Design of mixed-longitudinal studies

Cross-sectional designs, longitudinal designs in which a single cohort is followed over time, and mixed-longitudinal designs in which several cohorts are followed for a shorter period are compared by their precision, potential for bias due to age, time and cohort effects, and feasibility. Mixed longitudinal studies have two advantages over longitudinal studies: isolation of time and age effects and shorter completion time. Though the advantages of mixed-longitudinal studies are clear, choosing an optimal design is difficult, especially given the number of possible combinations of the number of cohorts and number of overlapping intervals between cohorts. The purpose of this paper is to determine the optimal design for detecting differences in group growth rates.^ The type of mixed-longitudinal study appropriate for modeling both individual and group growth rates is called a "multiple-longitudinal" design. A multiple-longitudinal study typically requires uniform or simultaneous entry of subjects, who are each observed till the end of the study.^ While recommendations for designing pure-longitudinal studies have been made by Schlesselman (1973b), Lefant (1990) and Helms (1991), design recommendations for multiple-longitudinal studies have never been published. It is shown that by using power analyses to determine the minimum number of occasions per cohort and minimum number of overlapping occasions between cohorts, in conjunction with a cost model, an optimal multiple-longitudinal design can be determined. An example of systolic blood pressure values for cohorts of males and cohorts of females, ages 8 to 18 years, is given. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^