Selected problems of inference on branching processes and poisson shock model

This dissertation explores the development of statistical methodology for some problems of branching processes and poisson shock model. Branching process methods have become extremely popular in recent days. This dissertation mainly explores two fundamental inference problems of Galton-Watson processes. The first problem is concerned with statistical inference regarding the nature of the process. Two methodologies have been developed to develop a statistical test for the null hypothesis that the process is supercritical versus an alternative hypothesis that the process is non-supercritical. Another problem we investigate involves the estimation of the \u27age\u27 of a Galton-Watson Process. Three different methods are discussed to estimate the \u27age\u27 with suitable numerical illustrations. Computational aspects of these methods have also been explored. The literature regarding non-parametric aging properties is quite extensive. Bhattacharjee (2005) recently introduced a new notion of non-parametric aging property known as Strong decreasing Failure rate (SDFR). This dissertation explores necessary and sufficient conditions for which this nonparametric aging property is preserved under Essary-Marshall-Proschan shock model. It has been proved that the discrete SDFR property is transmitted to continuous version of SDFR under a shock model operation. A counter example has been constructed to show that the converse is false

On the structure of a family of probability generating functions induced by shock models

We explore conditions for a class of functions defined via an integral representation to be a probability generating function of some positive integer valued random variable. Interest in and research on this question is motivated by an apparently surprising connection between a family of classic shock models due to Esary et. al. (1973) and the negatively aging nonparametric notion of ``strongly decreasing failure rate'' (SDFR) introduced by Bhattacharjee (2005). A counterexample shows that there exist probability generating functions with our integral representation which are not discrete SDFR, but when used as shock resistance probabilities can give rise to a SDFR survival distribution in continuous time.Comment: Published in at http://dx.doi.org/10.1214/193940307000000536 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

On fixed and uncertain mixture prior weights

This paper focuses on the specification of the weights for the components of mixture priors

Principal Stratum Strategy: Potential Role in Drug Development

A randomized trial allows estimation of the causal effect of an intervention compared to a control in the overall population and in subpopulations defined by baseline characteristics. Often, however, clinical questions also arise regarding the treatment effect in subpopulations of patients, which would experience clinical or disease related events post-randomization. Events that occur after treatment initiation and potentially affect the interpretation or the existence of the measurements are called {\it intercurrent events} in the ICH E9(R1) guideline. If the intercurrent event is a consequence of treatment, randomization alone is no longer sufficient to meaningfully estimate the treatment effect. Analyses comparing the subgroups of patients without the intercurrent events for intervention and control will not estimate a causal effect. This is well known, but post-hoc analyses of this kind are commonly performed in drug development. An alternative approach is the principal stratum strategy, which classifies subjects according to their potential occurrence of an intercurrent event on both study arms. We illustrate with examples that questions formulated through principal strata occur naturally in drug development and argue that approaching these questions with the ICH E9(R1) estimand framework has the potential to lead to more transparent assumptions as well as more adequate analyses and conclusions. In addition, we provide an overview of assumptions required for estimation of effects in principal strata. Most of these assumptions are unverifiable and should hence be based on solid scientific understanding. Sensitivity analyses are needed to assess robustness of conclusions

Robust meta-analytic-predictive priors in clinical trials with historical control information.

Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior-data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta-analytic-predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta-analytic-combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta-analytic-predictive prior, which is not available analytically. We propose two- or three-component mixtures of standard priors, which allow for good approximations and, for the one-parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy-tailed and therefore robust. Further robustness and a more rapid reaction to prior-data conflicts can be achieved by adding an extra weakly-informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior-data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof-of-concept trial with historical controls from four studies. Robust meta-analytic-predictive priors alleviate prior-data conflicts ' they should encourage better and more frequent use of historical data in clinical trials

Bayesian hierarchical model-based network meta-analysis to overcome survival extrapolation challenges caused by data immaturity

Aim: This research evaluated standard Weibull mixture cure (WMC) network meta-analysis (NMA) with Bayesian hierarchical (BH)WMCNMAto inform long-term survival of therapies. Materials & methods: Four trials in previously treated metastatic non-small-cell lung cancer with PD-L1 >1% were used comparing docetaxel with nivolumab, pembrolizumab and atezolizumab. Cure parameters related to a certain treatment class were assumed to share a common distribution. Results: Standard WMC NMA predicted cure rates were 0.03 (0.01; 0.07), 0.18 (0.12; 0.24), 0.07 (0.02; 0.15) and 0.03 (0.00; 0.09) for docetaxel, nivolumab, pembrolizumab and atezolizumab, respectively,with corresponding incremental life years (LY) of 3.11 (1.65; 4.66), 1.06 (0.41; 2.37) and 0.42 (-0.57; 1.68). The Bayesian hierarchical-WMC-NMA rates were 0.06 (0.03; 0.10), 0.17 (0.11; 0.23), 0.12 (0.05; 0.20) and 0.12 (0.03; 0.23), respectively, with incremental LY of 2.35 (1.04; 3.93), 1.67 (0.68; 2.96) and 1.36 (-0.05; 3.64). Conclusion: BH-WMC-NMA impacts incremental mean LYs and cost–effectiveness ratios, potentially affecting reimbursement decisions

The effect of tofacitinib on residual pain in patients with rheumatoid arthritis and psoriatic arthritis

Objective: Post hoc analysis of pooled data from 9 randomised controlled trials to assess the effect of tofacitinib (oral Janus kinase inhibitor for treatment of rheumatoid arthritis [RA] and psoriatic arthritis [PsA]) on residual pain in patients with RA or PsA with abrogated inflammation. Methods: Patients who received ≥1 dose of tofacitinib 5 mg twice daily (BID), adalimumab or placebo with/without background conventional synthetic disease-modifying antirheumatic drugs and had abrogated inflammation (swollen joint count [SJC]=0 and C reactive protein [CRP]<6 mg/L) after 3 months’ therapy were included. Assessments included Patient’s Assessment of Arthritis Pain at Month 3 (Visual Analogue Scale [VAS] 0–100 mm). Scores were summarised descriptively; treatment comparisons assessed by Bayesian network meta analyses (BNMA). Results: From the total RA/PsA population, 14.9% (382/2568), 17.1% (118/691) and 5.5% (50/909) of patients receiving tofacitinib, adalimumab and placebo, respectively, had abrogated inflammation after 3 months’ therapy. RA/PsA patients with abrogated inflammation receiving tofacitinib/adalimumab had higher baseline CRP versus placebo; RA patients receiving tofacitinib/adalimumab had lower SJC and longer disease duration versus placebo. Median residual pain (VAS) at Month 3 was 17.0, 19.0 and 33.5 in RA patients treated with tofacitinib, adalimumab or placebo, and 24.0, 21.0 and 27.0 in PsA patients, respectively. Residual pain reductions with tofacitinib/adalimumab versus placebo were less prominent in PsA versus RA patients, with no significant differences between tofacitinib/adalimumab, per BNMA. Conclusion: Patients with RA/PsA with abrogated inflammation receiving tofacitinib/adalimumab had greater residual pain reduction versus placebo at Month 3. Results were similar between tofacitinib/adalimumab