Sample Size Estimation for Negative Binomial Regression Comparing Rates of Recurrent Events with Unequal Follow-Up Time

Abstract Heart failure with mid-range ejection fraction (HFmrEF) has been recognized as a distinct HF phenotype, but wether patients on this category fare worse, similarly, or better than those with HF with reduced EF (HFrEF) or preserved EF (HFpEF) in terms of rehospitalization risk over time remains unclear. We therefore sought to characterize the mordibity burden of HFmrEF patients by evaluating the risk of recurrent hospitalizations following an admission for acute HF. Methods We prospectively included 2,961 consecutive patients discharged for acute HF in our institution from 2004 to 2017. Patients were categorized according to their ejection fraction (EF) obtained by an echocardiography during the index admission: HFmrEF (EF 41–49%), HFrEF (EF≤40%) and HFpEF (EF≥50%). Negative binomial regression method was used to evaluate the association between EF status and recurrent all-cause and HF-related admissions. Risk estimates were expressed as incidence ratio ratios (IRR). Results Mean age of the cohort was 73.9±11.1 years, 49% were women, and 46.0% had suffered from previous HF admissions. 472 patients (15.9%) had HFmrEF, 956 (32.3%) had HFrEF, and 1,533 (51.8%) had HFpEF. At a median (interquartile range) follow-up of 2.4 (4.4) years, 1,821 (61.5%) patients died and 6,035 all-cause readmissions were registered in 2,026 patients (68.4%), being 2,163 of them HF-related. Rates of all-cause readmission per 100 patients-years of follow-up were 43.4, 47.1 and 50.1 per HFrEF, HFmrEF and HFpEF categories, respectively. After multivariable adjustment, and compared to patients with HFrEF, HFmrEF status was not associated with a higher risk of all-cause or HF-related recurrent admissions (IRR=1.06; 95% confidence interval (CI), 0.93–1.20; p=0.89), and IRR=1.07; 95% CI, 0.91–1.26; p=0.389, respectively), whereas HFpEF status was associated with a non-significant increase in the risk of all-cause recurrent admissions but a similar risk of HF-related readmissions (IRR=1.10; 95% confidence interval (CI), 0.99–1.22; p=0.06, and IRR=1.01; 95% CI, 0.88–1.16; p=0.900, respectively) Conclusion Following an admission for acute HF, patients with HFmrEF have a similar all-cause and HF-related rehospitalization burden when compared to patients with HFrEF, by means of recurrent events analysis.

Download Full-text

A systematic review of the quality of conduct and reporting of survival analyses of tuberculosis outcomes in Africa

BMC Medical Research Methodology ◽

10.1186/s12874-021-01280-3 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Moses M. Ngari ◽

Susanne Schmitz ◽

Christopher Maronga ◽

Lazarus K. Mramba ◽

Michel Vaillant

Keyword(s):

Systematic Review ◽

Sample Size ◽

Survival Function ◽

Sample Size Estimation ◽

Size Estimation ◽

Survival Curves ◽

Survival Analyses ◽

Survival Regression

Abstract Background Survival analyses methods (SAMs) are central to analysing time-to-event outcomes. Appropriate application and reporting of such methods are important to ensure correct interpretation of the data. In this study, we systematically review the application and reporting of SAMs in studies of tuberculosis (TB) patients in Africa. It is the first review to assess the application and reporting of SAMs in this context. Methods Systematic review of studies involving TB patients from Africa published between January 2010 and April 2020 in English language. Studies were eligible if they reported use of SAMs. Application and reporting of SAMs were evaluated based on seven author-defined criteria. Results Seventy-six studies were included with patient numbers ranging from 56 to 182,890. Forty-three (57%) studies involved a statistician/epidemiologist. The number of published papers per year applying SAMs increased from two in 2010 to 18 in 2019 (P = 0.004). Sample size estimation was not reported by 67 (88%) studies. A total of 22 (29%) studies did not report summary follow-up time. The survival function was commonly presented using Kaplan-Meier survival curves (n = 51, (67%) studies) and group comparisons were performed using log-rank tests (n = 44, (58%) studies). Sixty seven (91%), 3 (4.1%) and 4 (5.4%) studies reported Cox proportional hazard, competing risk and parametric survival regression models, respectively. A total of 37 (49%) studies had hierarchical clustering, of which 28 (76%) did not adjust for the clustering in the analysis. Reporting was adequate among 4.0, 1.3 and 6.6% studies for sample size estimation, plotting of survival curves and test of survival regression underlying assumptions, respectively. Forty-five (59%), 52 (68%) and 73 (96%) studies adequately reported comparison of survival curves, follow-up time and measures of effect, respectively. Conclusion The quality of reporting survival analyses remains inadequate despite its increasing application. Because similar reporting deficiencies may be common in other diseases in low- and middle-income countries, reporting guidelines, additional training, and more capacity building are needed along with more vigilance by reviewers and journal editors.

