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In clinical trials and other medical studies, it has become increasingly common to observe simultaneously an event time of interest and longitudinal covariates. In the literature, joint modelling approaches have been employed to analyse both survival and longitudinal processes and to investigate their association. However, these approaches focus mostly on developing adaptive and flexible longitudinal processes based on a prespecified survival model, most commonly the Cox proportional hazards model. In this paper, we propose a general class of semiparametric hazard regression models, referred to as the extended hazard model, for the survival component. This class includes two popular survival models, the Cox proportional hazards model and the accelerated failure time model, as special cases. The proposed model is flexible for modelling event data, and its nested structure facilitates model selection for the survival component through likelihood ratio tests. A pseudo joint likelihood approach is proposed for estimating the unknown parameters and components via a Monte Carlo em algorithm. Asymptotic theory for the estimators is developed together with theory for the semiparametric likelihood ratio tests. The performance of the procedure is demonstrated through simulation studies. A case study featuring data from a Taiwanese HIV/AIDS cohort study further illustrates the usefulness of the extended hazard model.

Both varying-coe cient and additive models have been studied extensively in the literature as extensions to linear models. They have also been extended to functional response data. However, existing extensions are still not su ciently flexible to reflect the functional feature of the responses. In this paper, we extend both varying-coe cient and additive models to a much more flexible “varying-coe cient additive model” and propose a simple algorithm to estimate the nonparametric additive and varying-coe cient components of this model. We establish the L 2 rate of convergence for each component function and demonstrate the applicability of the new model through tra c data.

Joint modeling of survival and longitudinal data has been studied extensively in the recent literature. The likelihood approach is one of the most popular estimation methods employed within the joint modeling framework. Typically, the parameters are estimated using maximum likelihood, with computation performed by the expectation maximization (EM) algorithm. However, one drawback of this approach is that standard error (SE) estimates are not automatically produced when using the EM algorithm. Many different procedures have been proposed to obtain the asymptotic covariance matrix for the parameters when the number of parameters is typically small. In the joint modeling context, however, there may be an infinite-dimensional parameter, the baseline hazard function, which greatly complicates the problem, so that the existing methods cannot be readily applied. The profile likelihood and the bootstrap methods overcome the difficulty to some extent; however, they can be computationally intensive. In this paper, we propose two new methods for SE estimation using the EM algorithm that allow for more efficient computation of the SE of a subset of parametric components in a semiparametric or high-dimensional parametric model. The precision and computation time are evaluated through a thorough simulation study. We conclude with an application of our SE estimation method to analyze an HIV clinical trial dataset.

The additive model is an effective dimension-reduction approach that also provides flexibility in modeling the relation between a response variable and key covariates. The literature is largely developed to scalar response and vector covariates. In this article, more complex data are of interest, where both the response and the covariates are functions. We propose a functional additive model together with a new backfitting algorithm to estimate the unknown regression functions, whose components are time-dependent additive functions of the covariates. Such functional data may not be completely observed since measurements may only be collected intermittently at discrete time points. We develop a unified platform and an efficient approach that can cover both dense and sparse functional data and the needed theory for statistical inference. We also establish the oracle properties of the proposed estimators of the component functions.

In this article, we revisit Winfried Stute’s contributions to survival analysis, which constitute a significant portion of his publications. Instead of a comprehensive review of his work in survival analysis, we focus on four papers that are fundamental by themselves.

The reproductive ability of female tephritids can be limited and prevented by denying access to host plants and restricting the dietary precursors of vitellogenesis. The mechanisms underlying the delayed egg production in each case are initiated by different physiological processes that are anticipated to have dissimilar effects on lifespan and reproductive ability later in life. The egg laying abilities of laboratory reared females of the Mediterranean fruit fly (Ceratitis capitata Wiedmann) and melon fly (Bactrocera cucurbitae Coquillett) from Hawaii are delayed or suppressed by limiting access to host fruits and dietary protein. In each case, this is expected to prevent the loss of lifespan associated with reproduction until protein or hosts are introduced. Two trends are observed in each species: Firstly, access to protein at eclosion leads to a greater probability of survival and higher reproductive ability than if it is delayed, and secondly, that delayed host access reduces lifetime reproductive ability without improving life expectancy. When host access and protein availability are delayed, the rate of reproductive senescence is reduced in the medfly, whereas the rate of reproductive senescence is generally increased in the melon fly. Overall, delaying reproduction lowers the fitness of females by constraining their fecundity for the remainder of the lifespan without extending the lifespan.

