Mixture model of the Exponential, Gamma and Weibull distributions to analyse heterogeneous survival data

Aims: In this study a survival mixture model of three components is considered to analyse survival data of heterogeneous nature.The survival mixture model is of the Exponential, Gamma and Weibull distributions.Methodology: The proposed model was investigated and the Maximum Likelihood (ML) estimators of the parameters of the model were evaluated by the application of the Expectation Maximization Algorithm (EM).Graphs, log likelihood (LL) and the Akaike Information Criterion (AIC) were used to compare the proposed model with the pure classical parametric survival models corresponding to each component using real survival data.The model was compared with the survival mixture models corresponding to each component.Results: The graphs, LL and AIC values showed that the proposed model fits the real data better than the pure classical survival models corresponding to each component.Also the proposed model fits the real data better than the survival mixture models corresponding to each component. Conclusion: The proposed model showed that survival mixture models are flexible and maintain the features of the pure classical survival model and are better option for modelling heterogeneous survival data

Random Effect Models in the Statistical Analysis of Human Fecundability Data: Application to artificial insemination with sperm from donor.

The main aim of this dissertation is to explore methodological approaches to correlated binary data and to assess their suitability for the analysis of data on human fertility. The dataset concerns a study of Artificial Insemination by Donor (AID). AID represents an unusual research opportunity to study both male and female fecundability simultaneously. In each attempt to conceive, artificial insemination is carried out in consecutive ovulatory cycles until conception or change of treatment. The probability of conception may differ between women, so that the data are discrete time survival data with censoring and between-subject heterogeneity. There is also potential heterogeneity between donors. Non-systematic allocation of the donor to recipient ensures that the same woman receives semen from several donors, This added heterogeneity as well as other cycle dependent covariates have to be taken into account. The analysis must also take account of covariates, most of them time-varying. Our dataset have a crossed hierarchical structure due to the presence of both, female and male factors. The rather complicated "design" calls for unit specific regression models. These models are presented as well as their lack of tractability except in some rather specific cases. The motivation for choosing Gaussian random effects in unit specific regression models is discussed. We demonstrate the use of an approximate inference method (Penalized Quasi Likelihood). This method is shown to be a useful and practical way of carrying out preliminary data analysis. Finally a Bayesian procedure (Gibbs sampling) provides validation and more accurate results despite the intensive computation it needs. The main substantive finding of the analysis is the unexpectedly pronounced heterogeneity of donor fecundability, even after inclusion of conventional measures of sperm quality into the model. These measures were shown to be predictive at the donor level but not at the level of individual donation

The Temporal Organization of Operant Behavior: A Response Bout Analysis

abstract: Many behaviors are organized into bouts – brief periods of responding punctuated by pauses. This dissertation examines the operant bouts of the lever pressing rat. Chapter 1 provides a brief history of operant response bout analyses. Chapters 2, 3, 5, and 6 develop new probabilistic models to identify changes in response bout parameters. The parameters of those models are demonstrated to be uniquely sensitive to different experimental manipulations, such as food deprivation (Chapters 2 and 4), response requirements (Chapters 2, 4, and 5), and reinforcer availability (Chapters 2 and 3). Chapter 6 reveals the response bout parameters that underlie the operant hyperactivity of a common rodent model of attention deficit hyperactivity disorder (ADHD), the spontaneously hypertensive rat (SHR). Chapter 6 then ameliorates the SHR’s operant hyperactivity using training procedures developed from findings in Chapters 2 and 4. Collectively, this dissertation provides new tools for the assessment of response bouts and demonstrates their utility for discerning differences between experimental preparations and animal strains that may be otherwise indistinguishable with more primitive methods.Dissertation/ThesisDoctoral Dissertation Neuroscience 201

Use of Advanced Flexible Modeling Approaches for Survival Extrapolation from Early Follow-up Data in two Nivolumab Trials in Advanced NSCLC with Extended Follow-up

Objectives: Immuno-oncology (IO) therapies are often associated with delayed responses that are deep and durable, manifesting as long-term survival benefits in patients with metastatic cancer. Complex hazard functions arising from IO treatments may limit the accuracy of extrapolations from standard parametric models (SPMs). We evaluated the ability of flexible parametric models (FPMs) to improve survival extrapolations using data from 2 trials involving patients with non–small-cell lung cancer (NSCLC). Methods: Our analyses used consecutive database locks (DBLs) at 2-, 3-, and 5-y minimum follow-up from trials evaluating nivolumab versus docetaxel in patients with pretreated metastatic squamous (CheckMate-017) and nonsquamous (CheckMate-057) NSCLC. For each DBL, SPMs, as well as 3 FPMs—landmark response models (LRMs), mixture cure models (MCMs), and Bayesian multiparameter evidence synthesis (B-MPES)—were estimated on nivolumab overall survival (OS). The performance of each parametric model was assessed by comparing milestone restricted mean survival times (RMSTs) and survival probabilities with results obtained from externally validated SPMs. Results: For the 2- and 3-y DBLs of both trials, all models tended to underestimate 5-y OS. Predictions from nonvalidated SPMs fitted to the 2-y DBLs were highly unreliable, whereas extrapolations from FPMs were much more consistent between models fitted to successive DBLs. For CheckMate-017, in which an apparent survival plateau emerges in the 3-y DBL, MCMs fitted to this DBL estimated 5-y OS most accurately (11.6% v. 12.3% observed), and long-term predictions were similar to those from the 5-y validated SPM (20-y RMST: 30.2 v. 30.5 mo). For CheckMate-057, where there is no clear evidence of a survival plateau in the early DBLs, only B-MPES was able to accurately predict 5-y OS (14.1% v. 14.0% observed [3-y DBL]). Conclusions: We demonstrate that the use of FPMs for modeling OS in NSCLC patients from early follow-up data can yield accurate estimates for RMST observed with longer follow-up and provide similar long-term extrapolations to externally validated SPMs based on later data cuts. B-MPES generated reasonable predictions even when fitted to the 2-y DBLs of the studies, whereas MCMs were more reliant on longer-term data to estimate a plateau and therefore performed better from 3 y. Generally, LRM extrapolations were less reliable than those from alternative FPMs and validated SPMs but remained superior to nonvalidated SPMs. Our work demonstrates the potential benefits of using advanced parametric models that incorporate external data sources, such as B-MPES and MCMs, to allow for accurate evaluation of treatment clinical and cost-effectiveness from trial data with limited follow-up. Flexible advanced parametric modeling methods can provide improved survival extrapolations for immuno-oncology cost-effectiveness in health technology assessments from early clinical trial data that better anticipate extended follow-up. Advantages include leveraging additional observable trial data, the systematic integration of external data, and more detailed modeling of underlying processes. Bayesian multiparameter evidence synthesis performed particularly well, with well-matched external data. Mixture cure models also performed well but may require relatively longer follow-up to identify an emergent plateau, depending on the specific setting. Landmark response models offered marginal benefits in this scenario and may require greater numbers in each response group and/or increased follow-up to support improved extrapolation within each subgroup