Sample Size for Logistic Regression with Small Response Probability

Janus Kinase Inhibitor Therapy and Risk of Age-Related Macular Degeneration in Autoimmune Disease

Importance

The involvement of chronic inflammation in the pathogenesis of age-related macular degeneration (AMD) opens therapeutic possibilities to AMD management.

Objective

To determine whether Janus kinase inhibitors (JAKis) are associated with a reduced risk of AMD development in patients with autoimmune diseases.

Design, Setting, and Participants

This retrospective observational cohort study used administrative claims data from Merative MarketScan research databases (Commercial and Medicare Supplemental) and Optum Clinformatics Data Mart databases between January 1, 2010, and January 31, 2022. Patients with autoimmune diseases satisfying study eligibility criteria and who received JAKi treatment (9126 in MarketScan and 5667 in Optum) were propensity score matched (1:1) to identical numbers of study-eligible patients who received non-JAKi-based immunotherapy.

Exposure

Treatment duration of 6 months or longer.

Main Outcomes and Measures

Incidence rates of AMD (exudative and nonexudative) over the first 6 to 18 months of treatment were determined, and bayesian Poisson regression models were used to estimate incidence rate ratios, 95% CIs, and posterior probabilities of AMD.

Results

After matching, female sex represented the majority of the patient population in both MarketScan and Optum (14 019/18 252 [76.6%] and 8563/3364 [75.2%], respectively in the JAKi patient population). More than 60% of the patient population was older than 55 years of age in both cohorts. Over the specified treatment period, a 49% relative reduction in incidence of AMD was observed among patients who received JAKi therapy (10/9126 events; adjusted incidence rate ratio [AIRR], 0.51; 95% CI, 0.19-0.90) vs those who received non-JAKi therapy (43/9126 events; AIRR, 1 [reference]) in MarketScan, and a 73% relative reduction in incidence of AMD was observed among patients who received JAKi therapy (3/5667 events; AIRR, 0.27; 95% CI, 0.03-0.74) vs those who received non-JAKi therapy (21/5667 events; AIRR, 1 [reference]) in Optum. The absolute percentage reductions were 0.36% (MarketScan) and 0.32% (Optum), favoring patients who received JAKi therapy. Posterior probabilities of the adjusted risk being less than unity were 97.6% (MarketScan) and 98.9% (Optum) for those who received JAKi therapy vs those who received non-JAKi therapy in MarketScan and Optum, respectively.

Conclusions and Relevance

JAKi use may be associated with a reduced risk of incident AMD in US adults with major autoimmune diseases. The absolute percentage reduction is consistent with a potential role for JAKi in this population. Future studies with long-term follow-up are recommended to investigate the association between JAKi use and incident AMD in other disease indications. Investigation into the role of systemic inflammation and JAK-signal transducers and activators of transcription signaling in AMD may improve understanding of the pathophysiology of AMD and lead to new treatment options.

Calculating the power of a planned individual participant data meta-analysis to examine prognostic factor effects for a binary outcome

Collecting data for an individual participant data meta-analysis (IPDMA) project can be time consuming and resource intensive and could still have insufficient power to answer the question of interest. Therefore, researchers should consider the power of their planned IPDMA before collecting IPD. Here we propose a method to estimate the power of a planned IPDMA project aiming to synthesise multiple cohort studies to investigate the (unadjusted or adjusted) effects of potential prognostic factors for a binary outcome. We consider both binary and continuous factors and provide a three-step approach to estimating the power in advance of collecting IPD, under an assumption of the true prognostic effect of each factor of interest. The first step uses routinely available (published) aggregate data for each study to approximate Fisher's information matrix and thereby estimate the anticipated variance of the unadjusted prognostic factor effect in each study. These variances are then used in step 2 to estimate the anticipated variance of the summary prognostic effect from the IPDMA. Finally, step 3 uses this variance to estimate the corresponding IPDMA power, based on a two-sided Wald test and the assumed true effect. Extensions are provided to adjust the power calculation for the presence of additional covariates correlated with the prognostic factor of interest (by using a variance inflation factor) and to allow for between-study heterogeneity in prognostic effects. An example is provided for illustration, and Stata code is supplied to enable researchers to implement the method.

Community Health workers United to Reduce Colorectal cancer and cardiovascular disease among people at Higher risk (CHURCH): study protocol for a randomized controlled trial

BACKGROUND

Colorectal cancer (CRC) is the second most lethal cancer in the United States (U.S.) with the highest incidence and mortality rates among African Americans (AAs) compared to other racial groups. Despite these disparities, AAs are the least likely to undergo CRC screening, have precancerous colorectal polyps removed, and have CRC detected at stages early enough for curative excision. In addition, compelling evidence links inflammatory dietary patterns to increased CRC and cardiovascular disease risk. Studies show that AA churches can successfully engage in health promotion activities including those related to cancer control. The current study seeks to leverage church-placed Community Health Workers (CHWs) to increase CRC screening and reduce CRC risk.

DESIGN AND METHODS

We aim to (1) increase guideline concordant CRC screening uptake using church-placed CHWs trained in screening with a validated instrument, Brief Intervention using Motivational Interviewing, and Referral to Treatment (SBIRT); and (2) reduce dietary risk factors (inflammatory dietary patterns) linked to CRC. The latter will be addressed by culturally adapting an existing, web-based lifestyle program called Alive!. Using a Hybrid Type 1 Implementation-Effectiveness cluster randomized design, we will randomize 22 AA churches into either the dual intervention arm (CHW-led SBIRT intervention plus Alive!) or a usual care arm comprised of CRC prevention educational pamphlets and a list of CRC screening sites. We will recruit 440 subjects and evaluate the effects of both arms on screening uptake (colonoscopy, fecal DNA) (primary outcome) and dietary inflammation score (secondary outcome) at 6-month follow-up, and Life Simple7 (LS7)-a cardiovascular disease (CVD) risk score-at 6 months and 1 year (secondary outcome). Finally, guided by a racism-conscious adaptation of the Consolidated Framework for Implementation Research (CFIR), we will conduct a mixed-methods process evaluation with key stakeholders to understand multi-level influences on CRC screening and CVD risk behaviors.