Nonparametric estimation of mean and covariance functions is important in functional data analysis. We investigate the performance of local linear smoothers for both mean and covariance functions with a general weighing scheme, which includes two commonly used schemes, equal weight per observation (OBS), and equal weight per subject (SUBJ), as two special cases. We provide a comprehensive analysis of their asymptotic properties on a unified platform for all types of sampling plan, be it dense, sparse or neither. Three types of asymptotic properties are investigated in this paper: asymptotic normality, $L^{2}$ convergence and uniform convergence. The asymptotic theories are unified on two aspects: (1) the weighing scheme is very general; (2) the magnitude of the number $N_{i}$ of measurements for the $i$th subject relative to the sample size $n$ can vary freely. Based on the relative order of $N_{i}$ to $n$, functional data are partitioned into three types: non-dense, dense and ultra-dense functional data for the OBS and SUBJ schemes. These two weighing schemes are compared both theoretically and numerically. We also propose a new class of weighing schemes in terms of a mixture of the OBS and SUBJ weights, of which theoretical and numerical performances are examined and compared.

Functional covariates are common in many medical, biodemographic and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study the asymptotic properties of the maximum partial likelihood estimator and establish the asymptotic normality and efficiency of the estimator of the finite-dimensional estimator. Under the framework of reproducing kernel Hilbert space, the estimator of the coefficient function for a functional covariate achieves the minimax optimal rate of convergence under a weighted $L_{2}$-risk. This optimal rate is determined jointly by the censoring scheme, the reproducing kernel and the covariance kernel of the functional covariates. Implementation of the estimation approach and the selection of the smoothing parameter are discussed in detail. The finite sample performance is illustrated by simulated examples and a real application.

The epidemiological importance of the age structure and longevity potential of wild populations of mosquito disease vectors has been known for over 60 years. However, no routine method currently exists that provides reliable insights into the population age dynamics of this medically-important group of insects. In this paper we use a technique originally developed for studying wild fruit fly populations to study the post-capture longevity dynamics in populations of the West Nile virus mosquito Culex pipiens in Greece. This approach, referred to as the captive cohort method, analyzes and interprets the longevity trends in wild-caught Cx. pipiens to infer demographic changes in their field population. Approximately 10 adult females were captured each day from June through November, housed in individual cages in the laboratory, and their remaining longevity recorded. Strong differences were observed in the mean, variation, and extremes of post-capture longevity. Early season (June-July) mosquitoes lived the shortest and late-season the longest with a clear transition period in September. The mean levels of post-capture longevity were quite high at over two months in early season to over 85 days in late season when the vast majority of adults were nulliparous and likely preparing for hibernation. Implications for both basic and epidemiological research on the biodemography of aging in the wild are discussed.

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. These are both examples of functional data, which has become a commonly encountered type of data. Functional data analysis (FDA) encompasses the statistical methodology for such data. Broadly interpreted, FDA deals with the analysis and theory of data that are in the form of functions. This paper provides an overview of FDA, starting with simple statistical notions such as mean and covariance functions, then covering some core techniques, the most popular of which is functional principal component analysis (FPCA). FPCA is an important dimension reduction tool, and in sparse data situations it can be used to impute functional data that are sparsely observed. Other dimension reduction approaches are also discussed. In addition, we review another core technique, functional linear regression, as well as clustering and classification of functional data. Beyond linear and single- or multiple- index methods, we touch upon a few nonlinear approaches that are promising for certain applications. They include additive and other nonlinear functional regression models and models that feature time warping, manifold learning, and empirical differential equations. The paper concludes with a brief discussion of future directions.

Chronic hepatitis B virus (HBV) infection is a major health problem (1,2). Hepatitis B virus e antigen (HBeAg) seroconversion is an important goal of antiviral treatment (3). Spontaneous HBeAg seroconversion in children is associated with a relatively uneventful course and fewer events of HBeAg-negative hepatitis (4). Persistent HBeAg positivity beyond the third to fourth decades of life in chronic HBV–infected subjects is associated with a higher risk of HBV-related liver cirrhosis and hepatocellular carcinoma (5,6). Various host and viral factors associated with the spontaneous HBeAg seroconversion process have been mentioned (7–10). Some of these host factors such as earlier puberty onset in boys and the high interleukin-12 production genotype are associated with higher peak ALT levels before HBeAg seroconversion and predict earlier onset of spontaneous HBeAg seroconversion (9,10). The flare of serum ALT levels in subjects with chronic HBV infection indicates the breakdown of immune tolerance and entry into the immune clearance/inflammatory phase. Some finish the seroconversion after a dramatic flare of serum ALT levels and others with only mild elevation before the seroconversion. A lower serum ALT level cutoff in subjects with chronic liver disease may enhance the detection sensitivity and specificity of immune clearance/inflammatory phase occurrence (11). The present study investigated the cutoff of inflammatory phase and the longitudinal profiling of serial serum ALT levels based on a long-term prospective cohort design study from childhood to adulthood in determining the significant cutoff thresholds to predict spontaneous HBeAg seroconversion by a sophisticated statistical procedure.