Download Full-text

Abstract 16807: Burden and Timing of Hospitalizations in Heart Failure: A Community Study

Circulation ◽

10.1161/circ.130.suppl_2.16807 ◽

2014 ◽

Vol 130 (suppl_2) ◽

Author(s):

Alanna M Chamberlain ◽

Yariv Gerber ◽

Shannon M Dunlay ◽

Sheila M Manemann ◽

Susan A Weston ◽

...

Keyword(s):

Heart Failure ◽

Negative Binomial ◽

Negative Binomial Regression ◽

Community Study ◽

Olmsted County ◽

Comorbid Conditions ◽

Binomial Regression ◽

Time Periods ◽

Patients Experience

Background: Heart failure (HF) patients are experiencing an epidemic of hospitalizations. Nevertheless, data on the frequency and distribution of hospitalizations over the course of the disease are lacking. Methods: We determined the rates of hospitalizations during periods of follow-up in Olmsted County, MN residents with incident HF from 2000-2010. HF was identified using ICD-9 code 428 and validated by the Framingham criteria. All hospitalizations were obtained for the 2 years following incident HF and each was categorized as due to HF, other cardiovascular (ICD-9 codes 390-427, 429-459), or non-cardiovascular causes. Follow-up was divided into discrete time periods (epochs): 0-30, 31-182, 183-365, and 366-730 days. Negative binomial regression examined associations between epochs of follow-up time and hospitalizations. Results: Among 1702 incident HF patients (mean age 76, 44% male), 1143 (67%) were hospitalized at index. Over the 2 year follow-up, 3008 hospitalizations were observed among 1136 patients, and 351 patients were hospitalized within 30 days of incident HF (median time from HF to hospitalization: 11 days). The majority of hospitalizations were due to non-cardiovascular causes (63% vs. 14% HF, 23% other cardiovascular); however, a larger proportion of HF and other cardiovascular hospitalizations were observed within the first 30 days (52% non-cardiovascular, 18% HF, 30% other cardiovascular) compared to the other time periods. The rate of hospitalization was highest within the first 30 days and was similar across sex, presentation of incident HF (inpatient, outpatient), and type of HF (preserved (≥50%), reduced (<50%) ejection fraction) (Table). Conclusions: HF patients experience high rates of hospitalizations, particularly within the first 30 days, and the majority of hospitalizations are for non-cardiovascular causes. Continued efforts to manage comorbid conditions and reduce hospitalizations in HF patients are needed.

Download Full-text

Sample size calculations for the differential expression analysis of RNA-seq data using a negative binomial regression model

Statistical Applications in Genetics and Molecular Biology ◽

10.1515/sagmb-2018-0021 ◽

2019 ◽

Vol 18 (1) ◽

Cited By ~ 2

Author(s):

Xiaohong Li ◽

Dongfeng Wu ◽

Nigel G.F. Cooper ◽

Shesh N. Rai

Keyword(s):