DISCUSSION

Church-placed CHWs are trusted influential connectors between communities and health systems. Studies have shown that these CHWs can successfully implement health prevention protocols in churches, including those related to cancer control, making them potentially important community mediators of CRC screening uptake and CRC/CVD risk reduction.

TRIAL REGISTRATION

NCT05174286; clinicaltrials.gov; August 31st, 2023.

Community Health workers United to Reduce Colorectal cancer and cardiovascular disease among people at Higher risk (CHURCH): study protocol for a randomized controlled trial

Background: Colorectal cancer (CRC) is the second most lethal cancer in the United States (U.S.) with the highest incidence and mortality rates among African Americans (AAs) compared to other racial groups. Despite these disparities, AAs are the least likely to undergo CRC screening, have precancerous colorectal polys removed, and have CRC detected at stages early enough for curative excision. In addition, compelling evidence links inflammatory dietary patterns to increased CRC and cardiovascular disease risk. Studies show that AA churches can successfully engage in health promotion activities including those related to cancer control. The current study seeks to leverage church-placed Community Health Workers (CHWs) to increase CRC screening and reduce CRC risk. Design and Methods: We aim to (1) increase guideline concordant CRC screening uptake using church-placed CHWs trained in screening with a validated instrument, Brief Intervention using Motivational Interviewing, and Referral to Treatment (SBIRT); and (2) reduce dietary risk factors (inflammatory dietary patterns) linked to CRC. The latter will be addressed by culturally adapting an existing, web-based lifestyle program called Alive!. Using a Hybrid Type 1 Implementation-Effectiveness cluster randomized design, we will randomize 22 AA churches into either the dual intervention arm (CHW-led SBIRT intervention plus Alive!) or a usual care arm comprised of CRC prevention educational pamphlets and a list of CRC screening sites. We will recruit 440 subjects and evaluate the effects of both arms on screening uptake (colonoscopy, fecal DNA) (primary outcome) and dietary inflammation score (secondary outcome) at 6-months follow up, and Life Simple7 (LS7) - a cardiovascular disease (CVD) risk score - at 6 months and 1-year (secondary outcome). Finally, guided by a racism-conscious adaptation of the Consolidated Framework for Implementation Research (CFIR), we will conduct a mixed- methods process evaluation with key stakeholders to understand multi-level influences on CRC screening and CVD risk behaviors. Discussion: Church-placed CHWs are trusted influential connectors between communities and health systems. Studies have shown that these CHWs can successfully implement health prevention protocols in churches, including those related to cancer control, making them potentially important community mediators of CRC screening uptake and CRC/CVD risk reduction. Trial registration: NCT05174286.

Factors Associated With the Occurrence of Adverse Effects Resulting From Hypodermoclysis in Older Adults in Palliative Care: A Cohort Study

This study aimed to analyze the factors associated with local adverse effects resulting from hypodermoclysis in older adult patients in palliative care. The study involved 127 older adults undergoing palliative care at a hospital in southeastern Brazil. Data collection was performed from August to November 2019. Patients aged 60 years or older, with a prescription for hypodermoclysis at the time of admission and who were not receiving hypodermoclysis at the time of admission, were included. Data collected included sociodemographic, clinical, pharmacotherapeutic, and adverse effects of hypodermoclysis administration. Most participants were women (59.0%), with a mean age of 78.5 years. Frailty was the most prevalent diagnosis (26.8%), and 80.2% of patients were in the end-of-life stage. There was an incidence of 24.0% of adverse events, with catheter obstruction and swelling in the surrounding area of the hypodermoclysis site being the most frequent at 11.3% and 8.5%, respectively. Ondansetron administration by hypodermoclysis was 3 times more likely to have an adverse effect compared to not using this drug. In contrast, a protective factor was evident with the administration of 0.9% sodium chloride, which contributed to the reduction of complications. The occurrence of adverse effects from hypodermoclysis in the study population of older adults in palliative care was low.

Study protocol for comparing Screening, Brief Intervention, and Referral to Treatment (SBIRT) to referral as usual for depression in African American churches

Background

Depression is a leading cause of disability worldwide. African American adults, compared to White adults, are half as likely to be screened for depression in primary care settings. Disparities in depression screening contribute to poor clinical outcomes, as African Americans with depression are more disabled and sicker longer compared to Whites. African American churches are trusted settings that provide access to supports for depression. Indeed, in the first study of its kind, the investigators found that 20% of adults in African American churches screened positive for depression using the Patient Health Questionnaire-9 (PHQ-9). However, no subjects with a positive screen (PHQ-9 ≥ 10) accepted a treatment referral when offered by research personnel. Community Health Workers, who are trusted paraprofessionals from the target community, may bridge the gap between depression screening and treatment. The investigators have trained and certified 112 Community Health Workers from 45 African American churches in New York City to deliver an evidence-based intervention called Screening, Brief Intervention, and Referral to Treatment (SBIRT). Thus, the aim of the current study is to test the impact of Community Health Worker-delivered depression screening in Black churches on engagement with clinical services.

Methods

Using a hybrid type 1 effectiveness-implementation design, we propose a 2-arm, mixed-methods cluster randomized controlled trial. Church study sites will be randomized to either SBIRT (intervention arm) or referral as usual (usual care arm). This trial will be conducted with 600 church members across 30 churches (300 intervention; 300 usual care). Our primary outcome is treatment engagement, defined as attending a depression-related clinical visit. Secondary outcomes will be changes in Mental Health-Related Quality of Life and depressive symptoms at 3 and 6 months post-screening. Lastly, we will conduct a concurrent, mixed-methods (qualitative-quantitative) process evaluation to assess contextual facilitators and barriers of screening and referral.

