Nonparametric Benefit–Risk Assessment Using Marker Process in the Presence of a Terminal Event

<p>Benefit–risk assessment is a crucial step in medical decision process. In many biomedical studies, both longitudinal marker measurements and time to a terminal event serve as important endpoints for benefit–risk assessment. The effect of an intervention or a treatment on the longitudinal marker process, however, can be in conflict with its effect on the time to the terminal event. Thus, questions arise on how to evaluate treatment effects based on the two endpoints, for the purpose of deciding on which treatment is most likely to benefit the patients. In this article, we present a unified framework for benefit–risk assessment using the observed longitudinal markers and time to event data. We propose a cumulative weighted marker process to synthesize information from the two endpoints, and use its mean function at a prespecified time point as a benefit–risk summary measure. We consider nonparametric estimation of the summary measure under two scenarios: (i) the longitudinal marker is measured intermittently during the study period, and (ii) the value of the longitudinal marker is observed throughout the entire follow-up period. The large-sample properties of the estimators are derived and compared. Simulation studies and data examples exhibit that the proposed methods are easy to implement and reliable for practical use. Supplemental materials for this article are available online.</p

Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling

<p>Biased sampling occurs frequently in economics, epidemiology, and medical studies either by design or due to data collecting mechanism. Failing to take into account the sampling bias usually leads to incorrect inference. We propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes, including but not limited to the length-biased sampling, the case-cohort design, and variants thereof. We establish the uniform consistency and weak convergence of the proposed estimator as a process of the quantile level. We also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality. We further propose a new resampling method for inference, which differs from alternative procedures in that it does not require to repeatedly solve estimating equations. It is proved that the resampling method consistently estimates the asymptotic covariance matrix. The unified framework proposed in this article provides researchers and practitioners a convenient tool for analyzing data collected from various designs. Simulation studies and applications to real datasets are presented for illustration. Supplementary materials for this article are available online.</p

Joint Scale-Change Models for Recurrent Events and Failure Time

<p>Recurrent event data arise frequently in various fields such as biomedical sciences, public health, engineering, and social sciences. In many instances, the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event, such as treatment failure and death. In this article, we propose a joint scale-change model for the recurrent event process and the failure time, where a shared frailty variable is used to model the association between the two types of outcomes. In contrast to the popular Cox-type joint modeling approaches, the regression parameters in the proposed joint scale-change model have marginal interpretations. The proposed approach is robust in the sense that no parametric assumption is imposed on the distribution of the unobserved frailty and that we do not need the strong Poisson-type assumption for the recurrent event process. We establish consistency and asymptotic normality of the proposed semiparametric estimators under suitable regularity conditions. To estimate the corresponding variances of the estimators, we develop a computationally efficient resampling-based procedure. Simulation studies and an analysis of hospitalization data from the Danish Psychiatric Central Register illustrate the performance of the proposed method. Supplementary materials for this article are available online.</p

The Impact of Genetic Susceptibility to Systemic Lupus Erythematosus on Placental Malaria in Mice

<div><p>Severe malaria, including cerebral malaria (CM) and placental malaria (PM), have been recognized to have many of the features of uncontrolled inflammation. We recently showed that in mice genetic susceptibility to the lethal inflammatory autoimmune disease, systemic lupus erythematosus (SLE), conferred resistance to CM. Protection appeared to be mediated by immune mechanisms that allowed SLE-prone mice, prior to the onset of overt SLE symptoms, to better control their inflammatory response to <i>Plasmodium</i> infection. Here we extend these findings to ask does SLE susceptibility have 1) a cost to reproductive fitness and/or 2) an effect on PM in mice? The rates of conception for WT and SLE susceptible (SLE^s) mice were similar as were the number and viability of fetuses in pregnant WT and SLE^s mice indicating that SLE susceptibility does not have a reproductive cost. We found that <i>Plasmodium chabaudi</i> AS (<i>Pc)</i> infection disrupted early stages of pregnancy before the placenta was completely formed resulting in massive decidual necrosis 8 days after conception. <i>Pc</i>-infected pregnant SLE^s mice had significantly more fetuses (∼1.8 fold) but SLE did not significantly affect fetal viability in infected animals. This was despite the fact that <i>Pc</i>-infected pregnant SLE^s mice had more severe symptoms of malaria as compared to <i>Pc</i>-infected pregnant WT mice. Thus, although SLE susceptibility was not protective in PM in mice it also did not have a negative impact on reproductive fitness.</p></div

Working panel of proposed correlates of protection for the intracellular bacterium <i>Francisella.</i>

<p>*The median fold change of the indicated mediator for each indicated vaccine group is shown, with the range across all experiments in parenthesis. For the range in parentheses, fold change values over 2 were rounded to the nearest whole number, and those less than 2 were rounded to one decimal place. Results from 4 total experiments were included (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s006" target="_blank">Table S2</a>). p values for logistic regressions of associations between degree of gene expression and degree of survival were all<0.001 (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s008" target="_blank">Table S4</a>).</p

Relationship between gene expression and survival across all vaccines studied at six weeks after vaccination for IFN-γ, TNF-α, IL-6, and T-bet.