We examined experimentally the relationship between the period of unhealthy life and longevity in the medfly by using the first sign of supine behavior (upside down; immobile) in medflies as an indication of their poor health and by altering cohort longevity through dietary manipulations. Our main findings included the following: i) for longer lived medflies it was more likely to observe the supine behavior while shorter lived flies would more likely die before exhibiting the supine behavior. ii) males have similar total life expectancy as females but a longer healthy life expectancy; iii) the total number of healthy days, spent in the pre-supine period, and the amount of healthy life span as a fraction of the total lifespan varied with both sex and diet; iv) despite the large difference in longevity between both male and female medflies when reared on sugar-only diets versus on full diets, the differences in the fraction of their lifespans in the disabled state were relatively modest (64 vs 61% in females and 77 vs 72% in males). This finding that there is no significant change in the proportion of the life course in the unhealthy state is consistent with the ‘dynamic equilibrium’ model of healthy aging.

Reproductive data of individual insects are extremely hard to collect under natural conditions, thus the study of research questions related to oviposition has not advanced. Patterns of oviposition are often inferred only indirectly, through monitoring of host infestation, whereas the influence of age structure and several other factors on oviposition remains unknown. Using a new approach, in this article, we live-trapped wild Ceratitis capitata (Wiedemann) (Diptera: Tephritidae) females on the Greek island of Chios during two field seasons. For their remaining lifetime, these females were placed individually in small cages and their daily oviposition was monitored. Reproduction rates between cohorts from different collection dates were then compared. The results showed that in the different captive cohorts the average remaining lifetime and reproduction were highly variable within and between seasons. Multivariate regression analysis showed that the month of capture had a significant effect on captive life span, average daily reproduction, and patterns of egg laying. The effect of year was significant on reproduction, but not on captive life span. These differences between sampling periods probably reflect differences in the availability of hosts and other factors that vary during the season and affect age structure and reproduction. Using a non-parametric generalized additive model, we found a statistically significant correlation between the captive life span and the average daily reproduction. These findings and the experimental approach have several important implications.

We propose stringing, a class of methods where one views high-dimensional observations as functional data. Stringing takes advantage of the high dimension by representing such data as discretized and noisy observations that originate from a hidden smooth stochastic process. Assuming that the observations result from scrambling the original ordering of the observations of the process, stringing reorders the components of the high-dimensional vectors, followed by transforming the high-dimensional vector observations into functional data. Established techniques from functional data analysis can be applied for further statistical analysis once an underlying stochastic process and the corresponding random trajectory for each subject have been identified. Stringing of high-dimensional data is implemented with distance-based metric multidimensional scaling, mapping high-dimensional data to locations on a real interval, such that predictors that are close in a suitable sample metric also are located close to each...

Variation in lifespan may be linked to geographic factors. Although latitudinal variation in lifespan has been studied for a number of species, altitude variation has received much less attention, particularly in insects. We measured the lifespan of different populations of the Natal fruit fly, Ceratitis rosa, along an altitudinal cline. For the different populations, we first measured the residual longevity of wild flies by captive cohort approach and compared the F1 generation from the same populations. We showed an increase in lifespan with higher altitude for a part of the data obtained. For the field-collected flies (F0) the average remaining lifespan increased monotonically with altitude for males but not for females. For the F1 generation, the longevity of both males and females of the highest-altitude population was longer than for the two other lower-altitude populations. This relationship between altitude and lifespan may be explained by the effects of temperature on reproduction. Reproductive schedules in insects are linked to temperature: lower temperature, which is characteristic of high-altitude sites, generally slows down reproduction. Because of a strong trade-off between reproduction and longevity, we therefore observed a longer lifespan for the high-altitude populations. (Resume d'auteur)

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King, a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, λ(t|x) = exp{ψ(x)}λ(0)(t). The estimator, ψ̂(x), reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consistent and semiparametrically efficient for linear functionals of ψ(x). Moreover, Breslow-type estimation of the cumulative baseline hazard function, using the proposed estimator ψ̂(x), is proved to be efficient. The asymptotic bias and variance are derived under regularity conditions. Computation of the estimator involves an iterative but simple algorithm. Extensive simulation studies provide evidence supporting the theory. The method is illustrated with the Stanford heart transplant data set. The proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficient estimation of the slope parameter. This article has the supplementary materials online.