Discussion

This is the first randomized trial of a church-placed, community health worker-delivered intervention for depression in African American populations. This study may provide a novel and effective approach to increasing depression identification and treatment linkage in economically disadvantaged populations with high depression rates.

Trial registration

ClinicalTrials.govNCT04524767. Registered on 21 August 2020.

May the Fourth (Industrial) Revolution be with You: Value Convergence within Uber’s Sharing Economy

This research provides empirical insights to reveal how value convergence occurs within Uber’s sharing economy. Uber’s business model is built on a digital platform that links private vehicle owners and their under-utilized assets to be economic revenue generating units for on-demand transport requests from potential clients. By analyzing adoption values for drivers and users of Uber, we identify antecedent operational and behavioral values for Uber adoption. We add to extant Industry 4.0 research and show value convergence emanating from economic and convenience motives. On the basis of our findings, we develop propositions for value convergence leveraging on cyber-physical systems embedded in Industry 4.0, and its application for theory and practice within the broader domains of the sharing economy.

Designing efficient randomized trials: power and sample size calculation when using semiparametric efficient estimators

Trials enroll a large number of subjects in order to attain power, making them expensive and time-consuming. Sample size calculations are often performed with the assumption of an unadjusted analysis, even if the trial analysis plan specifies a more efficient estimator (e.g. ANCOVA). This leads to conservative estimates of required sample sizes and an opportunity for savings. Here we show that a relatively simple formula can be used to estimate the power of any two-arm, single-timepoint trial analyzed with a semiparametric efficient estimator, regardless of the domain of the outcome or kind of treatment effect (e.g. odds ratio, mean difference). Since an efficient estimator attains the minimum possible asymptotic variance, this allows for the design of trials that are as small as possible while still attaining design power and control of type I error. The required sample size calculation is parsimonious and requires the analyst to provide only a small number of population parameters. We verify in simulation that the large-sample properties of trials designed this way attain their nominal values. Lastly, we demonstrate how to use this formula in the "design" (and subsequent reanalysis) of a real randomized trial and show that fewer subjects are required to attain the same design power when a semiparametric efficient estimator is accounted for at the design stage.

Approximations of the power functions for Wald, likelihood ratio, and score tests and their applications to linear and logistic regressions

Traditionally, asymptotic tests are studied and applied under local alternative (Aivazian, et al., 1985). There exists a widespread opinion that the Wald, likelihood ratio, and score tests are asymptotically equivalent. We dispel this myth by showing that These tests have different statistical power in the presence of nuisance parameters. The local properties of the tests are described in terms of the first and second derivative evaluated at the null hypothesis. The comparison of the tests are illustrated with two popular regression models: linear regression with random predictor and logistic regression with binary covariate. We study the aberrant behavior of the tests when the distance between the null and alternative does not vanish with the sample size. We demonstrate that these tests have different asymptotic power. In particular, the score test is generally asymptotically biased but slightly superior for linear regression in a close neighborhood of the null. The power approximations are confirmed through simulations.

Sample size issues in time series regressions of counts on environmental exposures

Background

Regression analyses of time series of disease counts on environmental determinants are a prominent component of environmental epidemiology. For planning such studies, it can be useful to predict the precision of estimated coefficients and power to detect associations of given magnitude. Existing generic approaches for this have been found somewhat complex to apply and do not easily extend to multiple series studies analysed in two stages. We have sought a simpler approximate approach which can easily extend to multiple series and give insight into factors determining precision.

Methods

We derive approximate expressions for precision and hence power in single and multiple time series studies of counts from basic statistical theory, compare the precision predicted by these with that estimated by analysis in real data from 51 cities of varying size, and illustrate the use of these estimators in a realistic planning scenario.

Results

In single series studies with Poisson outcome distribution, precision and power depend only on the usable variation of exposure (i.e. that conditional on covariates) and the total number of disease events, regardless of how many days those are spread over. In multiple time series (eg multi-city) studies focusing on the meta-analytic mean coefficient, the usable exposure variation and the total number of events (in all series) are again the sole determinants if there is no between-series heterogeneity or within-series overdispersion. With heterogeneity, its extent and the number of series becomes important. For all but the crudest approximation the estimates of standard errors were on average within + 20% of those estimated in full analysis of actual data.

Conclusions

Predicting precision in coefficients from a planned time series study is possible simply and given limited information. The total number of disease events and usable exposure variation are the dominant factors when overdispersion and between-series heterogeneity are low.

Power and sample size for multivariate logistic modeling of unmatched case-control studies

Sample size calculations are needed to design and assess the feasibility of case-control studies. Although such calculations are readily available for simple case-control designs and univariate analyses, there is limited theory and software for multivariate unconditional logistic analysis of case-control data. Here we outline the theory needed to detect scalar exposure effects or scalar interactions while controlling for other covariates in logistic regression. Both analytical and simulation methods are presented, together with links to the corresponding software.

Statistical power of likelihood ratio and Wald tests in latent class models with covariates

This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.

Simulation-based sample-sizing and power calculations in logistic regression with partial prior information

There have been many approximations developed for sample sizing of a logistic regression model with a single normally-distributed stimulus. Despite this, it has been recognised that there is no consensus as to the best method. In pharmaceutical drug development, simulation provides a powerful tool to characterise the operating characteristics of complex adaptive designs and is an ideal method for determining the sample size for such a problem. In this paper, we address some issues associated with applying simulation to determine the sample size for a given power in the context of logistic regression. These include efficient methods for evaluating the convolution of a logistic function and a normal density and an efficient heuristic approach to searching for the appropriate sample size. We illustrate our approach with three case studies. Copyright © 2016 John Wiley & Sons, Ltd.

