Power and sample size calculations for longitudinal studies comparing rates of change with a time-varying exposure

Rationale and Design of the Impact of Air Pollution Due to DESERT Dust in Patients with HEART Failure (DESERT HEART)

AIMS

The main objective of this study is to determine whether exposure to Saharan dust causes airway inflammation and oxidative stress in patients with stable chronic heart failure (HF) and a left ventricular ejection fraction of less than 40%.

METHODS

A longitudinal study design is used, involving the inclusion of 40 patients with stable chronic HF and a left ventricular ejection fraction of less than 40%. Four sputum samplings will be taken from each patient, with one sampling taken each week over four consecutive weeks. The sputum samples will be used to analyze the degree of inflammation and oxidative stress. Air quality monitoring stations will be used to analyze the particulate matter (PM) exposure of each patient. The intrusion of desert dust will be identified using meteorological models. There will be 160 scheduled samplings in 40 patients with chronic HF. Mixed regression models will be used to assess the influence of the concentrations of PM (from the episodes of desert dust) upon the airway inflammation and oxidative stress markers.

CONCLUSION

The results of this study will test the hypothesis that exposure to high concentrations of Saharan dust affects the normal function of the respiratory epithelium due to the imbalance between the production of free radicals and antioxidant enzymes, thus causing increased pulmonary inflammation and oxidative stress in patients with HF that in turn may facilitate decompensations of their background disease condition.

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.

A randomized, open, controlled trial of tretinoin 0.05% cream vs. low-dose oral isotretinoin for the treatment of field cancerization

BACKGROUND

Sun exposure may lead to actinic keratoses (AKs), field cancerization, and skin cancer. Effective treatment of AKs and field cancerization is important. Oral and topical retinoids can be used for this purpose. To compare clinical, histological, and immunohistochemical effects of oral and topical retinoid for AKs and field cancerization on face and upper limbs of immunocompetent patients, as well as the impact on quality of life, safety, and tolerability.

METHODS

This study compared 10 mg/day oral isotretinoin (ISO) to 0.05% tretinoin cream (TRE) every other night, associated with sunscreen (SPF 60). Patients of both genders, aged 50-75 years, underwent cryotherapy with liquid nitrogen for AKs at baseline and after 120 days when they were randomized into two groups, TRE (n = 31) and ISO (n = 30), for 6 months. Outcome measures were: number of AKs, histological (thickness of stratum corneum and epithelium) and immunohistochemical parameters (p53, Bcl-2 and Bax), dermatology life quality index (DLQI), and adverse events.

RESULTS

Both treatments reduced the number of AKs (around 28%), the thickness of stratum corneum, and expression of p53 and Bax. By contrast, the epithelium thickness and Bcl-2 expression increased. There was no difference in the outcomes between TRE and ISO. Both treatments improved quality of life and were well tolerated with minimal side effects.

CONCLUSIONS

Retinoids are effective and safe for field cancerization. Classical treatments for field cancerization (imiquimod and ingenol mebutate) are used for a short period; retinoids may be a good choice to intercalate with them and can be used continuously.

No Association Between Consumption of Sweetened Beverages and Risk of Later-Onset Crohn's Disease or Ulcerative Colitis

BACKGROUND & AIMS

Consumption of sweetened beverages has been associated with inflammation based on measurements of C-reactive protein and tumor necrosis factor, as well as immune-mediated disorders including rheumatoid arthritis. We investigated associations with Crohn's disease (CD) or ulcerative colitis (UC).

METHODS

We conducted a prospective cohort study of 83,042 participants (age, 44-83 y) enrolled in the Cohort of Swedish Men or the Swedish Mammography Study. Dietary and lifestyle data were collected using a validated food frequency questionnaire at baseline in 1997. Diagnoses of CD and UC were ascertained from the Swedish Patient Register. We used Cox proportional hazards modeling to calculate hazard ratios and 95% CIs.

RESULTS

Through December of 2014, we confirmed 143 incident cases of CD (incidence rate, 11 cases/100,000 person-years) and 349 incident cases of UC (incidence rate, 28 cases/100,000 person-years) over 1,264,345 person-years of follow-up evaluation. Consumption of sweetened beverages was not associated with increased risk of CD (Ptrend = .34) or UC (Ptrend = .40). Compared with participants who reported no consumption of sweetened beverages, the multivariable-adjusted hazard ratios for 1 or more servings per day were 1.02 for CD (95% CI, 0.60-1.73) and 1.14 for UC (95% CI, 0.83-1.57). The association between consumption of sugar-sweetened beverages and risk of CD or UC were not modified by age, sex (cohort), body mass index, or smoking (all Pinteraction ≥ .12).

