Survival data from prevalent cases collected under a cross-sectional sampling scheme are subject to left-truncation. When fitting an additive hazards model to left-truncated data, the conditional estimating equation method (Lin & Ying, 1994), obtained by modifying the risk sets to account for left-truncation, can be very inefficient, as the marginal likelihood of the truncation times is not used in the estimation procedure. In this paper, we use a pairwise pseudolikelihood to eliminate nuisance parameters from the marginal likelihood and, by combining the marginal pairwise pseudo-score function and the conditional estimating function, propose an efficient estimator for the additive hazards model. The proposed estimator is shown to be consistent and asymptotically normally distributed with a sandwich-type covariance matrix that can be consistently estimated. Simulation studies show that the proposed estimator is more efficient than its competitors. A data analysis illustrates application of the method.

This paper proposes a new estimation procedure for the survival time distribution with left-truncated and right-censored data, where the distribution of the truncation time is known up to a finite-dimensional parameter vector. The paper expands on the Vardis multiplicative censoring model (Vardi, 1989. Multiplicative censoring, renewal processes, deconvolution and decreasing density: non-parametric estimation. Biometrika 76: , 751-761), establishes the connection between the likelihood under a generalized multiplicative censoring model and that for left-truncated and right-censored survival time data, and derives an Expectation-Maximization algorithm for model estimation. A formal test for checking the truncation time distribution is constructed based on the semiparametric likelihood ratio test statistic. In particular, testing the stationarity assumption that the underlying truncation time is uniformly distributed is performed by embedding the null uniform truncation time distribution in a smooth alternative (Neyman, 1937. Smooth test for goodness of fit. Skandinavisk Aktuarietidskrift 20: , 150-199). Asymptotic properties of the proposed estimator are established. Simulations are performed to evaluate the finite-sample performance of the proposed methods. The methods and theories are illustrated by analyzing the Canadian Study of Health and Aging and the Channing House data, where the stationarity assumption with respect to disease incidence holds for the former but not the latter.

It is well known that truncated survival data are subject to sampling bias, where the sampling weight depends on the underlying truncation time distribution. Recently, there has been a rising interest in developing methods to better exploit the information about the truncation time, thus the sampling weight function, to obtain more efficient estimation. In this paper, we propose to treat truncation and censoring as "missing data mechanism" and apply the missing information principle to develop a unified framework for analyzing left-truncated and right-censored data with unspecified or known truncation time distributions. Our framework is structured in a way that is easy to understand and enjoys a great flexibility for handling different types of models. Moreover, a new test for checking the independence between the underlying truncation time and survival time is derived along the same line. The proposed hypothesis testing procedure utilizes all observed data and hence can yield a much higher power than the conditional Kendall's tau test that only involves comparable pairs of observations under truncation. Simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. The proposed methodologies are applied to a dementia study and a nursing house study for illustration.

The novel coronavirus (COVID-19) is continuing its spread across the world, claiming more than 160,000 lives and sickening more than 2,400,000 people as of April 21, 2020. Early research has reported a basic reproduction number (R0) between 2.2 to 3.6, implying that the majority of the population is at risk of infection if no intervention measures were undertaken. The true size of the COVID-19 epidemic remains unknown, as a significant proportion of infected individuals only exhibit mild symptoms or are even asymptomatic. A timely assessment of the evolving epidemic size is crucial for resource allocation and triage decisions. In this article, we modify the back-calculation algorithm to obtain a lower bound estimate of the number of COVID-19 infected persons in China in and outside the Hubei province. We estimate the infection density among infected and show that the drastic control measures enforced throughout China following the lockdown of Wuhan City effectively slowed down the spread of the disease in two weeks. We also investigate the COVID-19 epidemic size in South Korea and find a similar effect of its test, trace, isolate, and treat strategy. Our findings are expected to provide guidelines and enlightenment for surveillance and control activities of COVID-19 in other countries around the world.