Recurrent event data are commonly encountered in longitudinal follow-up studies related to biomedical science, econometrics, reliability, and demography. In many studies, recurrent events serve as important measurements for evaluating disease progression, health deterioration, or insurance risk. When analyzing recurrent event data, an independent censoring condition is typically required for the construction of statistical methods. In some situations, however, the terminating time for observing recurrent events could be correlated with the recurrent event process, thus violating the assumption of independent censoring. In this article, we consider joint modeling of a recurrent event process and a failure time in which a common subject-specific latent variable is used to model the association between the intensity of the recurrent event process and the hazard of the failure time. The proposed joint model is flexible in that no parametric assumptions on the distributions of censoring times and latent variables are made, and under the model, informative censoring is allowed for observing both the recurrent events and failure times. We propose a “borrow-strength estimation procedure” by first estimating the value of the latent variable from recurrent event data, then using the estimated value in the failure time model. Some interesting implications and trajectories of the proposed model are presented. Properties of the regression parameter estimates and the estimated baseline cumulative hazard functions are also studied.
Borrow-strength method; Frailty; Informative censoring; Joint model; Nonstationary Poisson process
Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.
bootstrap; independent censoring; intensity function; kernel estimator; Poisson process; rate function; recurrent events
The Canadian Study of Health and Aging (CSHA) employed a prevalent cohort design to study survival after onset of dementia, where patients with dementia were sampled and the onset time of dementia was determined retrospectively. The prevalent cohort sampling scheme favors individuals who survive longer. Thus, the observed survival times are subject to length bias. In recent years, there has been a rising interest in developing estimation procedures for prevalent cohort survival data that not only account for length bias but also actually exploit the incidence distribution of the disease to improve efficiency. This article considers semiparametric estimation of the Cox model for the time from dementia onset to death under a stationarity assumption with respect to the disease incidence. Under the stationarity condition, the semiparametric maximum likelihood estimation is expected to be fully efficient yet difficult to perform for statistical practitioners, as the likelihood depends on the baseline hazard function in a complicated way. Moreover, the asymptotic properties of the semiparametric maximum likelihood estimator are not well-studied. Motivated by the composite likelihood method (Besag 1974), we develop a composite partial likelihood method that retains the simplicity of the popular partial likelihood estimator and can be easily performed using standard statistical software. When applied to the CSHA data, the proposed method estimates a significant difference in survival between the vascular dementia group and the possible Alzheimer’s disease group, while the partial likelihood method for left-truncated and right-censored data yields a greater standard error and a 95% confidence interval covering 0, thus highlighting the practical value of employing a more efficient methodology. To check the assumption of stable disease for the CSHA data, we also present new graphical and numerical tests in the article. The R code used to obtain the maximum composite partial likelihood estimator for the CSHA data is available in the online Supplementary Material, posted on the journal web site.
Backward and forward recurrence time; Cross-sectional sampling; Random truncation; Renewal processes
In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximising a conditional likelihood function of observed event counts and solving estimation equations. Large-sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumour study is presented.
Dependent censoring; Frailty; Poisson process; Rate function; Serial events
The pretest–posttest study design is commonly used in medical and social science research to assess the effect of a treatment or an intervention. Recently, interest has been rising in developing inference procedures that improve efficiency while relaxing assumptions used in the pretest–posttest data analysis, especially when the posttest measurement might be missing. In this article we propose a semiparametric estimation procedure based on empirical likelihood (EL) that incorporates the common baseline covariate information to improve efficiency. The proposed method also yields an asymptotically unbiased estimate of the response distribution. Thus functions of the response distribution, such as the median, can be estimated straightforwardly, and the EL method can provide a more appealing estimate of the treatment effect for skewed data. We show that, compared with existing methods, the proposed EL estimator has appealing theoretical properties, especially when the working model for the underlying relationship between the pretest and posttest measurements is misspecified. A series of simulation studies demonstrates that the EL-based estimator outperforms its competitors when the working model is misspecified and the data are missing at random. We illustrate the methods by analyzing data from an AIDS clinical trial (ACTG 175).