Sample Size for Joint Testing of Indirect Effects

This paper presents methods to calculate sample size for evaluating mediation by joint testing of both links in an indirect pathway from exposure to mediator to outcome. Calculations rely on simulations of the underlying data structure, with testing of the two links performed under the simplifying assumption that the two test statistics are asymptotically independent. Simulations show that the proposed methods are accurate. Continuous and binary exposures and mediators, as well as continuous, binary, count, and survival outcomes are accommodated, along with over-dispersion of count outcomes, design effects, and confounding of the exposure-mediator and mediator-outcome relationships. An illustrative example is provided, and a documented R program implementing the calculations is available online.

Exploring Differential Item Functioning in a 360-Degree Assessment: Rater Source and Method of Delivery

This research used logistic regression to model item responses from a popular 360-degree assessment-for-development survey. The model used method of survey delivery and rater group to identify items exhibiting differential item functioning (DIF). The methods of survey delivery were pencil-and-paper and online by Web page. The rater groups were self, boss, peer, and direct report. The sample consisted of 374 survey families where a survey family was a set of four surveys: self, boss, peer, and direct report. Half the survey families were pencil-and-paper administration; half were online administration. The flagging procedure used effect size from Wald chi-square statistics. Results indicated little evidence that DIF existed due to method of survey delivery, lending additional support for the use of the Internet to deliver 360-degree surveys. Approximately 10% of items exhibited DIF attributable to rater group, though in every instance the magnitude of the DIF was small, suggesting that the impact of DIF on the 360-degree feedback could be slight. There was no evidence of an interaction between method of delivery and rater group. The maximum likelihood parameter estimates indicated DIF resulted from either hierarchical complexity or contingency theory. This research suggested that such forms of DIF could be naturally occurring phenomena in 360- degree assessment because both contingency and complexity can influence the perceptions by raters of a manager’s performance.

Sample size calculations for skewed distributions

Background

Sample size calculations should correspond to the intended method of analysis. Nevertheless, for non-normal distributions, they are often done on the basis of normal approximations, even when the data are to be analysed using generalized linear models (GLMs).

Methods

For the case of comparison of two means, we use GLM theory to derive sample size formulae, with particular cases being the negative binomial, Poisson, binomial, and gamma families. By simulation we estimate the performance of normal approximations, which, via the identity link, are special cases of our approach, and for common link functions such as the log. The negative binomial and gamma scenarios are motivated by examples in hookworm vaccine trials and insecticide-treated materials, respectively.

Results

Calculations on the link function (log) scale work well for the negative binomial and gamma scenarios examined and are often superior to the normal approximations. However, they have little advantage for the Poisson and binomial distributions.

Conclusions

The proposed method is suitable for sample size calculations for comparisons of means of highly skewed outcome variables.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-015-0023-0) contains supplementary material, which is available to authorized users.

Sample size determination for logistic regression on a logit-normal distribution

Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination ([Formula: see text]) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for [Formula: see text] for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.

What factors are associated with the provision of assistive technologies: the Bogotá D.C. case

AIM

To examine what demographics and clinical factors are associated with the provision of assistive technology (AT) devices in a low-income country.

METHOD

Retrospective cross-sectional exploratory study design including 15 of the 20 localities across Bogotá D.C., Colombia, a city with 6,776,009 inhabitants.

RESULTS

The type of AT device provided was significantly dependent (p < 0.001) on the client's diagnosis, impairment, age, and socio-economic strata, whether the client has a care giver, the geographical zone in which the client lives, the year of the AT provision, and the total number of AT delivered. In contrast, the client's gender (p > 0.05) and the client's affiliated type of healthcare service had no effect. In addition to that, the client's age, the client's socio-economic strata, the number of AT devices provided to the client, and the diagnostic type were the factors with the strongest level of association with the type of AT device provided.

CONCLUSIONS

Our research showed that the provision of AT in Bogotá D.C. prioritizes both people who are at the highest levels of vulnerability, and as many people as possible with the budget. That is, the low socio-economic strata, younger and older people, and the provision of at least one AT device.

IMPLICATIONS FOR REHABILITATION

Provision of AT is intended for equal opportunities for the social participation of people with a disability. Also, people with disabilities have the right to access AT regardless of the type of limitation, gender, race, age or region where they live. Research regarding AT in developing countries is scarce; thus, there is a need to conduct studies in such contexts. This study provides scientific evidence to support the development of models, approaches and strategies of AT provision in low-income countries where resources for rehabilitation are scarce.

Recalibration and validation of a preoperative risk prediction model for mortality in major colorectal surgery

BACKGROUND

In 2009, Barwon Health designed a risk stratification model for mortality in major colorectal surgery with the use of only preoperative risk factors. The Barwon Health 2009 model was shown to predict mortality reliably, and it was comparable to other models, such as the original, POSSUM. However, the Barwon Health 2009 model was never validated with data other than those used to develop the model.

OBJECTIVE

The aim of this study was to perform temporal and external validation of the Barwon Health 2009 model and to compare it with other published models.

DESIGN

: The temporal validation was a prospective observational study, whereas the external validation was a retrospective observational study. The discrimination and calibration of the models were assessed by using the area under receiver operator characteristic and χ test of Hosmer-Lemeshow goodness-of-fi technique.

SETTINGS

This is a multi-institutional study. Data were collected from 2008 to 2010.

