene genotype, were considered in a linear model in which the design matrix of the genetic effects had unknown coefficients (which were estimated in individual basis). An actual data set from an inheritance study of partenocarpy in zucchini (Cucurbita pepo L.) was used for illustration. Model fitting included posterior probabilities for all individual genotypes. Analysis agrees with results in the literature but this approach was far more efficient than previous alternatives assuming that design matrix was known for the generations. Partenocarpy in zucchini is controlled by a major gene with important additive effect and partial dominance.

Association of HDL cholesterol and triglycerides with mortality in patients with heart failure

It has been demonstrated that there is an association between serum lipoproteins and survival rate in patients with ischemic cardiomyopathy, as well as in patients with non-ischemic causes of heart failure. We tested the hypothesis of an association between serum lipoprotein levels and prognosis in a cohort of outpatients with heart failure, including Chagas' heart disease. The lipid profile of 833 outpatients with heart failure in functional classes III and IV of the New York Heart Association, with a mean age of 46.9 ± 10.6 years, 655 (78.6%) men and 178 (21.4%) women, was studied from April 1991 to June 2003. The survival rate was estimated by the Kaplan-Meyer's method and the Cox proportional hazards models. Etiology of heart failure was ischemic cardiomyopathy in 171 (21%) patients, Chagas' heart disease in 144 (17%), hypertensive cardiomyopathy in 136 (16%), and other etiologies in 83 (10%). In 299 (36%) patients, heart failure was ascribed to idiopathic dilated cardiomyopathy. Variables significantly associated with mortality were age (hazard ratio, HR = 1.02; 95%CI = 1.01-1.03; P = 0.0074), male gender (HR = 1.77; 95%CI = 1.2-2.62; P = 0.004), idiopathic dilated cardiomyopathy (HR = 1.81; 95%CI = 1.16-2.82; P = 0.0085), serum triglycerides (HR = 0.97; 95%CI = 0.96-0.98; P < 0.0001), and HDL cholesterol (HR = 0.99; 95%CI = 0.99-1.0; P = 0.0280). Therefore, higher serum HDL cholesterol and higher serum triglycerides were associated with lower mortality in this cohort of outpatients with heart failure.

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.