Power and sample size calculations for longitudinal studies estimating a main effect of a time-varying exposure

New immune phenotypes for treatment response in high-grade serous ovarian carcinoma patients

Despite advances in surgical and therapeutic approaches, high-grade serous ovarian carcinoma (HGSOC) prognosis remains poor. Surgery is an indispensable component of therapeutic protocols, as removal of all visible tumor lesions (cytoreduction) profoundly improves the overall survival. Enhanced predictive tools for assessing cytoreduction are essential to optimize therapeutic precision. Patients' immune status broadly reflects the tumor cell biological behavior and the patient responses to disease and treatment. Serum cytokine profiling is a sensitive measure of immune adaption and deviation, yet its integration into treatment paradigms is underexplored. This study is part of the IMPACT trial (NCT03378297) and aimed to characterize immune responses before and during primary treatment for HGSOC to identify biomarkers for treatment selection and prognosis. Longitudinal serum samples from 22 patients were collected from diagnosis until response evaluation. Patients underwent primary cytoreductive surgery or neoadjuvant chemotherapy (NACT) based on laparoscopy scoring. Twenty-seven serum cytokines analyzed by Bio-Plex 200, revealed two immune phenotypes at diagnosis: Immune High with marked higher serum cytokine levels than Immune Low. The immune phenotypes reflected the laparoscopy scoring and allocation to surgical treatment. The five Immune High patients undergoing primary cytoreductive surgery exhibited immune mobilization and extended progression-free survival, compared to the Immune Low patients undergoing the same treatment. Both laparoscopy and cytoreductive surgery induced substantial and transient changes in serum cytokines, with upregulation of the inflammatory cytokine IL-6 and downregulation of the multifunctional cytokines IP-10, Eotaxin, IL-4, and IL-7. Over the study period, cytokine levels uniformly decreased in all patients, leading to the elimination of the initial immune phenotypes regardless of treatment choice. This study reveals distinct pre-treatment immune phenotypes in HGSOC patients that might be informative for treatment stratification and prognosis. This potential novel biomarker holds promise as a foundation for improved assessment of treatment responses in patients with HGSOC. ClinicalTrials.gov Identifier: NCT03378297.

Power and sample size analysis for longitudinal mixed models of health in populations exposed to environmental contaminants: a tutorial

BACKGROUND

When evaluating the impact of environmental exposures on human health, study designs often include a series of repeated measurements. The goal is to determine whether populations have different trajectories of the environmental exposure over time. Power analyses for longitudinal mixed models require multiple inputs, including clinically significant differences, standard deviations, and correlations of measurements. Further, methods for power analyses of longitudinal mixed models are complex and often challenging for the non-statistician. We discuss methods for extracting clinically relevant inputs from literature, and explain how to conduct a power analysis that appropriately accounts for longitudinal repeated measures. Finally, we provide careful recommendations for describing complex power analyses in a concise and clear manner.

METHODS

For longitudinal studies of health outcomes from environmental exposures, we show how to [1] conduct a power analysis that aligns with the planned mixed model data analysis, [2] gather the inputs required for the power analysis, and [3] conduct repeated measures power analysis with a highly-cited, validated, free, point-and-click, web-based, open source software platform which was developed specifically for scientists.

RESULTS

As an example, we describe the power analysis for a proposed study of repeated measures of per- and polyfluoroalkyl substances (PFAS) in human blood. We show how to align data analysis and power analysis plan to account for within-participant correlation across repeated measures. We illustrate how to perform a literature review to find inputs for the power analysis. We emphasize the need to examine the sensitivity of the power values by considering standard deviations and differences in means that are smaller and larger than the speculated, literature-based values. Finally, we provide an example power calculation and a summary checklist for describing power and sample size analysis.

CONCLUSIONS

This paper provides a detailed roadmap for conducting and describing power analyses for longitudinal studies of environmental exposures. It provides a template and checklist for those seeking to write power analyses for grant applications.