Regression Model ◽

Sample Size ◽

Negative Binomial ◽

Negative Binomial Regression ◽

Wald Test ◽

Maximum Likelihood Estimates ◽

Negative Binomial Regression Model ◽

Rna Seq ◽

Sample Sizes ◽

Binomial Regression

Abstract High throughput RNA sequencing (RNA-seq) technology is increasingly used in disease-related biomarker studies. A negative binomial distribution has become the popular choice for modeling read counts of genes in RNA-seq data due to over-dispersed read counts. In this study, we propose two explicit sample size calculation methods for RNA-seq data using a negative binomial regression model. To derive these new sample size formulas, the common dispersion parameter and the size factor as an offset via a natural logarithm link function are incorporated. A two-sided Wald test statistic derived from the coefficient parameter is used for testing a single gene at a nominal significance level 0.05 and multiple genes at a false discovery rate 0.05. The variance for the Wald test is computed from the variance-covariance matrix with the parameters estimated from the maximum likelihood estimates under the unrestricted and constrained scenarios. The performance and a side-by-side comparison of our new formulas with three existing methods with a Wald test, a likelihood ratio test or an exact test are evaluated via simulation studies. Since other methods are much computationally extensive, we recommend our M1 method for quick and direct estimation of sample sizes in an experimental design. Finally, we illustrate sample sizes estimation using an existing breast cancer RNA-seq data.

Download Full-text

Correction to: Sample size estimation for randomised controlled trials with repeated assessment of patient-reported outcomes: what correlation between baseline and follow-up outcomes should we assume?

Trials ◽

10.1186/s13063-019-3732-6 ◽

2019 ◽

Vol 20 (1) ◽

Author(s):

Stephen J. Walters ◽

Richard M. Jacques ◽

Inês Bonacho dos Anjos Henriques-Cadby ◽

Jane Candlish ◽

Nikki Totton ◽

...

Keyword(s):

Sample Size ◽

Randomised Controlled Trials ◽

Patient Reported Outcomes ◽

Sample Size Estimation ◽

Controlled Trials ◽

Size Estimation ◽

Patient Reported ◽

Randomised Controlled ◽

Repeated Assessment

Following publication of the original article [1], we have been notified that one of an error in the Conclusions section of the Abstract.

Download Full-text

Burden and trajectory of multimorbidity in rheumatoid arthritis: a matched cohort study from 2006 to 2015

Annals of the Rheumatic Diseases ◽

10.1136/annrheumdis-2020-218282 ◽

2020 ◽

pp. annrheumdis-2020-218282 ◽

Cited By ~ 1

Author(s):

Bryant R England ◽

Punyasha Roul ◽

Yangyuna Yang ◽

Harlan Sayles ◽

Fang Yu ◽

...

Keyword(s):

Rheumatoid Arthritis ◽

Cohort Study ◽

Chronic Conditions ◽

Negative Binomial ◽

Negative Binomial Regression ◽

Sensitivity Analyses ◽

Cross Sectional ◽

Diagnostic Codes ◽

Binomial Regression

ObjectivesTo compare the onset and trajectory of multimorbidity between individuals with and without rheumatoid arthritis (RA).MethodsA matched, retrospective cohort study was completed in a large, US commercial insurance database (MarketScan) from 2006 to 2015. Using validated algorithms, patients with RA (overall and incident) were age-matched and sex-matched to patients without RA. Diagnostic codes for 44 preidentified chronic conditions were selected to determine the presence (≥2 conditions) and burden (count) of multimorbidity. Cross-sectional comparisons were completed using the overall RA cohort and conditional logistic and negative binomial regression models. Trajectories of multimorbidity were assessed within the incident RA subcohort using generalised estimating equations.ResultsThe overall cohort (n=277 782) and incident subcohort (n=61 124) were female predominant (76.5%, 74.1%) with a mean age of 55.6 years and 54.5 years, respectively. The cross-sectional prevalence (OR 2.29, 95% CI 2.25 to 2.34) and burden (ratio of conditions 1.68, 95% CI 1.66 to 1.70) of multimorbidity were significantly higher in RA than non-RA in the overall cohort. Within the incident RA cohort, patients with RA had more chronic conditions than non-RA (β 1.13, 95% CI 1.10 to 1.17), and the rate of accruing chronic conditions was significantly higher in RA compared with non-RA (RA × follow-up year, β 0.21, 95% CI 0.20 to 0.21, p<0.001). Results were similar when including the pre-RA period and in several sensitivity analyses.ConclusionsMultimorbidity is highly prevalent in RA and progresses more rapidly in patients with RA than in patients without RA during and immediately following RA onset. Therefore, multimorbidity should be aggressively identified and targeted early in the RA disease course.