RESULTS

There were 474 major colorectal cases at Geelong Hospital (temporal validation) and 389 cases at Western Hospital (external validation). The overall mortality rate was 5.10% and 1.03%. In the comparison of the 2 demographics, Geelong Hospital had a higher proportion of patients who were older and had higher ASA scores and comorbidity counts, whereas Western Hospital surgeons were operating on a higher number of urgent cases. Despite the differences, the Barwon Health 2009 model was able to discriminate mortality reliably (area under receiver operator characteristic = 0.753) but had poor model calibration (p < 0.001) on temporal validation. Hence, the model was recalibrated to predict mortality accurately(area under receiver operator characteristic = 0.772; p = 0.83), and this was successfully validated at Western Hospital (area under receiver operator characteristic = 0.788; p = 0.24).

CONCLUSIONS

We have developed a model that can accurately predict mortality after major colorectal surgery by using only data that are available preoperatively. After recalibration, the model was successfully validated in a second hospital.

A revisit to sample size and power calculations for testing odds ratio in two independent binomials

We reexamine the subject of sample size determination (SSD) when testing logarithm of odds ratio (OR) against zero in two independent binomials. Four common approaches are considered: a closed-form SS formula based on the Wald test (nW), closed-form formulas that meet SS requirement by score and exact tests respectively (nS and nE), and a numerical approach to calculating SS based on likelihood ratio (LR) tests (nL). Several practically useful findings are presented. First, nW is a strictly convex function of OR for OR >1 and OR <1, respectively, implying that SS calculated by nW does not necessarily decrease as OR gets further away from 1. However, minimum SS often occurs at OR values that are deemed relatively extreme and rare in real life. nS, nE, and nL decrease monotonically as OR diverges from 1. Secondly, the optimal sampling ratio (OSR) between two independent binomials that yields maximum power for a given total SS is not always 1:1 but depends on the odds of outcome in each arm. nW benefits the most from the application of OSR in that total SS can be significantly reduced as compared to the commonly used 1:1 sampling ratio. Savings in SS by OSR in nS, nL and nE are relatively immaterial from a practical perspective. Finally, we use simulation studies to examine the power loyalty of each SS approach and explore penalized likelihood as a remedy for undermined power loyalty.

Sample size determination for clustered count data

We consider the problem of sample size determination for count data. Such data arise naturally in the context of multicenter (or cluster) randomized clinical trials, where patients are nested within research centers. We consider cluster-specific and population-averaged estimators (maximum likelihood based on generalized mixed-effect regression and generalized estimating equations, respectively) for subject-level and cluster-level randomized designs, respectively. We provide simple expressions for calculating the number of clusters when comparing event rates of two groups in cross-sectional studies. The expressions we derive have closed-form solutions and are based on either between-cluster variation or intercluster correlation for cross-sectional studies. We provide both theoretical and numerical comparisons of our methods with other existing methods. We specifically show that the performance of the proposed method is better for subject-level randomized designs, whereas the comparative performance depends on the rate ratio for the cluster-level randomized designs. We also provide a versatile method for longitudinal studies. Three real data examples illustrate the results.

A comparative study on entrepreneurial attitudes modeled with logistic regression and Bayes nets

Entrepreneurship research is receiving increasing attention in our context, as entrepreneurs are key social agents involved in economic development. We compare the success of the dichotomic logistic regression model and the Bayes simple classifier to predict entrepreneurship, after manipulating the percentage of missing data and the level of categorization in predictors. A sample of undergraduate university students (N = 1230) completed five scales (motivation, attitude towards business creation, obstacles, deficiencies, and training needs) and we found that each of them predicted different aspects of the tendency to business creation. Additionally, our results show that the receiver operating characteristic (ROC) curve is affected by the rate of missing data in both techniques, but logistic regression seems to be more vulnerable when faced with missing data, whereas Bayes nets underperform slightly when categorization has been manipulated. Our study sheds light on the potential entrepreneur profile and we propose to use Bayesian networks as an additional alternative to overcome the weaknesses of logistic regression when missing data are present in applied research.

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.

An Efficient Gatekeeper Algorithm for Detecting GxE

The risk for many complex diseases is believed to be a result of the interactive effects of genetic and environmental factors. Developing efficient techniques to identify gene-environment interactions (GxE) is important for unraveling the etiologic basis of many modern day diseases including cancer. The problem of false positives and false negatives continues to pose significant roadblocks to detecting GxE and informing targeted public health screening and intervention. A heuristic gatekeeper method is presented to guide the selection of single nucleotide polymorphisms (SNPs) in the design phase of a GxE study.

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

Existing study design formulas for longitudinal studies have assumed that the exposure is time-invariant. We derived sample size formulas for studies comparing rates of change by exposure when the exposure varies with time within a subject, focusing on observational studies where this variation is not controlled by the investigator. Two scenarios are considered, one assuming that the effect of exposure on the response is acute and the other assuming that it is cumulative. We show that accurate calculations can often be obtained by providing the intraclass correlation of exposure and the exposure prevalence at each time point. When comparing rates of change, studies with a time-varying exposure are, in general, less efficient than studies with a time-invariant one. We provide a public access program to perform the calculations described in the paper (http://www.hsph.harvard.edu/faculty/spiegelman/optitxs.html).

Bayesian approach to average power calculations for binary regression models with misclassified outcomes

We develop a simulation-based procedure for determining the required sample size in binomial regression risk assessment studies when response data are subject to misclassification. A Bayesian average power criterion is used to determine a sample size that provides high probability, averaged over the distribution of potential future data sets, of correctly establishing the direction of association between predictor variables and the probability of event occurrence. The method is broadly applicable to any parametric binomial regression model including, but not limited to, the popular logistic, probit, and complementary log-log models. We detail a common medical scenario wherein ascertainment of true disease status is impractical or otherwise impeded, and in its place the outcome of a single binary diagnostic test is used as a surrogate. These methods are then extended to the two diagnostic test setting. We illustrate the method with categorical covariates using one example that involves screening for human papillomavirus. This example coupled with results from simulated data highlights the utility of our Bayesian sample size procedure with error prone measurements.

