Analyzing pre-post designs using the analysis of covariance models with and without the interaction term in a heterogeneous study population

2019 ◽  
Vol 29 (1) ◽  
pp. 189-204 ◽  
Author(s):  
Fei Wan
Keyword(s):  
Treatment Effect ◽  
Treatment Strategies ◽  
Interaction Model ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Conditional Variance ◽  
Analysis Of Covariance ◽  
Parallel Group ◽  
Interaction Term ◽  
Variable Bias

Pre-post parallel group randomized designs have been frequently used to compare the effectiveness of competing treatment strategies and the ordinary least squares (OLS)-based analysis of covariance model (ANCOVA) is a routine analytic approach. In many scenarios, the associations between the baseline and the post-randomization scores could differ between the treatment and control arms, which justifies the inclusion of the treatment by baseline score interaction in ANCOVA. This heterogeneity may also cause heteroscedastic errors in ANCOVA. In this study, we compared the performances of the ANCOVA models with and without the interaction term in estimating the marginal treatment effect in a heterogeneous two-arm pre-post design. We explored the relationship between the two nested ANCOVA models from the perspective of an omitted variable bias problem and further revealed the reasons why the usual ANCOVA may fail in heterogeneous scenario through the discussion of the three types of variances associated with the ANCOVA estimators of the marginal treatment effect: the target unconditional variance, the conditional variance allowing unequal error variances, and the OLS conditional variance derived under the assumption of constant error variance. We demonstrated analytically and with simulations that the proposed heteroscadastic-consistent variance estimators provide valid unconditional inference for ANCOVA, and the ANCOVA interaction model is more powerful than the ANCOVA main effect model when a design is unbalanced.

Analyzing pre-post randomized studies with one post-randomization score using repeated measures and ANCOVA models

2018 ◽  
Vol 28 (10-11) ◽  
pp. 2952-2974 ◽  
Author(s):  
Fei Wan
Keyword(s):  
Least Squares ◽  
Treatment Effect ◽  
Repeated Measures ◽  
Interaction Model ◽  
Ordinary Least Squares ◽  
Analysis Of Covariance ◽  
Baseline Score ◽  
Sample Mean ◽  
Heterogeneity Of Treatment Effect ◽  
Randomized Studies

The analysis of covariance (ANCOVA) or repeated measures (RM) models are often used to compare the treatment effect between different arms in pre-post randomized studies. ANCOVA adjusts the baseline score as a covariate in regression models. RM treats both the baseline and post-randomization scores as outcome variables. We aim to establish the underlying connections between ANCOVA and a constrained RM (“cRM”). We start with the interrelated concepts in a pre-post randomized designs: homogeneous vs. heterogeneous study populations, the marginal vs. the conditional treatment effect, and homogeneity vs. heterogeneity of treatment effect. We then demonstrate the asymptotic equivalence between the ANCOVA and cRM estimators for the marginal treatment effect and discuss the conditions under which ANCOVA needs to include a baseline score by treatment interaction term. In particular, an ANCOVA interaction model with a mean centered baseline score can assess both the marginal treatment effect and the heterogeneity in the conditional treatment effect. However, the ordinary least squares (OLS)-based inference is not valid for unconditional inference because this interaction model typically has heteroskedastic errors, and ordinary least squares treats the sample mean of the baseline score as a known parameter. We propose a bootstrap and a heteroskedasticity consistent variance estimator for heteroskedastic ANCOVA. Our simulation studies demonstrate that the proposed methods provide valid inferences for testing both the marginal treatment effect and the heterogeneity of treatment effect using an ANCOVA interaction model. We used an acupuncture headache trial to elucidate the proposed approaches.

scholarly journals Statistical analysis of two arm randomized pre-post designs with one post-treatment measurement

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Fei Wan
Keyword(s):  
Treatment Effect ◽  
Repeated Measures ◽  
Informed Choice ◽  
Clinical Effectiveness ◽  
Change Score ◽  
Post Treatment ◽  
Analysis Of Covariance ◽  
Alternative Methods ◽  
Main Effect ◽  
Comparable Performance