CONCLUSIONS

In analyses of data from 2 large prospective cohort studies from Sweden, we observed no evidence for associations between consumption of sweetened beverages and later risk of CD or UC.

Daily self-weighing and weight gain prevention: a longitudinal study of college-aged women

Daily self-weighing has been suggested as an important factor for weight loss maintenance among samples with obesity. This study is a secondary analysis that examined daily self-weighing in association with weight and body composition outcomes over 2 years among young women with vulnerability for weight gain. Women (N = 294) of varying weight status completed self-weighing frequency questionnaires and weight was measured in the clinic at baseline, 6 months, 1, and 2 years; DXA scans were completed at baseline, 6 months and 2 years. Multilevel models examined the relationship between daily self-weighing (at any point in the study) and trajectories of BMI and body fat percentage. Daily self-weighing was associated with significant declines in BMI and body fat percent over time. Future research is needed to examine causal relations between daily self-weighing and weight gain prevention. Nonetheless, these data extend the possibility that daily self-weighing may be important for prevention of unwanted weight gain.

FPCA-based method to select optimal sampling schedules that capture between-subject variability in longitudinal studies

A critical component of longitudinal study design involves determining the sampling schedule. Criteria for optimal design often focus on accurate estimation of the mean profile, although capturing the between-subject variance of the longitudinal process is also important since variance patterns may be associated with covariates of interest or predict future outcomes. Existing design approaches have limited applicability when one wishes to optimize sampling schedules to capture between-individual variability. We propose an approach to derive optimal sampling schedules based on functional principal component analysis (FPCA), which separately characterizes the mean and the variability of longitudinal profiles and leads to a parsimonious representation of the temporal pattern of the variability. Simulation studies show that the new design approach performs equally well compared to an existing approach based on parametric mixed model (PMM) when a PMM is adequate for the data, and outperforms the PMM-based approach otherwise. We use the methods to design studies aiming to characterize daily salivary cortisol profiles and identify the optimal days within the menstrual cycle when urinary progesterone should be measured.

Swallowing dysfunction following endotracheal intubation: Age matters

To evaluate postextubation swallowing dysfunction (PSD) 21 days after endotracheal extubation and to examine whether PSD is time-limited and whether age matters.For this prospective cohort study, we evaluated 151 adult critical care patients (≥20 years) who were intubated for at least 48 hours and had no pre-existing neuromuscular disease or swallowing dysfunction. Participants were assessed for time (days) to pass bedside swallow evaluations (swallow 50 mL of water without difficulty) and to resume total oral intake. Outcomes were compared between younger (20-64 years) and older participants (≥65 years).PSD, defined as inability to swallow 50 mL of water within 48 hours after extubation, affected 92 participants (61.7% of our sample). At 21 days postextubation, 17 participants (15.5%) still failed to resume total oral intake and were feeding-tube dependent. We found that older participants had higher PSD rates at 7, 14, and 21 days postextubation, and took significantly longer to pass the bedside swallow evaluations (5.0 vs 3.0 days; P = 0.006) and to resume total oral intake (5.0 vs 3.0 days; P = 0.003) than their younger counterparts. Older participants also had significantly higher rates of subsequent feeding-tube dependence than younger patients (24.1 vs 5.8%; P = 0.008).Excluding patients with pre-existing neuromuscular dysfunction, PSD is common and prolonged. Age matters in the time needed to recover. Swallowing and oral intake should be monitored and interventions made, if needed, in the first 7 to 14 days postextubation, particularly for older patients.

Effect of zinc and multivitamin supplementation on the growth of Tanzanian children aged 6-84 wk: a randomized, placebo-controlled, double-blind trial

BACKGROUND

Poor child growth increases risks of mortality and morbidity. Micronutrient supplements have the potential to improve child growth.

OBJECTIVE

We assessed the effect of daily zinc, multivitamin (vitamins C, E, and B-complex), and zinc and multivitamin (Zn+MV) supplementation on growth in infants in Tanzania.

DESIGN

In this randomized, 2 × 2 factorial, double-blind trial, 2400 infants were randomly assigned to receive zinc, multivitamins, Zn+MVs, or a placebo at 6 wk of age and were followed up for 18 mo with monthly growth measurements. Mixed-effects models with restricted cubic splines for the mean change in anthropometric z scores were fit for each group. Likelihood ratio tests were used to compare the effect of supplements on growth trajectories. Cox proportional hazards models were used to compare incidences of stunting, wasting, and underweight.