Auxiliary information; Biased sampling; Causal inference; Observational study; Survey sampling
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 Plasmodium 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 (SLEs) mice were similar as were the number and viability of fetuses in pregnant WT and SLEs mice indicating that SLE susceptibility does not have a reproductive cost. We found that Plasmodium chabaudi AS (Pc) infection disrupted early stages of pregnancy before the placenta was completely formed resulting in massive decidual necrosis 8 days after conception. Pc-infected pregnant SLEs 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 Pc-infected pregnant SLEs mice had more severe symptoms of malaria as compared to Pc-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.
This paper considers semiparametric estimation of the Cox proportional hazards model for right-censored and length-biased data arising from prevalent sampling. To exploit the special structure of length-biased sampling, we propose a maximum pseudo-profile likelihood estimator, which can handle time-dependent covariates and is consistent under covariate-dependent censoring. Simulation studies show that the proposed estimator is more efficient than its competitors. A data analysis illustrates the methods and theory.
Approximate likelihood; Cross-sectional sampling; Product-limit estimator; Random truncation; Screening trials
H5N1 avian influenza represents an episodic zoonotic disease with potential to cause a pandemic, and resistance is of considerable concern. We sought to generate high titer H5N1 antibodies in healthy volunteers for the purpose of developing hyperimmune IVIG.
We conducted a dose escalating unblinded clinical trial involving 75 subjects between the ages of 18 and 59 years. Three cohorts of twenty-five subjects were enrolled sequentially receiving 90, 120, or 180 mcg of H5N1 A/Vietnam/1203/04 vaccine for four doses 28 days apart.
No significant dose related increases in the geometric mean titers (GMTs) of serum HAI were observed when comparing 90, 120, and 180 mcg. When analyzed together to determine the effect of additional vaccinations, HAI GMT after first, second, third and fourth vaccinations was 1:15.7, 1:22.2, 1:36.0, and 1:32.0, respectively (first vs baseline, P<0.0001; second vs first, P=0.02; third vs second, P<0.0001). The MN GMT after first, second, third, and fourth vaccinations was 1:17.5, 1:33.1, 1:55.7, and 1:68.4 respectively (all P<0.001).
Our study suggests that a third dose and fourth dose of the H5N1 A/Vietnam/1203/04 vaccine may result in a higher HA and MN GMT. There was no benefit to increasing the dose of the vaccine.
avian influenza; vaccination; passive immunotherapy; IVIG
Recurrent events are the natural outcome in many medical and epidemiology studies. To assess covariate effects on the gaps between consecutive recurrent events, the Cox proportional hazards model is frequently employed in data analysis. The validity of statistical inference, however, depends on the appropriateness of the Cox model. In this paper, we propose a class of graphical techniques and formal tests for checking the Cox model with recurrent gap time data. The building block of our model checking method is an averaged martingale-like process, based on which a class of multiparameter stochastic processes is proposed. This maneuver is very general and can be used to assess different aspects of model fit. Numerical simulations are conducted to examine finite-sample performance, and the proposed model checking techniques are illustrated with data from the Danish Psychiatric Central Register.
Correlated failure times; Induced-dependent censoring; Kaplan–Meier estimator; Renewal processes
Sera from H5N1 vaccinees and IVIG were analyzed for crossreactive Abs against HA of influenza A viruses. Data quantitatively shows the presence of two populations of heterosubtypic neutralizing Abs against either Group 1 only or Group 1 + 2 viruses.
(See the editorial commentary by Donis and Cox, on pages 1010–1012.)
Background. Lack of life-long immunity against influenza viruses represents a major global health care problem with profound medical and economic consequences. A greater understanding of the broad-spectrum “heterosubtypic” neutralizing human antibody (BnAb) response to influenza should bring us closer toward a universal influenza vaccine.
Methods. Serum samples obtained from 77 volunteers in an H5N1 vaccine study were analyzed for cross-reactive antibodies (Abs) against both subtype hemagglutinins (HAs) and a highly conserved pocket on the HA stem of Group 1 viruses. Cross-reactive Abs in commercial intravenous immunoglobulin were affinity purified using H5-coupled beads followed by step-wise monoclonal antibody competition or acid elution. Enzyme-linked immunosorbent assays were used to quantify cross-binding, and neutralization activity was determined with HA-pseudotyped viruses.
