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Abstract Background In sub-Saharan Africa (SSA), malaria caused by Plasmodium falciparum has historically been a major contributor to morbidity and mortality. Recent reports indicate a pronounced decline in infection and disease rates which are commonly ascribed to large-scale bed net programmes and improved case management. However, the decline has also occurred in areas with limited or no intervention. The present study assessed temporal changes in Anopheline populations in two highly malaria-endemic communities of NE Tanzania during the period 1998-2009. Methods Between 1998 and 2001 (1st period) and between 2003 and 2009 (2nd period), mosquitoes were collected weekly in 50 households using CDC light traps. Data on rainfall were obtained from the nearby climate station and were used to analyze the association between monthly rainfall and malaria mosquito populations. Results The average number of Anopheles gambiae and Anopheles funestus per trap decreased by 76.8% and 55.3%, respectively over the 1st period, and by 99.7% and 99.8% over the 2nd period. During the last year of sampling (2009), the use of 2368 traps produced a total of only 14 Anopheline mosquitoes. With the exception of the decline in An. gambiae during the 1st period, the results did not reveal any statistical association between mean trend in monthly rainfall and declining malaria vector populations. Conclusion A longitudinal decline in the density of malaria mosquito vectors was seen during both study periods despite the absence of organized vector control. Part of the decline could be associated with changes in the pattern of monthly rainfall, but other factors may also contribute to the dramatic downward trend. A similar decline in malaria vector densities could contribute to the decrease in levels of malaria infection reported from many parts of SSA.

Abstract Background Malaria due to Plasmodium falciparum is the leading cause of morbidity and mortality in Tanzania. According to health statistics, malaria accounts for about 30% and 15% of hospital admissions and deaths, respectively. The risk of P. falciparum infection varies across the country. This study describes the spatial variation and socio-economic determinants of P. falciparum infection in northeastern Tanzania. Methods The study was conducted in 14 villages located in highland, lowland and urban areas of Korogwe district. Four cross-sectional malaria surveys involving individuals aged 0-19 years were conducted during short (Nov-Dec) and long (May-Jun) rainy seasons from November 2005 to June 2007. Household socio-economic status (SES) data were collected between Jan-April 2006 and household's geographical positions were collected using hand-held geographical positioning system (GPS) unit. The effects of risk factors were determined using generalized estimating equation and spatial risk of P. falciparum infection was modelled using a kernel (non-parametric) method. Results There was a significant spatial variation of P. falciparum infection, and urban areas were at lower risk. Adjusting for covariates, high risk of P. falciparum infection was identified in rural areas of lowland and highland. Bed net coverage levels were independently associated with reduced risk of P. falciparum by 19.1% (95%CI: 8.9-28.2, p < 0.001) and by 39.3% (95%CI: 28.9-48.2, p < 0.001) in households with low and high coverage, respectively, compared to those without bed nets. Households with moderate and lower SES had risk of infection higher than 60% compared to those with higher SES; while inhabitants of houses built of mud walls were at 15.5% (95%CI: 0.1 - 33.3, p < 0.048) higher risk compared to those living in houses built by bricks. Individuals in houses with thatched roof had an excess risk of 17.3% (95%CI: 4.1 - 32.2, p < 0.009) compared to those living in houses roofed with iron sheet. Conclusions There was high spatial variation of risk of P. falciparum infection and urban area was at the lowest risk. High bed net coverage, better SES and good housing were among the important risk factors associated with low risk of P. falciparum infection.

Abstract Background In Sub-Sahara Africa, malaria due to Plasmodium falciparum is the main cause of ill health. Evaluation of malaria interventions, such as drugs and vaccines depends on clinical definition of the disease, which is still a challenge due to lack of distinct malaria specific clinical features. Parasite threshold is used in definition of clinical malaria in evaluation of interventions. This however, is likely to be influenced by other factors such as transmission intensity as well as individual level of immunity against malaria. Methods This paper describes step function and dose response model with threshold parameter as a tool for estimation of parasite threshold for onset of malaria fever in highlands (low transmission) and lowlands (high transmission intensity) strata. These models were fitted using logistic regression stratified by strata and age groups (0-1, 2-3, 4-5, 6-9, and 10-19 years). Dose response model was further extended to fit all age groups combined in each stratum. Sub-sampling bootstrap was used to compute confidence intervals. Cross-sectional and passive case detection data from Korogwe district, north eastern Tanzania were used. Results Dose response model was better in the estimation of parasite thresholds. Parasite thresholds (scale = log parasite/μL) were high in lowlands than in highlands. In the lowlands, children in age group 4-5 years had the highest parasite threshold (8.73) while individuals aged 10-19 years had the lowest (6.81). In the highlands, children aged 0-1 years had the highest threshold (7.12) and those aged 10-19 years had the lowest (4.62). Regression analysis with all ages combined showed similar pattern of thresholds in both strata, whereby, in the lowlands the threshold was highest in age group 2-5 years and lowest in older individuals, while in the highlands was highest in age group 0-1 and decreased with increased age. The sensitivity of parasite threshold by age group ranged from 64%-74% in the lowlands and 67%-97% in the highlands; while specificity ranged between 67%-90% in the lowlands and 37%-73% in the highlands. Conclusion Dose response model with threshold parameter can be used to estimate parasite threshold associated with malaria fever onset. Parasite threshold were lower in older individuals and in low malaria transmission area.