<p>Data from <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s006" target="_blank">Table S2</a>, all experiments, were analyzed by logistic regression across all vaccines and all time points as described in the text. For each individual gene, the plotted results shown depict the percent survival of LVS-challenged mice as a function of the standardized score of the log₁₀ fold difference in gene expression. All mediators depicted here exhibited a significant positive relationship between the degree of gene expression and survival (see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat-1002494-t001" target="_blank">Table 1</a> and <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s008" target="_blank">Table S4</a>).</p

Splenocytes from mice vaccinated with a panel of LVS-related vaccines exhibit a hierarchy of control of intramacrophage LVS growth.

<p>(A) BMMØs from C57BL/6J mice were infected with LVS at an MOI of 1∶20 (bacterium-to-macrophage ratio; “Mac alone”), and co-cultured with the indicated numbers of splenocytes obtained from either naive C57BL/6J mice or C57BL/6J mice vaccinated 1×10⁴ CFU LVS, 1×10⁴ LVS-G, or 1×10⁴ LVS-R 6 weeks previously. Here, for all co-cultures containing added splenocytes, “1x” = 5×10⁶ splenocytes per well (used in all previous experiments), and 0.5x, 0.25x, and 0.1x refer to corresponding decreases in the total number of added splenocytes. (B) BMMØs from C57BL/6J mice were infected with LVS at an MOI of 1∶20 (bacterium-to-macrophage ratio), and co-cultured with splenocytes obtained from either naive C57BL/6J mice or C57BL/6J mice vaccinated 1×10⁴ CFU LVS or 1×10⁸ HK-LVS 6 weeks previously. For both A and B, after three days of co-culture, BMMØ were washed, lysed, and plated to determine the recovery of intracellular bacteria. Values shown are the mean numbers of CFU/ml ± SD of viable bacteria for triplicate samples. Results shown are from one representative experiment of three (A) or four (B) independent experiments of similar design with similar outcome.</p

Relationship between relative differences in gene expression and type of vaccine for differentially regulated genes.

<p>Data from all four experiments using the full panel of vaccine candidates (<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s006" target="_blank">Table S2</a>, experiments 4 – 7) are used to provide a graphic representation of the relationship between type of vaccine and relative gene expression. All data were normalized in relationship to endogenous GAPDH standard curves, and values shown are median of the fold differences (ΔΔCt) in relationship to naive cells for each type of vaccine, as indicated. Panel A depicts the genes designated as Group 1 in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat-1002494-t001" target="_blank">Table 1</a> (all significant, p<0.0001); Panel B depicts the genes designated as Group 2 in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat-1002494-t001" target="_blank">Table 1</a> (all significant, p<0.0001); Panel C depicts the remaining up-regulated genes not included in Groups 1 or 2 of <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat-1002494-t001" target="_blank">Table 1</a> (IL-17A, IL-23a, CCR5, and STAT-1 significant with p<0.05, but IL-13 not significant; see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s008" target="_blank">Table S4</a> for exact p values); and Panel D depicts down-regulated genes (all non-significant; see <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1002494#ppat.1002494.s008" target="_blank">Table S4</a> for p values). The corresponding legends are shown immediately above or immediately below each panel.</p

Hierarchy of strength of protection against lethal systemic <i>F. tularensis</i> LVS challenge after vaccination of mice with LVS or the variants LVS-G, LVS-R, and heat-killed LVS.

<p>C57BL/6J mice were immunized by ID infection with 1×10⁴ CFU LVS, 1×10⁸ HK-LVS, 1×10⁴ LVS-G, or 1×10⁴ LVS-R. At 6 weeks after vaccination, mice vaccinated with PBS were challenged with 10³ or 10⁴ LVS IP; mice vaccinated with HK-LVS were challenged with 10³, 10⁴, or10⁵ LVS IP; and mice vaccinated with LVS, LVS-G, and LVS-R were challenged with 5×10⁴, 10⁵, 5×10⁵, or 10⁶ LVS IP, as indicated for each group, and monitored for survival. Results shown are from one representative experiment of three independent experiments of similar design with similar outcome.</p

Kinetics of vaccine-specific IgG levels in children during the dry season and after acute malaria.

<p><b>(A)</b> The study was designed to take advantage of the sharply demarcated and intense 6-month malaria season (July—December) and 6-month dry season (January—June; negligible malaria transmission) in Mali. Shown is the number of febrile malaria episodes per day over two years at the study site in a cohort of 695 children and adults. <b>(B)</b> IgG levels specific for routine vaccines administered under one year of age (tetanus, measles and Hepatitis B) were measured in plasma collected from 54 children at four time points (vertical arrows): before and after the 6-month dry season, 10 days after the first acute malaria episode of the ensuing malaria season, and after the second dry season. Shown for each subject are IgG titers specific for <b>(C)</b> tetanus, <b>(D)</b> measles and <b>(E)</b> hepatitis B vaccines at the time points indicated in <b>(B)</b>. The x-axis indicates the age at which the respective time points occurred for each subject. In red are subjects who experienced an accelerated decline in vaccine-specific IgG titers following acute malaria (between 2^nd and 3^rd time points) relative to each child’s own rate of change during the preceding dry season (between 1^st and 2^nd time points). The percentage of subjects for whom malaria was associated with an accelerated decline in IgG is shown in red text for each vaccine. A linear mixed effects model that included three time points over 18 months (before and after the first dry season, and after the second dry season) was used to estimate average IgG half-lives for all subjects (black dashed line) and separately for children aged ≤3 years (green dotted line) and >3 years of age (blue dash-dot line).</p