Results. Prevaccination serum samples have detectable levels of heterosubtypic HA binding activity to both Group 1 and 2 influenza A viruses, including subtypes H5 and H7, respectively, to which study subjects had not been vaccinated. Two different populations of Broadly neutralizing Abs (BnAbs) were purified from intravenous immunoglobulin by H5 beads: ∼0.01% of total immunoglobulin G can bind to HAs from both Group 1 and 2 and neutralize H1N1 and H5N1 viruses; ∼0.001% is F10-like Abs directed against the HA stem pocket on Group 1 viruses.
Conclusion. These data—to our knowledge, for the first time—quantitatively show the presence, albeit at low levels, of two populations of heterosubtypic BnAbs against influenza A in human serum. These observations warrant further investigation to determine their origin, host polymorphism(s) that may affect their expression levels and how to boost these BnAb responses by vaccination to reach sustainable protective levels.
This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory.
Backward and forward recurrence time; Cross-sectional sampling; Partial likelihood; Random truncation; Renewal process
In contrast with common human infections for which vaccine efficacy can be evaluated directly in field studies, alternative strategies are needed to evaluate efficacy for slowly developing or sporadic diseases like tularemia. For diseases such as these caused by intracellular bacteria, serological measures of antibodies are generally not predictive. Here, we used vaccines varying in efficacy to explore development of clinically useful correlates of protection for intracellular bacteria, using Francisella tularensis as an experimental model. F. tularensis is an intracellular bacterium classified as Category A bioterrorism agent which causes tularemia. The primary vaccine candidate in the U.S., called Live Vaccine Strain (LVS), has been the subject of ongoing clinical studies; however, safety and efficacy are not well established, and LVS is not licensed by the U.S. FDA. Using a mouse model, we compared the in vivo efficacy of a panel of qualitatively different Francisella vaccine candidates, the in vitro functional activity of immune lymphocytes derived from vaccinated mice, and relative gene expression in immune lymphocytes. Integrated analyses showed that the hierarchy of protection in vivo engendered by qualitatively different vaccines was reflected by the degree of lymphocytes' in vitro activity in controlling the intramacrophage growth of Francisella. Thus, this assay may be a functional correlate. Further, the strength of protection was significantly related to the degree of up-regulation of expression of a panel of genes in cells recovered from the assay. These included IFN-γ, IL-6, IL-12Rβ2, T-bet, SOCS-1, and IL-18bp. Taken together, the results indicate that an in vitro assay that detects control of bacterial growth, and/or a selected panel of mediators, may ultimately be developed to predict the outcome of vaccine efficacy and to complement clinical trials. The overall approach may be applicable to intracellular pathogens in general.
Diseases such as tuberculosis (caused by Mycobacterium tuberculosis) or tularemia (caused by Francisella tularensis) result from infections by microbes that live within cells of a person's body. New vaccines are being developed against such intracellular pathogens, but some will be difficult to test, because disease takes a long time to develop (e.g., tuberculosis) or because outbreaks are unpredictable (e.g., tularemia). Usually such infections are controlled by activities of T cells. However, there are no accepted measures of T cell function that reliably predict vaccine-induced protection. We studied two new ways to do so. We used a group of vaccine candidates against tularemia that stimulated good, fair, or poor protection of mice against Francisella challenge. We then measured whether Francisella–immune cells from vaccinated mice controlled the growth of bacteria inside cells, and/or whether the expression of immune genes in Francisella–immune cells was increased. We found that the degree of protection was matched by the degree of the cells' function in controlling intramacrophage bacterial growth. Further, the degree was predicted by relative amounts of gene expression for several immune mediators. Thus the two new options explored here may help predict protection, without waiting for the onset of disease.
A randomized, controlled clinical trial was started in the pre-HAART era to compare the efficacy of zidovudine (AZT) and interferon-alpha (IFN-α) either alone or in combination to reduce HIV viremia, maintain CD4+ cell count, and decrease time to AIDS progression and death. The purpose of the current study was to compare the effects of AZT and IFN on HIV load using modern technology. One hundred and eighty patients with CD4+ counts above 500 cells/mm3 were randomized to receive AZT alone, IFN-α alone, or AZT and IFN-α in combination. CD4+ cell count and HIV load at baseline and at the last follow-up visit were compared, and time to AIDS or death was calculated by treatment group. At a mean follow-up of 45 weeks, the mean change in log HIV RNA was −0.06 for the AZT alone group, −0.47 for the AZT plus IFN-α group (P = 0.01 versus AZT group), and −0.35 for the IFN-α alone group (P = 0.02 versus AZT group). There was no significant difference among groups in change in total CD4+ count or in time to AIDS or death. Since treatment with IFN-α produces significant decreases in HIV load, additional studies of IFN-α as part of a combination regimen are warranted.