Power and Sample Size for Fixed-Effects Inference in Reversible Linear Mixed Models

Despite the popularity of the general linear mixed model for data analysis, power and sample size methods and software are not generally available for commonly used test statistics and reference distributions. Statisticians resort to simulations with homegrown and uncertified programs or rough approximations which are misaligned with the data analysis. For a wide range of designs with longitudinal and clustering features, we provide accurate power and sample size approximations for inference about fixed effects in linear models we call reversible. We show that under widely applicable conditions, the general linear mixed-model Wald test has non-central distributions equivalent to well-studied multivariate tests. In turn, exact and approximate power and sample size results for the multivariate Hotelling-Lawley test provide exact and approximate power and sample size results for the mixed-model Wald test. The calculations are easily computed with a free, open-source product that requires only a web browser to use. Commercial software can be used for a smaller range of reversible models. Simple approximations allow accounting for modest amounts of missing data. A real-world example illustrates the methods. Sample size results are presented for a multicenter study on pregnancy. The proposed study, an extension of a funded project, has clustering within clinic. Exchangeability among participants allows averaging across them to remove the clustering structure. The resulting simplified design is a single level longitudinal study. Multivariate methods for power provide an approximate sample size. All proofs and inputs for the example are in the Supplementary Materials (available online).

Impact of change in neighborhood racial/ethnic segregation on cardiovascular health in minority youth attending a park-based afterschool program

Research on the mechanistic factors associating racial/ethnic residential segregation with health is needed to identify effective points of intervention to ultimately reduce health disparities in youth. We examined the association of changes in racial/ethnic segregation and cardiovascular health outcomes including body mass index percentile, sum of skinfold thicknesses, systolic and diastolic blood pressure percentile, and 400 m run time in non-Hispanic Black (NHB) and Hispanic youth (n = 2,250, mean age 9.1 years, 54% male; 51% Hispanic, 49% NHB; 49% high area poverty; 25% obese) attending Fit2Play™, a multisite park-based afterschool program in Miami, Florida, USA. A series of crude and adjusted two-level longitudinal generalized linear mixed models with random intercepts for park effects were fit to assess the association of change in segregation between home and program/park site and cardiovascular health outcomes for youth who participated for up to two school years in Fit2Play™. After adjusting for individual-level factors (sex, age, time, and park-area poverty) models showed significantly greater improvements in cardiovascular health if youth attended Fit2Play™ in an area less segregated than their home area (p < 0.05 for all outcomes) except 400 m run time and diastolic blood pressure percentile in Hispanics (p<.001 and p = 0.11, respectively). Area poverty was not found to confound or significantly modify this association. These findings have implications for youth programming focused on reducing health disparities and improving cardiovascular outcomes in NHB and Hispanic youth, particularly in light of a continually expanding obesity epidemic in these groups. Parks and Recreation Departments have potential to expand geographic mobility for minorities, therein supporting the national effort to reduce health inequalities.

Optimal combination of number of participants and number of repeated measurements in longitudinal studies with time-varying exposure

In the context of observational longitudinal studies, we explored the values of the number of participants and the number of repeated measurements that maximize the power to detect the hypothesized effect, given the total cost of the study. We considered two different models, one that assumes a transient effect of exposure and one that assumes a cumulative effect. Results were derived for a continuous response variable, whose covariance structure was assumed to be damped exponential, and a binary time-varying exposure. Under certain assumptions, we derived simple formulas for the approximate solution to the problem in the particular case in which the response covariance structure is assumed to be compound symmetry. Results showed the importance of the exposure intraclass correlation in determining the optimal combination of the number of participants and the number of repeated measurements, and therefore the optimized power. Thus, incorrectly assuming a time-invariant exposure leads to inefficient designs. We also analyzed the sensitivity of results to dropout, mis-specification of the response correlation structure, allowing a time-varying exposure prevalence and potential confounding impact. We illustrated some of these results in a real study. In addition, we provide software to perform all the calculations required to explore the combination of the number of participants and the number of repeated measurements.

Design Issues in Longitudinal Studies

In designing a longitudinal study one needs to decide on two critical components: duration of study and frequency of visits. In addition, other issues involving sample size, power, number of observations per subject must be addressed. If the study is meant to be completed within a certain time frame, would it better to have a fixed time between observations (which might allow the study to terminate early if its objectives are met) or to spread out the observations over the entire study period? At some point during the study, it may be of interest to see if additional data points would contribute substantially. Assume that the longitudinal data will be analyzed using a linear mixed-effects model. In this investigation we use the standard errors of estimates of model parameters as the criterion. We seek to address the issues using three approaches. First, subsets of a data set are constructed in a number of ways and the standard errors are examined. Second, using a variety of designs, the covariance matrix of the fixed-effects is computed and the standard errors are examined. Finally, a simulation study is conducted.