Abstract Background Randomized pre-post designs, with outcomes measured at baseline and after treatment, have been commonly used to compare the clinical effectiveness of two competing treatments. There are vast, but often conflicting, amount of information in current literature about the best analytic methods for pre-post designs. It is challenging for applied researchers to make an informed choice. Methods We discuss six methods commonly used in literature: one way analysis of variance (“ANOVA”), analysis of covariance main effect and interaction models on the post-treatment score (“ANCOVAI” and “ANCOVAII”), ANOVA on the change score between the baseline and post-treatment scores (“ANOVA-Change”), repeated measures (“RM”) and constrained repeated measures (“cRM”) models on the baseline and post-treatment scores as joint outcomes. We review a number of study endpoints in randomized pre-post designs and identify the mean difference in the post-treatment score as the common treatment effect that all six methods target. We delineate the underlying differences and connections between these competing methods in homogeneous and heterogeneous study populations. Results ANCOVA and cRM outperform other alternative methods because their treatment effect estimators have the smallest variances. cRM has comparable performance to ANCOVAI in the homogeneous scenario and to ANCOVAII in the heterogeneous scenario. In spite of that, ANCOVA has several advantages over cRM: i) the baseline score is adjusted as covariate because it is not an outcome by definition; ii) it is very convenient to incorporate other baseline variables and easy to handle complex heteroscedasticity patterns in a linear regression framework. Conclusions ANCOVA is a simple and the most efficient approach for analyzing pre-post randomized designs.

The Use of a Small Computer in Agricultural Research

1977 ◽  
Vol 13 (3) ◽  
pp. 257-264 ◽  
Author(s):  
S. C. Pearce
Keyword(s):  
Analysis Of Variance ◽  
Agricultural Research ◽  
Error Variance ◽  
Analysis Of Covariance ◽  
Research Worker ◽  
Small Computer ◽  
Disturbing Factor

SUMMARYIt is suggested that quite a small computer, in association with a minimal program for the analysis of variance, can be used to calculate quantities of use to the agronomic research worker beyond what he usually obtains. For example, without further programs it is possible to calculate an analysis of covariance, in which adjustment is made for some disturbing factor. It is also possible to find how much of the error variance arises from a particular plot, and to deal with situations in which data are incomplete or the yields from two plots have become mixed.

scholarly journals The ‘transportation disadvantaged’: Urban form, gender and automobile versus non-automobile travel in the Detroit region

Urban Studies ◽  
2017 ◽  
Vol 55 (11) ◽  
pp. 2470-2498 ◽  
Author(s):  
Jieun Lee ◽  
Igor Vojnovic ◽  
Sue C Grady
Keyword(s):  
Urban Form ◽  
Urban Poor ◽  
Travel Behaviour ◽  
Ordinary Least Squares ◽  
Analysis Of Covariance ◽  
Socioeconomically Disadvantaged ◽  
Socially Disadvantaged ◽  
The Usa ◽  
Single Use ◽  
Disadvantaged Neighbourhoods

Urban decentralisation in the USA during the past five decades has created an automobile-dependent landscape characterised by low-densities, largely single-use zoning and disconnected street networks. Longer distances between dispersing destinations, resulting from urban decentralisation, negatively affects the mobility of socially disadvantaged groups, including women, minorities and lower-income populations. Furthermore, the urban poor and minorities in communities experiencing severe disinvestment and decline, as evident in Detroit, suffer from greater transportation burdens in accessing basic necessities, such as employment and shopping. This study explores gendered travel patterns in six neighbourhoods within the Detroit region, including neighbourhoods experiencing severe disinvestment and decline. This analysis into the gendered dimensions of travel, with a particular focus placed on women, involves a full array of trips, including work and non-work. Ordinary Least Squares (OLS) regression analysis and ANCOVA (Analysis of Covariance) were used to further examine gender differences by childcare responsibility in an extensive array of disaggregated travel, including trips to work, shopping and personal services, restaurant visits and leisure destinations. This study reconfirms that the traditional gender role is reflected in women’s daily travel. It also reveals the burdens of travel placed on women living in racially segregated and socioeconomically disadvantaged neighbourhoods experiencing extreme disinvestment and decline. In addition, the research shows the importance of class and race in shaping travel behaviour.

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy

2019 ◽  
Vol 43 (6) ◽  
pp. 335-369
Author(s):  
J. R. Lockwood ◽  
Daniel F. McCaffrey
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Ordinary Least Squares ◽  
Analysis Of Covariance ◽  
Asymptotic Results ◽  
Teacher Effects ◽  
Intervention Effects ◽  
Ols Regression ◽  
Ancova Model

Background: Analysis of covariance (ANCOVA) is commonly used to adjust for potential confounders in observational studies of intervention effects. Measurement error in the covariates used in ANCOVA models can lead to inconsistent estimators of intervention effects. While errors-in-variables (EIV) regression can restore consistency, it requires surrogacy assumptions for the error-prone covariates that may be violated in practical settings. Objectives: The objectives of this article are (1) to derive asymptotic results for ANCOVA using EIV regression when measurement errors may not satisfy the standard surrogacy assumptions and (2) to demonstrate how these results can be used to explore the potential bias from ANCOVA models that either ignore measurement error by using ordinary least squares (OLS) regression or use EIV regression when its required assumptions do not hold. Results: The article derives asymptotic results for ANCOVA with error-prone covariates that cover a variety of cases relevant to applications. It then uses the results in a case study of choosing among ANCOVA model specifications for estimating teacher effects using longitudinal data from a large urban school system. It finds evidence that estimates of teacher effects computed using EIV regression may have smaller bias than estimates computed using OLS regression when the data available for adjusting for students’ prior achievement are limited.