We propose to model the cause-specific cumulative incidence function of multivariate competing risks data using a random effects model that allows for within-cluster dependence of both risk and timing. The model contains parameters that makes it possible to assess how the two are connected, e.g. if high-risk is related to early onset. Under the proposed model, the cumulative incidences of all failure causes are modeled and all cause-specific and cross-cause associations specified. Consequently, left-truncation and right-censoring are easily dealt with. The proposed model is assessed using simulation studies and applied in analysis of Danish register-based family data on breast cancer., (© The Author 2018. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Hip fracture patients often have comorbid conditions. We investigated whether the combination of comorbidity and hip fracture could explain the previously observed excess mortality among hip fracture patients as compared with the general population. Using a population-based matched study design with 38,126 Norwegian women who suffered a hip fracture during the period 2009-2015 and the same number of women in a matched comparison cohort, we matched participants on prefracture comorbidity, age, and education. We estimated relative survival and additive and multiplicative comorbidity-hip fracture interactions. An additive comorbidity-hip fracture interaction of 4 or 9 additional deaths per 100 patients, depending on Charlson Comorbidity Index (CCI) score, was observed 1 year after hip fracture. Among women with a CCI score of ≥3, 15 additional deaths per 100 patients were observed; of these, 9 deaths could be attributed to the interaction and 6 to the hip fracture per se. On the relative scale, we observed increasing heterogeneity in survival by comorbidity over time; survival was reduced by 39% after 6 years among patients with a CCI score of ≥3, while among women with no comorbidity, survival was reduced by 17% (hip fracture vs. no hip fracture). In summary, prefracture comorbidity was associated with short-term absolute excess mortality and long-term relative excess mortality.

The cumulative incidence function quantifies the probability of failure over time due to a specific cause for competing risks data. The generalized semiparametric regression models for the cumulative incidence functions with missing covariates are investigated. The effects of some covariates are modeled as non-parametric functions of time while others are modeled as parametric functions of time. Different link functions can be selected to add flexibility in modeling the cumulative incidence functions. The estimation procedures based on the direct binomial regression and the inverse probability weighting of complete cases are developed. This approach modifies the full data weighted least squares equations by weighting the contributions of observed members through the inverses of estimated sampling probabilities which depend on the censoring status and the event types among other subject characteristics. The asymptotic properties of the proposed estimators are established. The finite-sample performances of the proposed estimators and their relative efficiencies under different two-phase sampling designs are examined in simulations. The methods are applied to analyze data from the RV144 vaccine efficacy trial to investigate the associations of immune response biomarkers with the cumulative incidence of HIV-1 infection.

High-dimensional regression has become an increasingly important topic for many research fields. For example, biomedical research generates an increasing amount of data to characterize patients' bio-profiles (e.g. from a genomic high-throughput assay). The increasing complexity in the characterization of patients' bio-profiles is added to the complexity related to the prolonged follow-up of patients with the registration of the occurrence of possible adverse events. This information may offer useful insight into disease dynamics and in identifying subset of patients with worse prognosis and better response to the therapy. Although in the last years the number of contributions for coping with high and ultra-high-dimensional data in standard survival analysis have increased (Witten and Tibshirani, 2010. Survival analysis with high-dimensional covariates. Statistical Methods in Medical Research 19: (1), 29-51), the research regarding competing risks is less developed (Binder and others, 2009. Boosting for high-dimensional time-to-event data with competing risks. Bioinformatics 25: (7), 890-896). The aim of this work is to consider how to do penalized regression in the presence of competing events. The direct binomial regression model of Scheike and others (2008. Predicting cumulative incidence probability by direct binomial regression. Biometrika 95: (1), 205-220) is reformulated in a penalized framework to possibly fit a sparse regression model. The developed approach is easily implementable using existing high-performance software to do penalized regression. Results from simulation studies are presented together with an application to genomic data when the endpoint is progression-free survival. An R function is provided to perform regularized competing risks regression according to the binomial model in the package timereg (Scheike and Martinussen, 2006. Dynamic Regression models for survival data New York: Springer), available through CRAN., (© The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Twin and family data provide a key source for evaluating inheritance of specific diseases. A standard analysis of such data typically involves the computation of prevalences and different concordance measures such as the casewise concordance, that is the probability that one twin has the disease given that the co-twin has the disease. Most diseases have a varying age-of-onset that will lead to age-specific prevalence. Typically, this aspect is not considered, and this may lead to severe bias as well as make it very unclear exactly what population quantities that we are estimating. In addition, one will typically need to deal with censoring in the data, that is the fact that we for some subjects only know that they are alive at a specific age without having the disease. These subjects needs to be considered age specifically, and clearly if they are young there is still a risk that they will develop the disease. The aim of this contribution is to show that the standard casewise concordance and standard prevalence estimators do not work in general for age-of-onset data. We show how one can in fact do something easy and simple even with censored data. The key is to take age into account when analysing such data.

