We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all optimal designs, some prior information is needed to implement the proposed optimal designs. We demonstrate that this prior information may come from a pilot longitudinal study that has irregularly measured and noisy measurements, where for each subject one has available a small random number of repeated measurements that are randomly located on the domain. A second possibility of interest is that a pilot study consists of densely measured functional data and one intends to take only a few measurements at strategically placed locations in the domain for the future collection of similar data. We construct optimal designs by targeting two criteria:(a) Optimal designs to recover the unknown underlying smooth random trajectory for each subject from a few optimally placed measurements such that squared prediction errors are minimized; (b) Optimal designs that minimize prediction errors for functional linear regression with functional or longitudinal predictors and scalar responses, again from a few optimally placed measurements.The proposed optimal designs address the need for sparse data collection when planning longitudinal studies, by taking advantage of the close connections between longitudinal and functional data analysis. We demonstrate in simulations that the proposed designs perform considerably better than randomly chosen design points and include a motivating data example from the Baltimore longitudinal study of aging. The proposed designs are shown to have an asymptotic optimality property.

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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 2 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.