Download Full-text

Blinded sample size reestimation for negative binomial regression with baseline adjustment

Statistics in Medicine ◽

10.1002/sim.8525 ◽

2020 ◽

Vol 39 (14) ◽

pp. 1980-1998 ◽

Cited By ~ 1

Author(s):

Antonia Zapf ◽

Thomas Asendorf ◽

Christoph Anten ◽

Tobias Mütze ◽

Tim Friede

Keyword(s):

Sample Size ◽

Negative Binomial ◽

Negative Binomial Regression ◽

Binomial Regression ◽

Baseline Adjustment

Download Full-text

Modelling and sample size reestimation for longitudinal count data with incomplete follow up

Statistical Methods in Medical Research ◽

10.1177/0962280217715664 ◽

2017 ◽

Vol 28 (1) ◽

pp. 117-133 ◽

Cited By ~ 4

Author(s):

Thomas Asendorf ◽

Robin Henderson ◽

Heinz Schmidli ◽

Tim Friede

Keyword(s):

Multiple Sclerosis ◽

Clinical Trials ◽

Sample Size ◽

Count Data ◽

Negative Binomial ◽

Sample Size Estimation ◽

Type I ◽

Size Estimation ◽

Recent Trial ◽

Longitudinal Count Data

We consider modelling and inference as well as sample size estimation and reestimation for clinical trials with longitudinal count data as outcomes. Our approach is general but is rooted in design and analysis of multiple sclerosis trials where lesion counts obtained by magnetic resonance imaging are important endpoints. We adopt a binomial thinning model that allows for correlated counts with marginal Poisson or negative binomial distributions. Methods for sample size planning and blinded sample size reestimation for randomised controlled clinical trials with such outcomes are developed. The models and approaches are applicable to data with incomplete observations. A simulation study is conducted to assess the effectiveness of sample size estimation and blinded sample size reestimation methods. Sample sizes attained through these procedures are shown to maintain the desired study power without inflating the type I error. Data from a recent trial in patients with secondary progressive multiple sclerosis illustrate the modelling approach.

Download Full-text

Impact of community piped water coverage on re-infection with urogenital schistosomiasis in rural South Africa

eLife ◽

10.7554/elife.54012 ◽

2020 ◽

Vol 9 ◽

Cited By ~ 1

Author(s):

Polycarp Mogeni ◽

Alain Vandormael ◽

Diego Cuadros ◽

Christopher Appleton ◽

Frank Tanser

Keyword(s):

Negative Binomial ◽

Negative Binomial Regression ◽

Primary School Children ◽

Effective Control ◽

Urogenital Schistosomiasis ◽

Percentage Point Increase ◽

Piped Water ◽

Point Increase ◽

Binomial Regression

Previously, we demonstrated that coverage of piped water in the seven years preceding a parasitological survey was strongly predictive of Schistosomiasis haematobium infection in a nested cohort of 1976 primary school children (Tanser, 2018). Here, we report on the prospective follow up of infected members of this nested cohort (N = 333) for two successive rounds following treatment. Using a negative binomial regression fitted to egg count data, we found that every percentage point increase in piped water coverage was associated with 4.4% decline in intensity of re-infection (incidence rate ratio = 0.96, 95% CI: 0.93–0.98, p=0.004) among the treated children. We therefore provide further compelling evidence in support of the scaleup of piped water as an effective control strategy against Schistosoma haematobium transmission.

Download Full-text