RESULTS

Children in all groups experienced growth faltering. At 19 mo of age, prevalences of stunting, wasting, and underweight were 19.8%, 6.0%, and 10.8%, respectively. Changes in weight-for-age z scores (WAZs) and weight-for-height z scores (WHZs) were significantly different across the 4 groups (P < 0.001 for both). The mean ± SE decline in the WAZ from baseline to the end of follow-up in the Zn+MV group was significantly less than in the placebo group (-0.36 ± 0.04 compared with -0.50 ± 0.04; P = 0.020), whereas the decline in the WHZ was significantly greater in the zinc-only group than in the placebo group (-0.57 ± 0.07 compared with -0.35 ± 0.07; P = 0.021). Supplements did not have a significant effect on mean change in the height-for-age z score or on rates of stunting, wasting, or underweight.

CONCLUSIONS

Although there were small but significant improvements in the WAZ in the Zn+MV group, daily zinc supplementation alone, multivitamin supplementation alone, and the combined Zn+MV did not reduce the incidences of underweight, stunting, or wasting in Tanzanian infants. Alternative approaches to prevent growth faltering should be pursued. This trial was registered at clinicaltrials.gov as NCT00421668.

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.

: Online Power Computation for Linear Models with and without a Baseline Covariate

GLIMMPSE is a free, web-based software tool that calculates power and sample size for the general linear multivariate model with Gaussian errors (http://glimmpse.SampleSizeShop.org/). GLIMMPSE provides a user-friendly interface for the computation of power and sample size. We consider models with fixed predictors, and models with fixed predictors and a single Gaussian covariate. Validation experiments demonstrate that GLIMMPSE matches the accuracy of previously published results, and performs well against simulations. We provide several online tutorials based on research in head and neck cancer. The tutorials demonstrate the use of GLIMMPSE to calculate power and sample size.

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.

Effectiveness of a short message reminder in increasing compliance with pediatric cataract treatment: a randomized trial

OBJECTIVE

Regular follow-up is essential to successful management of childhood cataract. We sought to assess whether a mobile phone short message service (SMS) for parents of children with cataract could improve follow-up adherence and the proportion of procedures performed in timely fashion.

DESIGN

Randomized, controlled trial. This trial is registered with ClinicalTrials.gov, NCT01417819.

PARTICIPANTS

We included 258 parent-child pairs involved in the Childhood Cataract Program of the Chinese Ministry of Health.

METHODS

Participants were randomized (1:1) to a mobile phone SMS intervention or standard follow-up appointments. All participants were scheduled to attend ≥ 4 follow-up appointments according to the protocol. Parents in the intervention group received SMS automated reminders before scheduled appointments. The control group parents did not receive SMSs or any alternative reminder of scheduled appointments. Regular ocular examinations and analyses were performed by investigators masked to group allocation; however, study participants and the manager in charge of randomization and sending SMSs were not masked.

MAIN OUTCOME MEASURES

Number of follow-up appointments attended, additional surgeries, laser treatments, changes in eyeglasses prescription, and occurrence of secondary ocular hypertension.

RESULTS

Among parent-child participants, 135 were randomly assigned to the SMS intervention and 123 to standard appointments. Attendance rates for the SMS group (first visit, 97.8%; second, 91.9%; third, 92.6%; fourth, 83%) were significantly higher than those for the control group (first visit, 87.8%; second, 69.9%; third, 56.9%; fourth, 33.3%). The increase in attendance rate for total number of follow-up visits with SMS reminders was 47.2% (relative risk [RR] for attendance, 1.47; 95% confidence interval [CI], 1.16-1.78; P = 0.003). The number needed to remind (NNR) to gain 1 additional visit by 1 child was 3 (95% CI, 1.8-4.2). A total of 247 clinical interventions were carried out in the SMS group and 134 in the control group (RR, 1.68; 95% CI, 1.37-1.99; P = 0.007). The NNR to result in 1 additional clinical intervention was 5 (95% CI, 3.5-6.5).

CONCLUSIONS

The SMS reminders significantly improved follow-up adherence in pediatric cataract treatment. Using readily available mobile phone resources may be an effective and economic strategy to improve management of childhood cataract in China.

FINANCIAL DISCLOSURE(S)

The authors have no proprietary or commercial interest in any of the materials discussed in this article.

