For longitudinal studies with multivariate observations, we propose statistical methods to identify clusters of archetypal subjects by using techniques from functional data analysis and to relate longitudinal patterns to outcomes. We demonstrate how this approach can be applied to examine associations between multiple time-varying exposures and subsequent health outcomes, where the former are recorded sparsely and irregularly in time, with emphasis on the utility of multiple longitudinal observations in the framework of dimension reduction techniques. In applications to children’s growth data, we investigate archetypes of infant growth patterns and identify subgroups that are related to cognitive development in childhood. Specifically, “Stunting” and “Faltering” time-dynamic patterns of head circumference, body length and weight in the first 12 months are associated with lower levels of long-term cognitive development in comparison to “Generally Large” and “Catch-up” growth. Our findings provide evidence for the statistical association between multivariate growth patterns in infancy and long-term cognitive development.

Define K-disjoint partitions (I k : 1 ≤ k ≤ K) of an index set {1, . . . , n} such thatThen (i) we set a baseline bandwidth vectord ) for each sub-sample X n,(−k) , and (ii) compute the prediction performance of the trained model on the test set k) ) are the back transformed density estimators (2.5) from the smooth backfitting log-quantile density estimators ĝ(•, X i ; X n,(−k) , αh (k) ) based on the sub-sample X n,(−k) with bandwidth αh (k) . Also, fi are the marginal density estimators of f i defined as in (2.9), based on Y i , respectively.

Increasingly, medical research is dependent on data collected for non-research purposes, such as electronic health records data. Health records data and other large databases can be prone to measurement error in key exposures, and unadjusted analyses of error-prone data can bias study results. Validating a subset of records is a cost-effective way of gaining information on the error structure, which in turn can be used to adjust analyses for this error and improve inference. We extend the mean score method for the two-phase analysis of discrete-time survival models, which uses the unvalidated covariates as auxiliary variables that act as surrogates for the unobserved true exposures. This method relies on a two-phase sampling design and an estimation approach that preserves the consistency of complete case regression parameter estimates in the validated subset, with increased precision leveraged from the auxiliary data. Furthermore, we develop optimal sampling strategies which minimize the variance of the mean score estimator for a target exposure under a fixed cost constraint. We consider the setting where an internal pilot is necessary for the optimal design so that the phase two sample is split into a pilot and an adaptive optimal sample. Through simulations and data example, we evaluate efficiency gains of the mean score estimator using the derived optimal validation design compared to balanced and simple random sampling for the phase two sample. We also empirically explore efficiency gains that the proposed discrete optimal design can provide for the Cox proportional hazards model in the setting of a continuous-time survival outcome.

We study nonparametric additive regression models when noisy covariates are observed within measurement errors. Based on deconvolution techniques, we construct an iterative algorithm for smooth backfitting of additive function in the presence of errors-in-variables. We show that the smooth backfitting achieves univariate accuracy of the standard deconvolution for estimating each component function under certain conditions. Deconvolving noise on backfitting is confined into negligible magnitude that rate of convergence of the proposed estimator is accelerated when the smoothness of measurement errors falls into a certain range. We also present finite sample performance of the deconvolution smooth backfitting in comparison with a naive application of the standard smooth backfitting ignoring measurement errors. Monte Carlo simulation is demonstrated that our method gives smaller mean integrated squared errors than the naive one in average.

We study smooth backfitting when there are errors-in-variables, which is motivated by functional additive models for a functional regression model with a scalar response and multiple functional predictors that are additive in the functional principal components of the predictor processes. The development of a new smooth backfitting technique for the estimation of the additive component functions in functional additive models with multiple functional predictors requires to address the difficulty that the eigenfunctions and therefore the functional principal components of the predictor processes, which are the arguments of the proposed additive model, are unknown and need to be estimated from the data. The available estimated functional principal components contain an error that is small for large samples but nevertheless affects the estimation of the additive component functions. This error-in-variables situation requires to develop new asymptotic theory for smooth backfitting. Our analysis also pertains to general situations where one encounters errors in the predictors for an additive model, when the errors become smaller asymptotically. We also study the finite sample properties of the proposed method for the application in functional additive regression through a simulation study and a real data example.