Semiparametric likelihood inference for heterogeneous survival data under double truncation based on a Poisson birth process

We study a selective sampling scheme in which survival data are observed during a data collection period if and only if a specific failure event is experienced. Individual units belong to one of a finite number of subpopulations, which may exhibit different survival behaviour, and thus cause heterogeneity. Based on a Poisson process model for individual emergence of population units, we derive a semiparametric likelihood model, in which the birth distribution is modeled nonparametrically and the lifetime distributions parametrically, and define maximum likelihood estimators. We propose a Newton–Raphson-type optimization method to address numerical challenges caused by the high-dimensional parameter space. The finite-sample properties and computational performance of the proposed algorithms are assessed in a simulation study. Personal insolvencies are studied as a special case of double truncation and we fit the semiparametric model to a medium-sized dataset to estimate the mean age at insolvency and the birth distribution of the underlying population.

SEMIPARAMETRIC INDEPENDENCE TESTING FOR TIME SERIES OF COUNTS AND THE ROLE OF THE SUPPORT

This article considers testing for independence in a time series of small counts within an Integer Autoregressive (INAR) model, taking a semiparametric approach that avoids any distributional assumption on the arrivals process of the model. The nature of the testing problem is shown to differ depending on whether or not the support of the arrivals distribution is the full set of natural numbers (as would be the case for Poisson or Negative Binomial distributions for example) or some strict subset of the natural numbers (such as for a Binomial or Uniform distribution). The theory for these two cases is studied separately.For the case where the arrivals have support on the natural numbers, a new asymptotically efficient semiparametric test, the effective score (Neyman-Rao) test, is derived. The semiparametric Likelihood-Ratio, Wald and score tests are shown to be asymptotically equivalent to the effective score test, and hence also asymptotically efficient. Asymptotic relative efficiency calculations demonstrate that the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation coefficient, which is most commonly applied in practice.For the case where the arrivals have support that is a strict subset of the natural numbers, the theory is considerably altered because the support of the observations becomes different under the null and alternative hypotheses. The semiparametric Likelihood-Ratio, Wald and score tests become asymptotically degenerate in this case, while the effective score test remains valid. Remarkably, in this case the effective score test is also found to have power against local alternatives that shrink to the null at the rate T−1. In rare cases where the arrival support is partly or totally known, additional tests exploiting this information are considered.Finite sample properties of the tests in these various cases demonstrate the semiparametric effective score test can provide substantial power advantages over the first order autocorrelation test implied by a parametric Poisson specification. The simulations also reveal situations in which the first order autocorrelation is preferable in finite samples, so a hybrid of the effective score and autocorrelation tests is proposed to capture most of the benefits of each test.

Likelihood-based methods for evaluating principal surrogacy in augmented vaccine trials

There is growing interest in assessing immune biomarkers, which are quick to measure and potentially predictive of long-term efficacy, as surrogate endpoints in randomized, placebo-controlled vaccine trials. This can be done under a principal stratification approach, with principal strata defined using a subject’s potential immune responses to vaccine and placebo (the latter may be assumed to be zero). In this context, principal surrogacy refers to the extent to which vaccine efficacy varies across principal strata. Because a placebo recipient’s potential immune response to vaccine is unobserved in a standard vaccine trial, augmented vaccine trials have been proposed to produce the information needed to evaluate principal surrogacy. This article reviews existing methods based on an estimated likelihood and a pseudo-score (PS) and proposes two new methods based on a semiparametric likelihood (SL) and a pseudo-likelihood (PL), for analyzing augmented vaccine trials. Unlike the PS method, the SL method does not require a model for missingness, which can be advantageous when immune response data are missing by happenstance. The SL method is shown to be asymptotically efficient, and it performs similarly to the PS and PL methods in simulation experiments. The PL method appears to have a computational advantage over the PS and SL methods.