In polygynous insect species, male reproductive success is directly related to lifetime mating success. However, the costs for males of sexual activities such as courting, signaling, and mating are largely unknown. We studied the cost of sexual activities in male Mediterranean fruit flies, Ceratitis capitata (Tephritidae), a polygynous lekking species, by keeping cohorts of individual male flies under relaxed crowding conditions in the laboratory. We used 5 cohorts among which individuals differed in their opportunities to interact with con-specifics and recorded life span, and in one treatment, mating rate. We found that males kept singly lived more than twice as long as males that interacted intensively with mature virgin females, while male–male interactions caused a smaller reduction in longevity. Because longevity of males that could court but not mate was not significantly different from those that could court and mate, we conclude that courting (not mating) was responsible for the observed longevity reduction. Moreover, we detected high variability in male mating success, when 5 virgin females were offered daily. In contrast to the cohort level, individual males that mated at a high rate lived relatively long, thus indicating heterogeneity in quality or sexual strategy among males.

This study was concerned with the impact of different levels of artificial impairment (leg amputations) on male and female survival and female reproduction in the Mexican fruit fly, Anastrepha ludens . We monitored the demographic responses in a total of 100 flies of each sex that were maintained individually in 4 × 4 × 10 cm cages and subject to 1-of-11 different leg amputations (plus intact control) including cohorts in which either one front, one middle or one rear leg was severed (3 cohorts total), in which two legs were severed in different front–middle–rear combinations (6 cohorts total), or in which the two middle and one additional leg were severed (2 cohorts total). The two main findings were that: (i) although the effects on mortality of impairments were sex-specific, no universal patterns emerged that applied to either sex; and (ii) reproduction occurred in all cohorts of impaired females. Moderately-impaired flies (e.g. amputation of a single middle leg) laid nearly as many eggs in their lifetime as did intact controls. However, severely impaired flies (i.e. 3 legs amputated) laid significantly fewer eggs.

Several studies have shown that resveratrol can extend lifespan in yeast, worm, fruit fly and short-lived fish, as well as mice under a high-fat diet, probably acting through molecular pathways similar to dietary restriction. However, the putative prolongevity effect of resveratrol has not been observed in other studies. To evaluate the robustness of the prolongevity effects of resveratrol, we designed a nutritional study to address the question, Under what nutritional conditions does resveratrol affect lifespan and reproduction? We fed 2592 individual tephritid fruit fly of the species, Anastrepha ludens, 24 diets of different sugar:yeast ratios supplemented with or without 100 μM resveratrol. Sex-specific survival and daily egg laying in females were recorded. Resveratrol was found to have no or little effect on lifespan of males in all the treatments, as well as on lifespan and reproduction of females. Only under one diet combination, resveratrol appears to increase mean lifespan of females but not at a statistically significant level after multiple comparison adjustment. These findings suggest that the prolongevity effect of resveratrol is at most limited to a narrow range of dietary composition and calorie content in this fruit fly. Coupled with a recent study indicating that resveratrol does not extend lifespan of mice fed the standard diet, our findings further question the ability of resveratrol to increase lifespan in organisms under normal conditions.

Fruit-feeding butterflies can experience a more nutrient rich adult diet than nectar-feeding species, and can be expected to use these nutrients for egg production. Here we compare life span, and reproduction parameters of wild-caught females of large and long-lived species on either a sucrose or a mashed banana diet. With small sample sizes per species, but rich longitudinal data for each individual, we examined the longitudinal reproduction pattern, egg size and hatchability of these butterflies in captivity. Diet significantly affected mortality in captivity in a time-dependent manner. On average, we found that butterflies fed mashed banana laid 1.855 times more eggs than those fed sugar. They laid significantly more eggs when they laid and conserved egg size with age while butterflies fed sucrose showed significantly declining egg sizes. Egg hatchability was not significantly affected by diet. Long pre-oviposition periods, significantly smaller first eggs, and absence of age at capture effects on intensity of reproduction indicate low reproduction rates in the field that are due to low food availability. With our small sample sizes, we did not detect significant differences between the species in their response to the diet treatments.

Fruit-feeding butterflies are among the longest lived Lepidoptera. While the use of pollen-derived amino acids by Heliconius butterflies has been interpreted as important for the evolution of extended lifespans, very little is known about the life-history consequences of frugivory. This issue is addressed by investigating effects of four adult diets (sugar, sugar with amino acids, banana, and moistened banana) on lifespan and reproduction in the fruit-feeding butterfly Charaxes fulvescens Aurivillius (Lepidoptera: Nymphalidae). Female butterflies were collected from Kibale National Park, Uganda, and kept individually in cages near their natural habitat and data were collected on lifespan, oviposition, and hatching of eggs. Lifespan in captivity was longer for the sugar and the amino acid cohort, than for the banana cohorts. The longitudinal pattern of oviposition was erratic, with many days without oviposition and few periods with high numbers of eggs laid. Butterflies typically did not lay eggs during their 1st week in captivity and the length of the period between capture and first reproduction was significantly shorter for butterflies fed moistened banana. The length of the reproduction period (first reproduction–last reproduction in captivity) and the reproduction rate (total number of eggs/length of the reproduction period) did not differ significantly between the diet treatments. Those fed with amino acid and moistened banana had significantly higher egg hatchability than those fed with sugar and banana. We found no evidence for a lifespan cost of reproduction. Our results show that (1) female C. fulvescens can use amino acids in their diet for laying fertile eggs, (2) more wing-wear does correlate with lower survival in captivity (indicating aging in the wild), but not with intensity of reproduction (providing no evidence for reproductive aging), and (3) fruit-feeding butterflies may be dietary restricted in the field.