Sample size calculations for evaluating mediation

This paper presents sample size calculations for testing the mediation of the effect of a primary predictor by an intermediate variable. This problem is related to validating surrogate markers and to testing the effect of a primary predictor in the presence of confounders. For those problems, proposals for sample size calculation exist in the literature and can be adapted to the problem of mediation. Methods based on the variance inflation factor in linear regression provide exact sample size calculations for the linear model and approximations for the logistic, Poisson, and Cox models. We propose another procedure based on simulation of the underlying data structure, with applications to the logistic and Cox models. For the Poisson model, a new analytic method is also proposed. The behavior of the different proposals is investigated by means of simulation studies.

Sample size and optimal design for logistic regression with binary interaction

There is no consensus on what test to use as the basis for sample size determination and power analysis. Some authors advocate the Wald test and some the likelihood-ratio test. We argue that the Wald test should be used because the Z-score is commonly applied for regression coefficient significance testing and therefore the same statistic should be used in the power function. We correct a widespread mistake on sample size determination when the variance of the maximum likelihood estimate (MLE) is estimated at null value. In our previous paper, we developed a correct sample size formula for logistic regression with single exposure (Statist. Med. 2007; 26(18):3385-3397). In the present paper, closed-form formulas are derived for interaction studies with binary exposure and covariate in logistic regression. The formula for the optimal control-case ratio is derived such that it maximizes the power function given other parameters. Our sample size and power calculations with interaction can be carried out online at www.dartmouth.edu/ approximately eugened.

A practical approach to computing power for generalized linear models with nominal, count, or ordinal responses

Data analysts facing study design questions on a regular basis could derive substantial benefit from a straightforward and unified approach to power calculations for generalized linear models. Many current proposals for dealing with binary, ordinal, or count outcomes are conceptually or computationally demanding, limited in terms of accommodating covariates, and/or have not been extensively assessed for accuracy assuming moderate sample sizes. Here, we present a simple method for estimating conditional power that requires only standard software for fitting the desired generalized linear model for a non-continuous outcome. The model is fit to an appropriate expanded data set using easily calculated weights that represent response probabilities given the assumed values of the parameters. The variance-covariance matrix resulting from this fit is then used in conjunction with an established non-central chi square approximation to the distribution of the Wald statistic. Alternatively, the model can be re-fit under the null hypothesis to approximate power based on the likelihood ratio statistic. We provide guidelines for constructing a representative expanded data set to allow close approximation of unconditional power based on the assumed joint distribution of the covariates. Relative to prior proposals, the approach proves particularly flexible for handling one or more continuous covariates without any need for discretizing. We illustrate the method for a variety of outcome types and covariate patterns, using simulations to demonstrate its accuracy for realistic sample sizes.

Sample size determination for logistic regression revisited

There is no consensus on the approach to compute the power and sample size with logistic regression. Some authors use the likelihood ratio test; some use the test on proportions; some suggest various approximations to handle the multivariate case. We advocate the use of the Wald test since the Z-score is routinely used for statistical significance testing of regression coefficients. The null-variance formula became popular from early studies, which contradicts modern software, which utilizes the method of maximum likelihood estimation (MLE), when the variance of the MLE is estimated at the MLE, not at the null. We derive general Wald-based power and sample size formulas for logistic regression and then apply them to binary exposure and confounder to obtain a closed-form expression. These formulas are applied to minimize the total sample size in a case-control study to achieve a given power by optimizing the ratio of controls to cases. Approximately, the optimal number of controls to cases is equal to the square root of the alternative odds ratio. Our sample size and power calculations can be carried out online at www.dartmouth.edu/ approximately eugened.

Factors related to posttraumatic stress in adolescent survivors of childhood cancer and their parents

GOALS OF WORK

The purpose of this study was to investigate factors related to severe posttraumatic stress symptoms (PTSS) in adolescent survivors of childhood cancer and their parents.

MATERIALS AND METHODS

Eighty-nine families (88 adolescent survivors of childhood cancer, 87 mothers, 72 fathers) completed a self-report questionnaire. Multivariate logistic regression analyses were performed using the following risk factors for severe PTSS: trait anxiety, family functioning, demographic and medical variables.

MAIN RESULTS

Severe PTSS were reported by 10.9% (n=9) of the survivors, 20.7% (n=18) of the mothers, and 22.2% (n=16) of the fathers. Preliminary analyses found significant correlations of PTSS between mother-survivor (Spearman's gamma=0.377, p<0.01) and mother-father (Spearman's gamma=0.483, p<0.01). The results of multivariate analyses indicated that higher trait anxiety [odds ratio (OR):1.16; 95% confidence interval (CI): 1.03-1.31; p<0.05] and having medical sequelae (OR: 5.85; 95% CI:1.02-33.72; p<0.05) were significant factors related to PTSS for survivors. For mothers, the significant PTSS-related factors were: higher trait anxiety (OR:1.13; 95% CI:1.04-1.23; p<0.01); 5- to 9-year interval from the first diagnosis to the present investigation, compared to more than a 10-year interval (OR: 6.45; 95% CI:1.67-24.89; p<0.01); and a relatively lower rating on "roles" of family functioning (OR: 12.34; 95% CI:1.11-136.97; p<0.05). For fathers, trait anxiety was a significant related factor (OR: 1.07; 95% CI:1.01-1.14; p<0.05).

CONCLUSIONS

Survivors and their parents suffered from PTSS after long interval from completion of treatment, and PTSS-related factors varied for each family member. Appropriate allocation of responsibility for family functioning may promote the ability to decrease PTSS, especially for mothers.

