A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development

This research examines the simultaneous influences of height and weight on longitudinally measured systolic and diastolic blood pressure in children. Previous studies have shown that both height and weight are positively associated with blood pressure. In children, however, the concurrent increases of height and weight have made it all but impossible to discern the effect of height from that of weight. To better understand these influences, we propose to examine the joint effect of height and weight on blood pressure. Bivariate thin plate spline surfaces are used to accommodate the potentially nonlinear effects as well as the interaction between height and weight. Moreover, we consider a joint model for paired blood pressure measures, that is, systolic and diastolic blood pressure, to account for the underlying correlation between the two measures within the same individual. The bivariate spline surfaces are allowed to vary across different groups of interest. We have developed related model fitting and inference procedures. The proposed method is used to analyze data from a real clinical investigation.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS567 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Minimally sufficient numbers of measurements for validation of 24-hour blood pressure monitoring in chronic kidney disease

Ambulatory blood pressure monitoring (ABPM) remains a reference standard, but the minimal number of ABPM readings required to diagnose hypertension has not been empirically validated. Among 360 patients with chronic kidney disease and 38 healthy controls, 24-hour blood pressure was recorded 2 times per hour during the night and 3 times per hour during the day. All subjects had at least 90% of the expected readings recorded. From this full set of ABPM recordings, we selected variable numbers of measurements and compared the performance of the selected readings against that of the full sample under either random or sequential sampling schemes. With 8 randomly selected systolic blood pressure readings, we were able to make diagnostic decisions in concordance with that from the full ABPM sample 91.0% of the time (kappa 0.804). With 15 randomly selected diastolic blood pressure readings, we made concordant decisions 96.3% of the time (kappa 0.810). A serial selection scheme generally required a greater number of readings to achieve the same levels of concordance with the full ABPM data. With a random selection scheme, 26 readings provided 95% confidence that the sample mean will be within 5 mm Hg of the true systolic blood pressure mean, and within 3.5 mm Hg of the true diastolic blood pressure mean

Large-sample estimation and inference in multivariate single-index models

By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indee

A Spline-Based Lack-of-Fit Test for Independent Variable Effect

In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given

Optimizing strategies for population-based chlamydia infection screening among young women: an age-structured system dynamics approach

BACKGROUND: Chlamydia infection (CT) is one of the most commonly reported sexually transmitted diseases. It is often referred to as a "silent" disease with the majority of infected people having no symptoms. Without early detection, it can progress to serious reproductive and other health problems. Economical identification of asymptomatically infected is a key public health challenge. Increasing evidence suggests that CT infection risk varies over the range of adolescence. Hence, age-dependent screening strategies with more frequent testing for certain age groups of higher risk may be cost-saving in controlling the disease. METHODS: We study the optimization of age-dependent screening strategies for population-based chlamydia infection screening among young women. We develop an age-structured compartment model for CT natural progress, screening, and treatment. We apply parameter optimization on the resultant PDE-based system dynamical models with the objective of minimizing the total care spending, including screening and treatment costs during the program period and anticipated costs of treating the sequelae afterwards). For ease of practical implementation, we also search for the best screening initiation age for strategies with a constant screening frequency. RESULTS: The optimal age-dependent strategies identified outperform the current CDC recommendations both in terms of total care spending and disease prevalence at the termination of the program. For example, the age-dependent strategy that allows monthly screening rate changes can save about 5% of the total spending. Our results suggest early initiation of CT screening is likely beneficial to the cost saving and prevalence reduction. Finally, our results imply that the strategy design may not be sensitive to accurate quantification of the age-specific CT infection risk if screening initiation age and screening rate are the only decisions to make. CONCLUSIONS: Our research demonstrates the potential economic benefit of age-dependent screening strategy design for population-based screening programs. It also showcases the applicability of age-structured system dynamical modeling to infectious disease control with increasing evidence on the age differences in infection risk. The research can be further improved with consideration of the difference between first-time infection and reinfection, as well as population heterogeneity in sexual partnership

A generalized semiparametric mixed model for analysis of multivariate health care utilization data

Health care utilization is an outcome of interest in health services research. Two frequently studied forms of utilization are counts of emergency department (ED) visits and hospital admissions. These counts collectively convey a sense of disease exacerbation and cost escalation. Different types of event counts from the same patient form a vector of correlated outcomes. Traditional analysis typically model such outcomes one at a time, ignoring the natural correlations between different events, and thus failing to provide a full picture of patient care utilization. In this research, we propose a multivariate semiparametric modeling framework for the analysis of multiple health care events following the exponential family of distributions in a longitudinal setting. Bivariate nonparametric functions are incorporated to assess the concurrent nonlinear influences of independent variables as well as their interaction effects on the outcomes. The smooth functions are estimated using the thin plate regression splines. A maximum penalized likelihood method is used for parameter estimation. The performance of the proposed method was evaluated through simulation studies. To illustrate the method, we analyzed data from a clinical trial in which ED visits and hospital admissions were considered as bivariate outcomes

A sexually transmitted infection screening algorithm based on semiparametric regression models

Sexually transmitted infections (STIs) with Chlamydia trachomatis, Neisseria gonorrhoeae, and Trichomonas vaginalis are among the most common infectious diseases in the United States, disproportionately affecting young women. Because a significant portion of the infections present no symptoms, infection control relies primarily on disease screening. However, universal STI screening in a large population can be expensive. In this paper, we propose a semiparametric model-based screening algorithm. The model quantifies organism-specific infection risks in individual subjects and accounts for the within-subject interdependence of the infection outcomes of different organisms and the serial correlations among the repeated assessments of the same organism. Bivariate thin-plate regression spline surfaces are incorporated to depict the concurrent influences of age and sexual partners on infection acquisition. Model parameters are estimated by using a penalized likelihood method. For inference, we develop a likelihood-based resampling procedure to compare the bivariate effect surfaces across outcomes. Simulation studies are conducted to evaluate the model fitting performance. A screening algorithm is developed using data collected from an epidemiological study of young women at increased risk of STIs. We present evidence that the three organisms have distinct age and partner effect patterns; for C. trachomatis, the partner effect is more pronounced in younger adolescents. Predictive performance of the proposed screening algorithm is assessed through a receiver operating characteristic analysis. We show that the model-based screening algorithm has excellent accuracy in identifying individuals at increased risk, and thus can be used to assist STI screening in clinical practice

Distribution‐free estimation of local growth rates around interval censored anchoring events

Biological processes are usually defined on timelines that are anchored by specific events. For example, cancer growth is typically measured by the change in tumor size from the time of oncogenesis. In the absence of such anchoring events, longitudinal assessments of the outcome lose their temporal reference. In this paper, we considered the estimation of local change rates in the outcomes when the anchoring events are interval‐censored. Viewing the subject‐specific anchoring event times as random variables from an unspecified distribution, we proposed a distribution‐free estimation method for the local growth rates around the unobserved anchoring events. We expressed the rate parameters as stochastic functionals of the anchoring time distribution and showed that under mild regularity conditions, consistent and asymptotically normal estimates of the rate parameters could be achieved, with a biom13015-gra-0001 convergence rate. We conducted a carefully designed simulation study to evaluate the finite sample performance of the method. To motivate and illustrate the use of the proposed method, we estimated the skeletal growth rates of male and female adolescents, before and after the unobserved pubertal growth spurt (PGS) times