Although it is widely known that dietary restriction (DR) not only extends the longevity of a wide range of species but also reduces their reproductive output, the interrelationship of DR, longevity extension and reproduction is not well understood in any organism. Here we address the question: 'Under what nutritional conditions do the longevity-enhancing effects resulting from food restriction either counteract, complement or reinforce the mortality costs of reproduction? To answer this question we designed a fine-grained DR study involving 4800 individuals of the tephritid fruit fly, Anastrepha ludens, in which we measured sex-specific survival and daily reproduction in females in each of 20 different treatments (sugar : yeast ratios) plus 4 starvation controls. The database generated from this 3-year study consisted of approximately 100 000 life-days for each sex and 750 000 eggs distributed over the reproductive lives of 2400 females. The fertility and longevity-extending responses were used to create contour maps (X-Y grid) that show the demographic responses (Z-axis) across dietary gradients that range from complete starvation to both ad libitum sugar-only and ad libitum standard diet (3 : 1 sugar : yeast). The topographic perspectives reveal demographic equivalencies along nutritional gradients, differences in the graded responses of males and females, egg production costs that are sensitive to the interaction of food amounts and constituents, and orthogonal contours (equivalencies in longevity or reproduction) representing demographic thresholds related to both caloric content and sugar : yeast ratios. In general, the finding that lifespan and reproductive maxima occur at much different nutritional coordinates poses a major challenge for the use of food restriction (or a mimetic) in humans to improve health and extend longevity in humans.

In clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients.

The main purpose of this study was to test the hypotheses that major changes in age structure occur in wild populations of the Mediterranean fruit fly (medfly) and that a substantial fraction of individuals survive to middle age and beyond (> 3–4 weeks). We thus brought reference life tables and deconvolution models to bear on medfly mortality data gathered from a 3-year study of field-captured individuals that were monitored in the laboratory. The average time-to-death of captured females differed between sampling dates by 23.9, 22.7, and 37.0 days in the 2003, 2004, and 2005 field seasons, respectively. These shifts in average times-to-death provided evidence of changes in population age structure. Estimates indicated that middle-aged medflies (> 30 days) were common in the population. A surprise in the study was the extraordinary longevity observed in field-captured medflies. For example, 19 captured females but no reference females survived in the laboratory for 140 days or more, and 6 captured but no reference males survived in the laboratory for 170 days or more. This paper advances the study of aging in the wild by introducing a new method for estimating age structure in insect populations, demonstrating that major changes in age structure occur in field populations of insects, showing that middle-aged individuals are common in the wild, and revealing the extraordinary lifespans of wild-caught individuals due to their early life experience in the field.

In this article, we introduce dynamical correlation, a new method for quantifying synchrony between 2 variables with intensive longitudinal data. Dynamical correlation is a functional data analysis technique developed to measure the similarity of 2 curves. It has advantages over existing methods for studying synchrony, such as multilevel modeling. In particular, it is a nonparametric approach that does not require a prespecified functional form, and it places no assumption on homogeneity of the sample. Dynamical correlation can be easily estimated with irregularly spaced observations and tested to draw population-level inferences. We illustrate this flexible statistical technique with a simulation example and empirical data from an experiment examining interpersonal physiological synchrony between romantic partners. We discuss the advantages and limitations of the method, and how it can be extended and applied in psychological research. We also provide a set of R code for other researchers to estimate and test for dynamical correlation. (PsycINFO Database Record

Despite the importance of trauma in healthspan and lifespan in humans as well as in non-human species, with one important exception the literature in both gerontology and ecology contains virtually no experimental demographic studies concerned with trauma in any species. We used dietary manipulation [full diet (F) versus sugar-only (S)] to produce four levels of frailty in 55-day old tephritid fruit flies (Anastrepha ludens) that were then subject to the trauma of cage transfer stress (n = 900/sex in each of the 4 treatments). The key results included the following: (1) there is a trauma effect caused by the transfer that depends on previous diet before transfer, new diet after transfer and gender of the fly; (2) males are more vulnerable than females; (3) if initial diet was F, flies are relatively immune against the trauma, and the subsequent diet (F or S) does not matter; (4) however if initial diet was S, then the effect of the trauma depends largely on the diet after the transfer; (5) flies transferred from S to F diets do very well in terms of remaining longevity (i.e. greatest remaining longevity), while flies transferred from S to S diet do poorly (i.e. shortest remaining longevity). We discuss both the strengths and weaknesses of this study and implications of the results.