The relationship of medical comorbidity and depression in older, primary care patients

Comorbid medical illnesses are a key feature of geriatric mood disorders, yet the specificity of such associations remains unclear. In a sample of 546 primary care patients age >or=65 years, pathology in several organ systems (respiratory, eye/ear/nose/throat, gastrointestinal, central nervous system, endocrine) and several chronic conditions (neurological disease, low vision, chronic obstructive pulmonary disease, diabetes) were associated with depression. However, notwithstanding these specific associations, global (overall) medical burden was most powerfully and independently associated with depression, largely independent of functional status. This generates the hypothesis that, in general primary care populations, the relationship of medical illness to depression may be multimodal and/or may involve shared pathobiological or psychosocial mechanisms.

Planning a dose-response study with subject-specific doses

This article is concerned with a dose-response study where the doses are subject-specific. The motivating example is a study on the use of radioiodine in metastatic thyroid cancer where the dose is individualized for each subject based on pharmacokinetic models of clearance of the agent. The goal is to design a study that will estimate the probability of response within a specified precision. This setup does not fit into well-studied dose-response designs primarily because doses are subject-specific. Here the dose-response relationship is modelled using logistic regression and a second-order approximation to the asymptotic variance of the model parameters is developed. The resulting procedure is simple to apply and requires minimal assumptions regarding the distribution of the dose levels. Simulation studies establish that, for a reasonable range of parameter values, the approximation is reasonably accurate. A Monte Carlo procedure is developed as well for cases when the approximation performs poorly. The proposed method is applied to the thyroid cancer study, including elicitation of parameters and a sensitivity analysis. Computer code in SAS and R are provided in the Appendix.

A simple approach to power and sample size calculations in logistic regression and Cox regression models

For a given regression problem it is possible to identify a suitably defined equivalent two-sample problem such that the power or sample size obtained for the two-sample problem also applies to the regression problem. For a standard linear regression model the equivalent two-sample problem is easily identified, but for generalized linear models and for Cox regression models the situation is more complicated. An approximately equivalent two-sample problem may, however, also be identified here. In particular, we show that for logistic regression and Cox regression models the equivalent two-sample problem is obtained by selecting two equally sized samples for which the parameters differ by a value equal to the slope times twice the standard deviation of the independent variable and further requiring that the overall expected number of events is unchanged. In a simulation study we examine the validity of this approach to power calculations in logistic regression and Cox regression models. Several different covariate distributions are considered for selected values of the overall response probability and a range of alternatives. For the Cox regression model we consider both constant and non-constant hazard rates. The results show that in general the approach is remarkably accurate even in relatively small samples. Some discrepancies are, however, found in small samples with few events and a highly skewed covariate distribution. Comparison with results based on alternative methods for logistic regression models with a single continuous covariate indicates that the proposed method is at least as good as its competitors. The method is easy to implement and therefore provides a simple way to extend the range of problems that can be covered by the usual formulas for power and sample size determination.

Subjective Perceptions and Physiological Variables During Weaning From Mechanical Ventilation

• Background As costs related to mechanical ventilation increase, clear indicators of patients’ readiness to be weaned are needed. Research has not yet yielded a consensus on physiological variables that are consistent correlates of weaning outcomes. Subjective perceptions rarely have been examined for their contribution to successful weaning.

• Objective To explore the subjective perceptions of dyspnea, fatigue, and self-efficacy and selected physiological variables in patients being weaned from mechanical ventilation.

• Methods Data were collected prospectively on 68 patients being weaned from mechanical ventilation. Subjective perceptions were measured by using 3 visual analog scales; physiological variables were measured by using the Burns Weaning Assessment Program and a patient profile. Weaning outcomes were recorded 24 hours after data collection.

• Results Participants were primarily white women and required mechanical ventilation for a mean of less than 4 days. Participants reported mild dyspnea, moderate fatigue, and high weaning self-efficacy. High Pao2, low Paco2, stable hemodynamic status, adequate cough and swallow reflexes, no metabolic changes, and no abdominal problems were associated with complete weaning (P = .05). Subjective perceptions were associated with physiological variables but not with weaning outcomes.

• Conclusions Multidimensional assessment of both primary and secondary indicators of readiness to be weaned is necessary for timely, efficient weaning from mechanical ventilation. Primary assessments include physiological variables related to gas exchange, hemodynamic status, diaphragmatic expansion, and airway clearance. Secondary assessments include perceptions related to key physiological variables. Additional research is needed to determine the predictive value of physiological variables and perceptions of dyspnea, fatigue, and self-efficacy.

Sample size calculation for a historically controlled clinical trial with adjustment for covariates

We present a Bayesian approach to determining the optimal sample size for a historically controlled clinical trial. This work is motivated by a trial of a new coronary stent that uses a retrospective control group formed from seven trials of coronary stents currently marketed in the United States. In studies involving nonrandomized control groups, hierarchical regression, propensity score methods, or other sophisticated models are typically required to account for heterogeneity among groups which, if ignored could bias the results. Sample size calculations for historically controlled trials of medical devices are often based on formulae derived for randomized trials and fail to account for estimation of model parameters, correlation of observations, and uncertainty in the distribution of covariates of the patients recruited in the new trial. We propose methodology based on stochastic optimization that overcomes these deficiencies. The methodology is demonstrated using an objective function based on the power of the trial from a Bayesian approach. Analytic approximations based on a covariate-free analysis that convey features of the power function are developed. Our principle conclusions are that exact sample size calculations can be substantially different from current approximations, and stochastic optimization provides a convenient method of computation.

Effects of intravenous secretin on language and behavior of children with autism and gastrointestinal symptoms: a single-blinded, open-label pilot study

BACKGROUND

Autism is a severe developmental disorder with poorly understood etiology. A recently published case series describes 3 autistic children with gastrointestinal symptoms who underwent endoscopy and intravenous administration of secretin and were subsequently noted by their parents to demonstrate improved language skills over a 5-week period. This report sparked tremendous public interest, and investigators at several sites moved quickly to design controlled trials to test the efficacy of secretin as a therapy for autistic children. However, this is the first effort specifically designed to replicate the initial reported findings in terms of patient age, presenting symptoms, and drug administration.