Antibodies play a key role in controlling blood stage malaria infections, and an effective blood stage malaria vaccine will likely require that it induce vaccine-specific memory B cells (MBCs). Our previous studies showed that the addition of the TLR9 agonist CpG to Plasmodium falciparum protein subunit vaccines greatly increased their efficacy in inducing MBCs in nonimmune U.S. volunteers. Here we show that in contrast the same CpG-containing malaria vaccine did not enhance the acquisition of MBCs in semi-immune adults living in Mali. Understanding the molecular basis of this apparent refractoriness to TLR9 agonist will be of significant interest in vaccine design.
Memory B cells; Plasmodium falciparum; Malaria; Toll-like receptor 9
Despite the central role of memory B cells (MBC) in protective immune responses, little is understood about how they are acquired in naïve individuals in response to antigen exposure, and how this process is influenced by concurrent activation of the innate immune system’s Toll-like receptors (TLR). In this longitudinal study of malaria-naïve individuals, we examined the MBC response to two candidate malaria vaccines administered with or without CpG, a TLR9 ligand. We show that the acquisition of MBC is a dynamic process in which the vaccine-specific MBC pool rapidly expands and then contracts, and that CpG enhances the kinetics, magnitude, and longevity of this response. We observed that the percentage of vaccine-specific MBC present at the time of re-immunization predicts vaccine-specific Ab levels 14 days later; and that at steady state, there is a positive correlation between vaccine-specific MBC and Ab levels. An examination of the total circulating MBC and plasma cell (PC) pools also suggests that MBC differentiate into PC through polyclonal activation, independent of antigen specificity. These results provide important insights into the human MBC response which can inform the development of vaccines against malaria and other pathogens that disrupt immunological memory.
Human; B cells; Memory; Parasitic-Protozoan; Vaccination
Antifungal effects of iron chelators (lactoferrin, deferoxamine, deferiprone, and ciclopirox) were tested alone and in combination with antifungal drugs against Aspergillus fumigatus B5233 conidia. Lactoferrin, ciclopirox, and deferiprone inhibited whereas deferoxamine enhanced fungal growth. Antifungal synergy against conidia was observed for combinations of ketoconazole with ciclopirox or deferiprone, lactoferrin with amphotericin B, and fluconazole with deferiprone. Iron chelation alone or combined with antifungal drugs may be useful for prevention and treatment of mycosis.
Immunity to the asexual blood stage of Plasmodium falciparum is complex and likely involves several effector mechanisms. Antibodies are thought to play a critical role in malaria immunity, and a corresponding in vitro correlate of antibody-mediated immunity has long been sought to facilitate malaria vaccine development. The growth inhibition assay (GIA) measures the capacity of antibodies to limit red blood cell (RBC) invasion and/or growth of P. falciparum in vitro. In humans, naturally acquired and vaccine-induced P. falciparum-specific antibodies have growth-inhibitory activity, but it is unclear if growth-inhibitory activity correlates with protection from clinical disease. In a longitudinal study in Mali, purified IgGs, obtained from plasmas collected before the malaria season from 220 individuals aged 2 to 10 and 18 to 25 years, were assayed for growth-inhibitory activity. Malaria episodes were recorded by passive surveillance over the subsequent 6-month malaria season. Logistic regression showed that greater age (odds ratio [OR], 0.78; 95% confidence interval [95% CI], 0.63 to 0.95; P = 0.02) and growth-inhibitory activity (OR, 0.50; 95% CI, 0.30 to 0.85; P = 0.01) were significantly associated with decreased malaria risk in children. A growth-inhibitory activity level of 40% was determined to be the optimal cutoff for discriminating malaria-immune and susceptible individuals in this cohort, with a sensitivity of 97.0%, but a low specificity of 24.3%, which limited the assay's ability to accurately predict protective immunity and to serve as an in vitro correlate of antibody-mediated immunity. These data suggest that antibodies which block merozoite invasion of RBC and/or inhibit the intra-RBC growth of the parasite contribute to but are not sufficient for the acquisition of malaria immunity.