We monitored survival and reproduction of 1000 individuals of Caenorhabditis elegans wild type (N2) and 800 individuals of clk-1 and daf-2, and used biodemographic analysis to address fitness as the integrative consequence of the entire age-specific schedules of survival and reproduction. Relative to N2, the mutants clk-1 and daf-2 extended average life span by 27% and 111%, respectively, but reduced net reproductive rate by 44% and 18%. The net result of differences in survival and fertility was a significant differential in fitness, with both clk-1 (lambda = 2.74) and daf-2 (lambda = 3.78) at a disadvantage relative to N2 (lambda = 3.85). Demographic life table response experiment (LTRE) analysis revealed that the fitness differentials were due to negative effects in mutants on reproduction in the first 6-7 days of life. Fitness costs in clk-1 and daf-2 of C. elegans are consistent with the theory of antagonistic pleiotropy for the evolution of senescence.

Parametric bootstrap methods for the construction of confidence intervals for the effective dose at level α(EDα) under the probit model for the dose-response relationship are investigated. The standard maximum likelihood confidence intervals and percentile, centered percentile, studentized, bias corrected and better bias corrected bootstrap methods are compared in a simulation with 1000 Monte Carlo runs and 1000 bootstrap samples. Among the bootstrap methods, studentized and centered percentile methods are found to behave unfavorably with respect to observed coverage probability, whereas the bias corrected and better bias corrected bootstrap sometimes improve on the maximum likelihood method. The maximum likelihood method yielded very mixed results, but in our simulation none of the currently available bootstrap methods improved uniformly on this standard method. The methods are illustrated by an application to a bioassay.

Although variation in mortality is considered by virtually all vector-borne disease specialists to be one of the most important determinants of an arthropod's capacity to transmit pathogens, the operational assumption often is that insect vector mortality is independent of age. Acceptance of the non-senescence assumption leads to the erroneous conclusion that mosquito age is unimportant, results in misleading predictions regarding disease reductions after vector control, and represses study of other aspects of mosquito biology that change with age. We brought large-scale laboratory life table techniques (N > 100,000) to bear on the question of age-dependent mortality in the mosquito vector of dengue virus, Aedes aegypti. Mortality was highly age dependent in both sexes. Mortality was low at young ages (< 10 days old), steadily increased at middle ages, and decelerated at older ages. A newly derived age-dependent model of pathogen transmission shows the importance of young mosquitoes and population age structure to transmission dynamics. Departure from the age-independent mortality paradigm encourages research on overlooked complexities in mosquito biology, the need for innovative methods to study mosquito population dynamics, and the need to study age-dependent changes for an accurate understanding of mosquito biology and pathogen transmission.

The maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies. Random effects in the longitudinal process are often used to model the survival times through a proportional hazards model, and this invokes an EM algorithm to search for the maximum likelihood estimates (MLEs). Several intriguing issues are examined here, including the robustness of the MLEs against departure from the normal random effects assumption, and difficulties with the profile likelihood approach to provide reliable estimates for the standard error of the MLEs. We provide insights into the robustness property and suggest to overcome the difficulty of reliable estimates for the standard errors by using bootstrap procedures. Numerical studies and data analysis illustrate our points.

Age of sexual maturity, daily and lifetime reproductive rates, and life span were recorded in a laboratory cohort of Mexican fruit flies consisting of over 1100 females maintained individually. The results revealed that, relative to the medfly, the Mexfly is slower maturing (14 vs 17 days), more fecund (1400 vs 650-1100 eggs/female), and longer lived (50 vs 35 days). The results reinforced the generality of several earlier findings on the medfly including the deceleration of mortality at older ages and the weakness of the correlation between the rate of egg laying at early ages and both subsequent reproduction and remaining longevity. Discussion includes perspectives on the role of artificial selection in shaping the demographic traits of the mass-reared strain of Mexfly used in this study, as well as the overall significance of large scale biodemographic studies in understanding aging and longevity.

SUMMARY The accelerated failure time model is an attractive alternative to the Cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates. Several complications arise when the covariates are measured intermittently at different time points for different subjects, possibly with measurement errors, or measurements are not available after the failure time. Joint modelling of the failure time and longitudinal data offers a solution to such complications. We explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors. The procedure is based on maximising the joint likelihood function with random effects treated as missing data. A Monte Carlo EM algorithm is used to estimate all the unknown parameters, including the unknown baseline hazard function. The performance of the proposed procedure is checked in simulation studies. A case study of reproductive egg-laying data for female Mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure.

We propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data. The method aims at irregularly spaced longitudinal data, where the number of repeated measurements available per subject is small. In contrast, classical functional data analysis requires a large number of regularly spaced measurements per subject. We assume that the repeated measurements are located randomly with a random number of repetitions for each subject and are determined by an underlying smooth random (subject-specific) trajectory plus measurement errors. Basic elements of our approach are the parsimonious estimation of the covariance structure and mean function of the trajectories, and the estimation of the variance of the measurement errors. The eigenfunction basis is estimated from the data, and functional principal components score estimates are obtained by a conditioning step. This conditional estimation method is conceptually simple and straightforward to implement...

Summary We address the problem of establishing a survival schedule for wild populations. A demographic key identity is established, leading to a method whereby age-specific survival and mortality can be deduced from a marked cohort life table established for individuals that are randomly sampled at unknown age and marked, with subsequent recording of time-to-death. This identity permits the construction of life tables from data where the birth date of subjects is unknown. An analogous key identity is established for the continuous case in which the survival schedule of the wild population is related to the density of the survival distribution in the marked cohort. These identities are explored for both life tables and continuous lifetime data. For the continuous case, they are implemented with statistical methods using non-parametric density estimation methods to obtain flexible estimates for the unknown survival distribution of the wild population. The analytical model provided here serves as a starting point to develop more complex models for residual demography, i.e. models for estimating survival of wild populations in which age-at-entry is unknown and using remaining information in randomly encountered individuals. This is a first step towards a broad new concept of 'expressed demographic information content of marked or captured individuals'.

We consider estimates for functional canonical correlations and canonical weight functions. Four computational methods for the estimation of functional canonical correlation and canonical weight functions are proposed and compared, including one which is a slight variation of the spline method proposed by Leurgans et al. (J. Roy. Statist. Soc. Ser. B 55 (1993) 725). We propose dimension reduction and dimension augmentation procedures to address the dimensionality problems of functional canonical analysis (FCA) that are associated with computational break-down. Cross-validation is used for the automatic selection of tuning parameters, based on the minimax property of FCA. This allows to estimate several canonical correlations and canonical weight functions simultaneously and reasonably well as we show in simulations. The proposed estimation methods are compared and their use is demonstrated with medfly mortality data.

SummaryWe propose a class of semiparametric functional regression models to describe the influence of vector-valued covariates on a sample of response curves. Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single-index models that include unknown smooth link and variance functions. The parametric components of the single-index models are estimated via quasi-score estimating equations with link and variance functions being estimated nonparametrically. We obtain several basic asymptotic results. The functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female Mediterranean fruit-flies (medflies).

We study the extension of canonical correlation from pairs of random vectors to the case where a data sample consists of pairs of square integrable stochastic processes. Basic questions concerning the definition and existence of functional canonical correlation are addressed and sufficient criteria for the existence of functional canonical correlation are presented. Various properties of functional canonical analysis are discussed. We consider a canonical decomposition, in which the original processes are approximated by means of their canonical components.

Hypotheses exploring the influence of dietary conditions on the life history trade-off between survival and reproductive success are extensively tested in female insects, but are rarely explored in males. Here, the impact of dietary quality and female access on age-specific reproduction and survival of male Mexican fruit flies, Anastrepha ludens Loew (Diptera: Tephritidae), are examined. There is a clear cost of female access for males with access to dietary protein, measurable as a decrease in life expectancy, which is further influenced by the age when females are introduced. A protein deficient diet reduces the lifespan benefit of virginity and masks the detrimental effect of female access on male life expectancy. Dietary protein is not necessary for reproductive success, but access to protein at eclosion improves the lifetime reproductive success of males compared to when it is delayed. Overall, reproductive success diminishes as the male flies age, regardless of the dietary conditions, providing evidence for reproductive senescence in males. Delaying the males’ access to a protein source fails to influence the negative effect of age on reproductive ability. Because age specific reproductive rates decline with age, regardless of diet, male fitness does not benefit from lifespan extension. Therefore, males can be expected to allocate available resources towards reproductive effort in favour of extended lifespan, regardless of mate and protein availability.

The purpose of this study was to investigate medfly longevity and reproduction across a broad spectrum of diet restriction using a protocol similar to those applied in most rodent studies. Age-specific reproduction and age of death were monitored for 1200 adult males and 1200 females, each individually maintained on one of 12 diets from ad libitum to 30% of ad libitum. Diet was provided in a fixed volume of solution that was fully consumed each day, ensuring control of total nutrient consumption for every fly. Contrary to expectation and precedence, increased longevity was not observed at any level of diet restriction. Among females, reproduction continued across all diet levels despite the cost in terms of increased mortality. Among males, life expectancy exceeded that of females at most diet levels. However, in both sexes, mortality increased more sharply and the pattern of survival changed abruptly once the diet level fell to 50% of ad libitum or below, even though the energetic demands of egg production has no obvious counterpart in males. We believe that a more complete picture of the life table response to dietary restriction will emerge when studies are conducted on a wider range of species and include both sexes, more levels of diet, and the opportunity for mating and reproduction.