The cross-odds ratio is defined as the ratio of the conditional odds of the occurrence of one cause-specific event for one subject given the occurrence of the same or a different cause-specific event for another subject in the same cluster over the unconditional odds of occurrence of the cause-specific event. It is a measure of the association between the correlated cause-specific failure times within a cluster. The joint cumulative incidence function can be expressed as a function of the marginal cumulative incidence functions and the cross-odds ratio. Assuming that the marginal cumulative incidence functions follow a generalized semiparametric model, this paper studies the parametric regression modeling of the cross-odds ratio. A set of estimating equations are proposed for the unknown parameters and the asymptotic properties of the estimators are explored. Non-parametric estimation of the cross-odds ratio is also discussed. The proposed procedures are applied to the Danish twin data to model the associations between twins in their times to natural menopause and to investigate whether the association differs among monozygotic and dizygotic twins and how these associations have changed over time.

An additive hazards model may be used to quantify the effect of genetic and environmental predictors on flowering of sugar beet plants recorded as data-grouped time-to-event data. Estimated predictor effects have an intuitive interpretation rooted in the underlying time dynamics of the flowering process. However, agricultural experiments are often designed using several plots containing a large number of plants that are subsequently being monitored. In this article, we consider an additive hazards model with an additional plot structure induced by latent shared frailty variables. This approach enables us to derive a method to assess the quality of predictors in terms of how much plot variation they explain. We apply the method to a large data set exploring flowering of sugar beet and conclude that the genetic predictor biotype, which has a strong effect, also explains a substantial amount of the plot variation. The method is also applied to a data set from medical research concerning days to virus positivity of serum samples in AIDS patients., (© 2011, The International Biometric Society.)

In this paper we consider a problem from bone marrow transplant (BMT) studies where there is interest on assessing the effect of haplotype match for donor and patient on the overall survival. The BMT study we consider is based on donors and patients that are genotype matched, and this therefore leads to a missing data problem. We show how Aalen's additive risk model can be applied in this setting with the benefit that the time-varying haplo-match effect can be easily studied. This problem has not been considered before, and the standard approach where one would use the EM-algorithm cannot be applied for this model because the likelihood is hard to evaluate without additional assumptions. We suggest an approach based on multivariate estimating equations that are solved using a recursive structure. This approach leads to an estimator where the large sample properties can be developed using product-integration theory. Small sample properties are investigated using simulations in a setting that mimics the motivating haplo-match problem.

In this paper we describe flexible competing risks regression models using the comp.risk() function available in the timereg package for R based on Scheike et al. (2008). Regression models are specified for the transition probabilities, that is the cumulative incidence in the competing risks setting. The model contains the Fine and Gray (1999) model as a special case. This can be used to do goodness-of-fit test for the subdistribution hazards' proportionality assumption (Scheike and Zhang 2008). The program can also construct confidence bands for predicted cumulative incidence curves.We apply the methods to data on follicular cell lymphoma from Pintilie (2007), where the competing risks are disease relapse and death without relapse. There is important non-proportionality present in the data, and it is demonstrated how one can analyze these data using the flexible regression models.

Genetic association studies often investigate the effect of haplotypes on an outcome of interest. Haplotypes are not observed directly, and this complicates the inclusion of such effects in survival models. We describe a new estimating equations approach for Cox's regression model to assess haplotype effects for survival data. These estimating equations are simple to implement and avoid the use of the EM algorithm, which may be slow in the context of the semiparametric Cox model with incomplete covariate information. These estimating equations also lead to easily computable, direct estimators of standard errors, and thus overcome some of the difficulty in obtaining variance estimators based on the EM algorithm in this setting. We also develop an easily implemented goodness-of-fit procedure for Cox's regression model including haplotype effects. Finally, we apply the procedures presented in this article to investigate possible haplotype effects of the PAF-receptor on cardiovascular events in patients with coronary artery disease, and compare our results to those based on the EM algorithm., (© 2009, The International Biometric Society.)