Administration of IL-2 to HIV-infected patients leads to significant increases in CD4 T cell counts. Previously we have shown that IL-2 induces increased proliferation and survival of CD4 T cells. Deuterium labeling studies were undertaken to study the relationship between IL-2 induced increases in CD4 T cell numbers and IL-2 effects on cell proliferation and survival. A strong inverse correlation was seen between the decay rate of label in CD4 cells and increases in CD4 cell numbers (R= -0.67; p<0.001). This correlation was not seen with the level of proliferating cells. Although the baseline CD4 cell count and number of CD4 cells expressing CD25 were also predictive of CD4 cell increases, the decay rate remained the most statistically significant predictor in multivariate regression models. Thus, increase in survival of CD4 T cells appears to be the critical mechanism leading to sustained CD4 cell increases in HIV-infected patients receiving intermittent IL-2 therapy.
IL-2; deuterium; T cell survival
The World Health Organization (WHO) recently recommended that the time to first malaria episode serve as the primary endpoint in phase III malaria vaccine trials—the first of which will be held in Africa. Although common red blood cell (RBC) polymorphisms such as sickle hemoglobin (Hb) S are known to protect against malaria in Africa, their impact on this endpoint has not been investigated.
A longitudinal study of 225 individuals aged 2-25 years was conducted in Mali. The association between common RBC polymorphisms and the time to first malaria episode was evaluated.
Among children aged 2-10 years, sickle cell trait (HbAS) was associated with a 34-day delay in the median time to first malaria episode (p=0.017). Cox regression analysis showed that age (hazard ratio [HR] 0.87 [95% CI, 0.80-0.94]; p=0.001), HbAS (HR 0.48 [95% CI, 0.26-0.91]; p=0.024), and asymptomatic parasitemia at enrollment (HR 0.35 [95% CI, 0.14-0.85]; p=0.021) were associated with decreased malaria risk.
Given the delay in the time to first malaria episode associated with HbAS, it would be advisable for clinical trials and observational studies that use this endpoint to include Hb typing in the study design where HbAS is prevalent.
Plasmodium falciparum malaria; red blood cell polymorphisms; sickle cell trait; vaccines; survival analysis; Mali; longitudinal study; observational study; alpha-thalassemia; G6PD deficiency
Immunity to Plasmodium falciparum (Pf) malaria is only acquired after years of repeated infections and wanes rapidly without ongoing parasite exposure. Antibodies are central to malaria immunity, yet little is known about the B-cell biology that underlies the inefficient acquisition of Pf-specific humoral immunity. This year-long prospective study in Mali of 185 individuals aged 2 to 25 years shows that Pf-specific memory B-cells and antibodies are acquired gradually in a stepwise fashion over years of repeated Pf exposure. Both Pf-specific memory B cells and antibody titers increased after acute malaria and then, after six months of decreased Pf exposure, contracted to a point slightly higher than pre-infection levels. This inefficient, stepwise expansion of both the Pf-specific memory B-cell and long-lived antibody compartments depends on Pf exposure rather than age, based on the comparator response to tetanus vaccination that was efficient and stable. These observations lend new insights into the cellular basis of the delayed acquisition of malaria immunity.
Plasmodium falciparum (Pf) is a mosquito-borne parasite that causes over 500 million cases of malaria annually, one million of which result in death, primarily among African children. The development of an effective malaria vaccine would be a critical step toward the control and eventual elimination of this disease. To date, most licensed vaccines are for pathogens that induce long-lived protective antibodies after a single infection. In contrast, immunity to malaria is only acquired after repeated infections. Antibodies play a key role in protection from malaria, yet several studies indicate that antibodies against some Pf proteins are generated inefficiently and lost rapidly. The cells that are responsible for the maintenance of antibodies over the human lifespan are memory B-cells and long-lived plasma cells. To determine how these cells are generated and maintained in response to Pf infection, we conducted a year-long study in an area of Mali that experiences a six-month malaria season. We found memory B-cells and long-lived antibodies specific for the parasite were generated in a gradual, step-wise fashion over years despite intense Pf exposure. This contrasts sharply with the efficient response to tetanus vaccination in the same population. This study lends new insights into the delayed acquisition of malaria immunity. Future studies of the cellular and molecular basis of these observations could open the door to strategies for the development of a highly effective malaria vaccine.