Spatial access to sterile syringes and the odds of injecting with an unsterile syringe among injectors: a longitudinal multilevel study

Despite the 2010 repeal of the ban on spending federal monies to fund syringe exchange programs (SEPs) in the U.S.A., these interventions--and specifically SEP site locations--remain controversial. To further inform discussions about the location of SEP sites, this longitudinal multilevel study investigates the relationship between spatial access to sterile syringes distributed by SEPs in New York City (NYC) United Hospital Fund (UHF) districts and injecting with an unsterile syringe among injectors over time (1995-2006). Annual measures of spatial access to syringes in each UHF district (N = 42) were created using data on SEP site locations and site-specific syringe distribution data. Individual-level data on unsterile injecting among injectors (N = 4,067) living in these districts, and on individual-level covariates, were drawn from the Risk Factors study, an ongoing cross-sectional study of NYC drug users. We used multilevel models to explore the relationship of district-level access to syringes to the odds of injecting with an unsterile syringe in >75% of injection events in the past 6 months, and to test whether this relationship varied by district-level arrest rates (per 1,000 residents) for drug and drug paraphernalia possession. The relationship between district-level access to syringes and the odds of injecting with an unsterile syringe depended on district-level arrest rates. In districts with low baseline arrest rates, better syringe access was associated with a decline in the odds of frequently injecting with an unsterile syringe (AOR, 0.95). In districts with no baseline syringe access, higher arrest rates were associated with increased odds of frequently injecting with an unsterile syringe (AOR, 1.02) When both interventions were present, arrest rates eroded the protective effects of spatial access to syringes. Spatial access to syringes in small geographic areas appears to reduce the odds of injecting with an unsterile syringe among local injectors, and arrest rates elevate these odds. Policies and practices that curtail syringe flow in geographic areas (e.g., restrictions on SEP locations or syringe distribution) or that make it difficult for injectors to use the sterile syringes they have acquired may damage local injectors' efforts to reduce HIV transmission and other injection-related harms.

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

Existing study design formulas for longitudinal studies assume that the exposure is time invariant or that it varies in a manner that is controlled by design. However, in observational studies, the investigator does not control how exposure varies within subjects over time. Typically, a large number of exposure patterns are observed, with differences in the number of exposed periods per participant and with changes in the cross-sectional mean of exposure over time. This article provides formulas for study design calculations that incorporate these features for studies with a continuous outcome and a time-varying exposure, for cases where the effect of exposure on the response is assumed to be constant over time. We show that incorrectly using the formulas for time-invariant exposure can produce substantial overestimation of the required sample size. It is shown that the exposure mean, variance and intraclass correlation are the only additional parameters needed for exact solutions for the required sample size, if compound symmetry of residuals can be assumed, or to a good approximation if residuals follow a damped exponential correlation structure. The methods are applied to several examples. A publicly available programme to perform the calculations is provided.

Drug-related arrest rates and spatial access to syringe exchange programs in New York City health districts: combined effects on the risk of injection-related infections among injectors

Drug-related law enforcement activities may undermine the protective effects of syringe exchange programs (SEPs) on local injectors' risk of injection-related infections. We explored the spatial overlap of drug-related arrest rates and access to SEPs over time (1995-2006) in New York City health districts, and used multilevel models to investigate the relationship of these two district-level exposures to the odds of injecting with an unsterile syringe. Districts with better SEP access had higher arrest rates, and arrest rates undermined SEPs' protective relationship with unsterile injecting. Drug-related enforcement strategies targeting drug users should be de-emphasized in areas surrounding SEPs.

Simulation study of power and sample size for repeated measures with multinomial outcomes: an application to sound direction identification experiments (SDIE)

This study focuses on sample size determination in repeated measures studies with multinomial outcomes from multiple factors. In settings where multiple factors have repeated measures, a single subject could have hundreds of observations. Sample size selection may then refer to the number of subjects, the number of levels within a factor, or the number of repetitions within the level. We simulate multinomial data through a generalized linear mixed model (GLMM) with and without overdispersion, compute the empirical power of detecting group difference for several analytical methods and contrast their performance in group comparison studies with repeated multinomial data. We use four spatial functions to model the spatial correlation structures among observations. We evaluate the factors affecting the power under various scenarios. We also present a dataset typical in hearing studies for sound localization, in which a spatially distributed array of audio loudspeakers plays multiple sounds in order to compare two programming schemes for a hearing aid device.