OBJECTIVE

To rigorously apply the scientific method by assessing the reproducibility of the reported effects of intravenous secretin on the language of young children with autism and gastrointestinal symptoms.

METHODS

We performed a single-blinded, prospective, open-label trial by conducting formal language testing and blinded behavioral rating both before and repeatedly after a standardized infusion of secretin. We selected autistic children who were similar in age and profile to those described in the published retrospective case review. Inclusion criteria for study participation included age (3-6 years), confirmed diagnosis of autism, and reported gastrointestinal symptoms (16 had chronic diarrhea, 2 had gastroesophageal reflux, and 2 had chronic constipation). Twenty children (18 male) were admitted to the Pediatric Clinical Research Center at the University of California, San Francisco after administration of the Preschool Language Scale-3 (PLS-3). A 3 CU/kg dose of secretin (Secretin-Ferring) was administered intravenously (upper endoscopy was not performed). Behavioral ratings were derived using the Autism Observation Scale applied to a 30-minute time sample of the child's behavior consisting of a videotape of the PLS-3 (structured setting) and a second free play session with a standard set of developmentally appropriate toys. Participants then returned for follow-up evaluations, with readministrations of the PLS-3 at 1, 2, 3, and 5 weeks' postinfusion, and videotaping of each session for later blinded review by 2 independent observers using the Autism Observation Scale, uninformed about week of posttreatment. We also surveyed parents of our study children about their impressions of the effects of secretin using a 5-point Likert scale for parents to rate changes seen in their child.

RESULTS

With a total study completion rate across all participants of 96%, repeated measures analyses of variance revealed no significant increases in children's language skills from baseline across all 5 study time periods after a single infusion of secretin. Similarly, neither significant decreases in atypical behaviors nor increases in prosocial behaviors and developmentally appropriate play skills emerged. Furthermore, no relationship was found between parental reports of change and observable improvement in the sample. Despite the objective lack of drug effect, 70% of parents in our study reported moderate to high change in their child's language and behavior. Furthermore, 85% of parents reported that they felt that their child would obtain at least some additional benefits from another infusion of secretin.

CONCLUSIONS

The results of our pilot study indicate that intravenous secretin had no effects in a 5-week period on the language and behavior of 20 children with autism and gastrointestinal symptoms. The open-label, prospective design of our study with blinded reviews of patients both before and after secretin administration follows the scientific method by seeking to reproduce an observed phenomenon using validating and reliable outcome measures. Pilot studies remain a mandatory step for the design of future randomized, clinical trials investigating potential treatments for children with autism.

On power and sample size calculations for likelihood ratio tests in generalized linear models

A direct extension of the approach described in Self, Mauritsen, and Ohara (1992, Biometrics 48, 31-39) for power and sample size calculations in generalized linear models is presented. The major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations. Furthermore, for the approximation of the noncentrality of the noncentral chi-square distribution for the likelihood ratio statistic, a simplification is provided that not only reduces substantial computation but also maintains the accuracy. Simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions.

Sample size considerations for the evaluation of prognostic factors in survival analysis

When the role of a new prognostic factor is investigated, careful planning of an appropriate study is required. This includes an assessment of the power of the study in terms of sample sizes. An adequate analysis of the independent prognostic effect of a new factor has to be adjusted for the existing standard factors. With survival time as endpoint this will usually be done with the Cox proportional hazards model. Sample size and power formulae in survival analysis have been developed by Schoenfeld for randomized treatment comparisons. In the analysis of prognostic factors the covariates included are expected to be correlated with the factor of primary interest. In this situation, the existing sample size and power formulae are not valid and may not be applied. In this paper, Schoenfeld's formula is first extended to the situation where a correlated factor is included in the analysis. The validity of the resulting approximate asymptotic formula is investigated for its asymptotic behaviour by numerical integration and for its finite behaviour by simulation. Second, an approximate formula for sample size and power is provided to detect an interaction between the interesting and a second correlated factor. This extends the formula for independent effects. Finally, the approach is illustrated by an example on the prognostic impact of DNA ploidy and other factors in advanced ovarian cancer.

Solvent accessibility and purifying selection within proteins of Escherichia coli and Salmonella enterica

The neutral theory of molecular evolution predicts that variation within species is inversely related to the strength of purifying selection, but the strength of purifying selection itself must be related to physical constraints imposed by protein folding and function. In this paper, we analyzed five enzymes for which polymorphic sequence variation within Escherichia coli and/or Salmonella enterica was available, along with a protein structure. Single and multivariate logistic regression models are presented that evaluate amino acid size, physicochemical properties, solvent accessibility, and secondary structure as predictors of polymorphism. A model that contains a positive coefficient of association between polymorphism and solvent accessibility and separate intercepts for each secondary-structure element is sufficient to explain the observed variation in polymorphism between sites. The model predicts an increase in the probability of amino acid polymorphism with increasing solvent accessibility for each protein regardless of physicochemical properties, secondary-structure element, or size of the amino acid. This result, when compared with the distribution of synonymous polymorphism, which shows no association with solvent accessibility, suggests a strong decrease in purifying selection with increasing solvent accessibility.

Sample size in clinical trials with dichotomous endpoints: use of covariables

In many clinical trials, the primary endpoint is dichotomous. In this article, we examine the possibility of reducing the required sample size by removing variation associated with baseline covariables. Three measures are used to study the size of the reduction. Simulation studies based on a database of head trauma and of stroke patients suggested that a substantial reduction in the sample size can be achieved when the correlation between the endpoint and covariables is strong. A simple ad hoc formula for approximating the required sample size is proposed.