We propose a semiparametric random effects model for multivariate competing risks data when the failures of a particular type are of interest. Under this model, the marginal cumulative incidence functions follow a generalized semiparametric additive model. The associations between the cause-specific failure times can be studied through dependence parameters of copula functions that are allowed to depend on cluster-level covariates. A cross-odds ratio-type measure is proposed to describe the associations between cause-specific failure times, and its relationship to the dependence parameters is explored. We develop a two-stage estimation procedure where the marginal models are estimated in the first stage and the dependence parameters are estimated in the second stage. The large sample properties of the proposed estimators are derived. The proposed procedures are applied to Danish twin data to model the cumulative incidence for the age of natural menopause and to investigate the association in the onset of natural menopause between monozygotic and dizygotic twins.

The Cox hazards model (Cox, 1972, Journal of the Royal Statistical Society, Series B34, 187-220) for survival data is routinely used in many applied fields, sometimes, however, with too little emphasis on the fit of the model. A useful alternative to the Cox model is the Aalen additive hazards model (Aalen, 1980, in Lecture Notes in Statistics-2, 1-25) that can easily accommodate time changing covariate effects. It is of interest to decide which of the two models that are most appropriate to apply in a given application. This is a nontrivial problem as these two classes of models are nonnested except only for special cases. In this article we explore the Mizon-Richard encompassing test for this particular problem. It turns out that it corresponds to fitting of the Aalen model to the martingale residuals obtained from the Cox regression analysis. We also consider a variant of this method, which relates to the proportional excess model (Martinussen and Scheike, 2002, Biometrika 89, 283-298). Large sample properties of the suggested methods under the two rival models are derived. The finite-sample properties of the proposed procedures are assessed through a simulation study. The methods are further applied to the well-known primary biliary cirrhosis data set.

Background: Trends in biologic fertility are elusive. Possible negative trends in male reproductive health are still debated, and their effect on human fertility might be negligible. Time-to-pregnancy (TTP) is a functional measure of couple fecundability., Methods: We analyzed data on TTP among 832,000 primiparous women 20 years of age and older in the nationwide Swedish Medical Birth Registry from 1983 through 2002. This age restriction led to an exclusion of 10% of primiparous pregnancies. Subfertility (TTP > or =1 year) was analyzed as a function of maternal age, calendar time at initiation of attempt, and birth cohort-taking into account the truncation problems that are inherent in birth-based retrospective sampling., Results: Subfertility generally decreased over successive birth cohorts. When studied as a period effect, a transient increase in subfertility was seen in the early 1990s. Subfertility increased with age, except that for women in their late 1930s, an apparent decrease was observed, particularly among the early cohorts., Conclusion: We found decreasing subfertility over time. We speculate that these patterns might be related to a Sweden-specific decrease over time in sexually transmitted diseases, to changes in sexual behavior induced by socioeconomic conditions, or to broader biologic or educational trends.

Nested case-control sampling is designed to reduce the costs of large cohort studies. It is important to estimate the parameters of interest as efficiently as possible. We present a new maximum likelihood estimator (MLE) for nested case-control sampling in the context of Cox's proportional hazards model. The MLE is computed by the EM-algorithm, which is easy to implement in the proportional hazards setting. Standard errors are estimated by a numerical profile likelihood approach based on EM aided differentiation. The work was motivated by a nested case-control study that hypothesized that insulin-like growth factor I was associated with ischemic heart disease. The study was based on a population of 3784 Danes and 231 cases of ischemic heart disease where controls were matched on age and gender. We illustrate the use of the MLE for these data and show how the maximum likelihood framework can be used to obtain information additional to the relative risk estimates of covariates.

Cox's regression model is the standard regression tool for survival analysis in most applications. Often, however, the model only provides a rough summary of the effect of some covariates. Therefore, if the aim is to give a detailed description of covariate effects and to consequently calculate predicted probabilities, more flexible models are needed. In another article, Scheike and Zhang (2002, Scandinavian Journal of Statistics 29, 75-88), we suggested a flexible extension of Cox's regression model, which aimed at extending the Cox model only for those covariates where additional flexibility are needed. One important advantage of the suggested approach is that even though covariates are allowed a nonparametric effect, the hassle and difficulty of finding smoothing parameters are not needed. We show how the extended model also leads to simple formulae for predicted probabilities and their standard errors, for example, in the competing risk framework.

Time to pregnancy, the number of menstrual cycles it takes a couple to conceive, and various covariates have been collected among couples ultimately achieving conception. To assess the influence of the covariates, we constructed a discrete survival model that allows time-dependent covariates. A random effect was included to account for unobserved heterogeneity. The collected waiting times are obtained through retrospective ascertainment and are analyzed as truncated data. Maximum likelihood estimation was implemented by Fisher scoring through iteratively reweighted least squares.