scholarly journals The association of genetic factors, educational attainment, and their interaction, with kidney function outcomes

2020 ◽  
Author(s):  
Chris H L Thio ◽  
Sander K R van Zon ◽  
Peter J van der Most ◽  
Harold Snieder ◽  
Ute Bültmann ◽  
...  
Keyword(s):  
Chronic Kidney Disease ◽  
Kidney Disease ◽  
Educational Attainment ◽  
Kidney Function ◽  
Genetic Risk ◽  
Ordinary Least Squares ◽  
Environment Interaction ◽  
Genetic Score ◽  
Interaction Term ◽  
Egfr Decline

Abstract Both genetic predisposition and low educational attainment (EA) are associated with higher risk of chronic kidney disease. We examined the interaction of EA and genetic risk in kidney function outcomes. We included 3,597 participants from the Prevention of REnal and Vascular ENd stage Disease Cohort Study, a longitudinal study in a community-based sample from Groningen, the Netherlands (median follow-up 11 years, 1997-2012). Kidney function was approximated by estimating glomerular filtration rate (eGFR) from serum creatinine and cystatin C. Individual longitudinal linear eGFR trajectories were derived from linear mixed models. Genotype data on 63 single nucleotide polymorphisms, with known associations to eGFR, were used to calculate an allele-weighted genetic score (WGS). EA was categorized into high, medium, and low. In ordinary least squares analysis, higher WGS and lower EA showed additive effects on reduced baseline eGFR; the interaction term was non-significant. In analysis of eGFR decline, the significant interaction term suggested amplification of genetic risk by low EA. Adjustment for known renal risk factors did not affect our results. This study presents the first evidence of gene-environment interaction between EA and a WGS on eGFR decline, and provides population-level insights into the mechanisms underlying socioeconomic disparities in chronic kidney disease.

scholarly journals Oral nitrate supplementation to enhance pulmonary rehabilitation in COPD: ON-EPIC a multicentre, double-blind, placebo-controlled, randomised parallel group study

Thorax ◽  
2020 ◽  
Vol 75 (7) ◽  
pp. 547-555
Author(s):  
Matthew J Pavitt ◽  
Rebecca Jayne Tanner ◽  
Adam Lewis ◽  
Sara Buttery ◽  
Bhavin Mehta ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Active Treatment ◽  
Treatment Effect ◽  
Pulmonary Rehabilitation ◽  
Activity Level ◽  
Double Blind ◽  
Dietary Nitrate ◽  
Double Blind Placebo ◽  
Parallel Group ◽  
Nitrate Supplementation

RationaleDietary nitrate supplementation has been proposed as a strategy to improve exercise performance, both in healthy individuals and in people with COPD. We aimed to assess whether it could enhance the effect of pulmonary rehabilitation (PR) in COPD.MethodsThis double-blind, placebo-controlled, parallel group, randomised controlled study performed at four UK centres, enrolled adults with Global Initiative for Chronic Obstructive Lung Disease grade II–IV COPD and Medical Research Council dyspnoea score 3–5 or functional limitation to undertake a twice weekly 8-week PR programme. They were randomly assigned (1:1) to either 140 mL of nitrate-rich beetroot juice (BRJ) (12.9 mmol nitrate), or placebo nitrate-deplete BRJ, consumed 3 hours prior to undertaking each PR session. Allocation used computer-generated block randomisation.MeasurementsThe primary outcome was change in incremental shuttle walk test (ISWT) distance. Secondary outcomes included quality of life, physical activity level, endothelial function via flow-mediated dilatation, fat-free mass index and blood pressure parameters.Results165 participants were recruited, 78 randomised to nitrate-rich BRJ and 87 randomised to placebo. Exercise capacity increased more with active treatment (n=57) than placebo (n=65); median (IQR) change in ISWT distance +60 m (10, 85) vs +30 m (0, 70), estimated treatment effect 30 m (95% CI 10 to 40); p=0.027. Active treatment also impacted on systolic blood pressure: treatment group −5.0 mm Hg (−5.0, –3.0) versus control +6.0 mm Hg (−1.0, 15.5), estimated treatment effect −7 mm Hg (95% CI 7 to −20) (p<0.0005). No significant serious adverse events or side effects were reported.ConclusionsDietary nitrate supplementation appears to be a well-tolerated and effective strategy to augment the benefits of PR in COPD.Trial registration numberISRCTN27860457.