Summary 1. Inasmuch as virtually all studies on mortality and reproduction in insects are conducted under conditions in which food availability is constant, little is known about the demographic response of insects to variable food environments. For example, it is not known if and to what extent the life expectancy of insects subjected to shortages of high-quality food will increase and/or whether this increase is associated with major decreases in lifetime reproduction. 2. Therefore cohorts of 100 individual female medflies were subjected to different sets of conditions of protein availability (interspersed with sugar-only diets) including ad libitum sugar-only (no protein), ad libitum protein and full (protein) diet either every 2nd, 4th, 6th, 11th or 21st day, as well as two lag-treatments (1 day full diet followed by 30 days sugar-only, followed by one of two cyclical treatments). 3. Both life expectancy and lifetime reproduction were strongly affected by specific treatments. Specifically (i) mortality was inversely related to frequency of protein availability whereas lifetime reproduction was directly related; (ii) distinct cycles in reproduction began to appear when food pulse cycles were as short as every 4 days. However, egg-laying peaks and troughs were particularly pronounced in the 10- and 20-day food pulse cycles; (iii) the peak and trough levels were inversely related to cycle length; and (iv) the within-cycle height was independent of cycle length, occurring 4 days after protein food was made available to the cohort whether the cycle length was 5, 10 or 20 days. 4. The results shed new light on the within- and between-cycle and lifetime dynamics of reproduction when insects are subjected to variable food environments and indicate that medfly females track food level very closely.

Density and failure rate estimation are valuable tools to assess and explore the occurrence and timing of failures in reliability and quality control. This article focuses on nonparametric approaches such as histograms, the kernel method, and other smoothing procedures. Nonparametric density and failure rate estimation is particularly valuable for exploratory data analysis and in situations where available information is insufficient to specify a parametric model, as these methods “let the data speak for themselves”, and no assumptions are needed beyond smoothness of the functions to be estimated. Issues specific for nonparametric approaches are finite bias behavior and choice of the necessary smoothing parameter. For failure rate estimation, available data are sometimes incompletely observed (censored) or available in aggregated form only, necessitating appropriate adjustments. Shape restrictions such as increasing failure rate (IFR) are also occasionally of interest in reliability. Keywords: Aalen estimator; failure rate; hazard rate; histogram; kernel estimator; local linear fitting; nonparametric estimation; smoothing

The nonparametric approach to estimate hazard rates for lifetime data is flexible, model-free, and data-driven. No shape assumption is imposed other than that the hazard function is a smooth function. Such an approach typically involves smoothing of an initial hazard estimate, with arbitrary choice of smoother. We describe methods for grouped lifetime data observed at certain time intervals and for continuously observed lifetime data. There are some intrinsic differences between the smoothing approaches for these two types of data. More specifically, smoothing an initial hazard estimate based on the life table is adopted for grouped lifetime data; while for continuous data, smoothing is employed to increments of the Nelson–Aalen cumulative hazard estimate aiming at the derivative of the cumulative hazard function. A few nonparametric hazard regression methods are also discussed. Keywords: life table; Nelson–Aalen estimator; nonparametric smoothing methods; bandwidth choices; boundary effects; hazard regression

Ongoing variability in neural signaling is an intrinsic property of the brain. Often this variability is considered to be noise and ignored. However, an alternative view is that this variability is fundamental to perception and cognition and may be particularly important in decision-making. Here, we show that a momentary measure of occipital alpha-band power (8–13 Hz) predicts choices about where human participants will focus spatial attention on a trial-by-trial basis. This finding provides evidence for a mechanistic account of decision-making by demonstrating that ongoing neural activity biases voluntary decisions about where to attend within a given moment.

Sliced inverse regression (Duan and Li [Ann. Statist. 19 (1991) 505-530], Li [J. Amer. Statist. Assoc. 86 (1991) 316-342]) is an appealing dimension reduction method for regression models with multivariate covariates. It has been extended by Ferr\'{e} and Yao [Statistics 37 (2003) 475-488, Statist. Sinica 15 (2005) 665-683] and Hsing and Ren [Ann. Statist. 37 (2009) 726-755] to functional covariates where the whole trajectories of random functional covariates are completely observed. The focus of this paper is to develop sliced inverse regression for intermittently and sparsely measured longitudinal covariates. We develop asymptotic theory for the new procedure and show, under some regularity conditions, that the estimated directions attain the optimal rate of convergence. Simulation studies and data analysis are also provided to demonstrate the performance of our method., Comment: Published in at http://dx.doi.org/10.1214/13-AOS1193 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org). With Corrections