scholarly journals Clinical and cost-effectiveness of bracing in symptomatic knee osteoarthritis management: protocol for a multicentre, primary care, randomised, parallel-group, superiority trial

BMJ Open ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. e048196
Author(s):  
Melanie A Holden ◽  
Michael Callaghan ◽  
David Felson ◽  
Fraser Birrell ◽  
Elaine Nicholls ◽  
...  
Keyword(s):  
Cost Effectiveness ◽  
Knee Osteoarthritis ◽  
Controlled Trial ◽  
Analysis Of Covariance ◽  
Written Information ◽  
Parallel Group ◽  
Management Protocol ◽  
Adherence Support ◽  
Symptomatic Knee Osteoarthritis ◽  
Symptomatic Knee

BackgroundBrace effectiveness for knee osteoarthritis (OA) remains unclear and international guidelines offer conflicting recommendations. Our trial will determine the clinical and cost-effectiveness of adding knee bracing (matched to patients’ clinical and radiographic presentation and with adherence support) to a package of advice, written information and exercise instruction delivered by physiotherapists.Methods and analysisA multicentre, pragmatic, two-parallel group, single-blind, superiority, randomised controlled trial with internal pilot and nested qualitative study. 434 eligible participants with symptomatic knee OA identified from general practice, physiotherapy referrals and self-referral will be randomised 1:1 to advice, written information and exercise instruction and knee brace versus advice, written information and exercise instruction alone. The primary analysis will be intention-to-treat comparing treatment arms on the primary outcome (Knee Osteoarthritis Outcomes Score (KOOS)-5) (composite knee score) at the primary endpoint (6 months) adjusted for prespecified covariates. Secondary analysis of KOOS subscales (pain, other symptoms, activities of daily living, function in sport and recreation, knee-related quality of life), self-reported pain, instability (buckling), treatment response, physical activity, social participation, self-efficacy and treatment acceptability will occur at 3, 6, and 12 months postrandomisation. Analysis of covariance and logistic regression will model continuous and dichotomous outcomes, respectively. Treatment effect estimates will be presented as mean differences or ORs with 95% CIs. Economic evaluation will estimate cost-effectiveness. Semistructured interviews to explore acceptability and experiences of trial interventions will be conducted with participants and physiotherapists delivering interventions.Ethics and disseminationNorth West Preston Research Ethics Committee, the Health Research Authority and Health and Care Research in Wales approved the study (REC Reference: 19/NW/0183; IRAS Reference: 247370). This protocol has been coproduced with stakeholders including patients and public. Findings will be disseminated to patients and a range of stakeholders.Trial registration numberISRCTN28555470.

scholarly journals The Stimulation Effect of Auricular Magnetic Press Pellets on Older Female Adults with Sleep Disturbance Undergoing Polysomnographic Evaluation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chyi Lo ◽  
Wen-Chun Liao ◽  
Jen-Jiuan Liaw ◽  
Liang-Wen Hang ◽  
Jaung-Geng Lin
Keyword(s):  
Sleep Quality ◽  
Sleep Disturbance ◽  
Depression Scale ◽  
Analysis Of Covariance ◽  
Sleep Stages ◽  
Control Group ◽  
Parallel Group ◽  
Sleep Parameters ◽  
Auricular Therapy ◽  
Experimental Group

Study Objectives. To examine the stimulation effect of auricular magnetic press pellet therapy on older female adults with sleep disturbance as determined by polysomnography (PSG).Design. Randomized, single-blind, experimental-controlled, parallel-group.Setting. Community.Participants. Twenty-seven older female adults with sleep disturbance according to the Pittsburgh Sleep Quality Index (PSQI) >5 for at least 3 months were recruited. Participants were screened by both the Hospital Anxiety and Depression Scale (HADS) and the Mini-Mental State Examination (MMSE), as well as polysomnography prior to randomization.Interventions. All eligible participants were randomly allocated into the experimental or control group. Both groups were taped with magnetic press pellet on auricular points for 3 weeks. The experimental group was treated by applying pressure on the magnetic press pellets 3 times per day while no stimulation was applied on the control group.Measurements and Results. Both groups were measured by PSG and PSQI at the beginning of the study and 3 weeks after the study. Both groups showed improvements on PSQI scores compared to the baseline. One-way analysis of covariance adjusted for baseline scores showed that significant improvements of PSG-derived sleep parameters, such as sleep efficiency, were found in the experimental group. However, no significant differences between groups were observed in the proportion of sleep stages with the exception of Stage 2.Conclusions. Auricular therapy using magnetic pellets and stimulation by pressing was more effective in improving the sleep quality compared to auricular therapy without any stimulation.

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