The analysis of covariance.

2021 ◽  
pp. 285-297
Author(s):  
Edward F. Durner
Keyword(s):  
Treatment Effect ◽  
Null Hypothesis ◽  
Error Term ◽  
Treatment Effects ◽  
Analysis Of Covariance ◽  
Significant Variability

Abstract This chapter focuses on the analysis of covariance. In the analysis of covariance, there is some measurable characteristic associated with experimental units which seems to be contributing significant variability to an experiment. This variability inflates the error term and makes it harder to reject the null hypothesis of no treatment effect. If one could pull this variability out of the error term, a larger F-value will be obtained, and therefore possibly reject the null hypothesis. This is increasing precision. Treatment effects on nematode populations in the soil and yield were taken as examples.

Bias for Treatment Effect by Measurement Error in Pretest in ANCOVA Analysis

2022 ◽  
pp. 001316442110688
Author(s):  
Yasuo Miyazaki ◽  
Akihito Kamata ◽  
Kazuaki Uekawa ◽  
Yizhi Sun
Keyword(s):  
Measurement Error ◽  
Treatment Effect ◽  
Measurement Errors ◽  
Treatment Effects ◽  
Population Group ◽  
Analysis Of Covariance ◽  
Negative Effects ◽  
Ancova Model ◽  
Positive Treatment ◽  
True Scores

This paper investigated consequences of measurement error in the pretest on the estimate of the treatment effect in a pretest–posttest design with the analysis of covariance (ANCOVA) model, focusing on both the direction and magnitude of its bias. Some prior studies have examined the magnitude of the bias due to measurement error and suggested ways to correct it. However, none of them clarified how the direction of bias is affected by measurement error. This study analytically derived a formula for the asymptotic bias for the treatment effect. The derived formula is a function of the reliability of the pretest, the standardized population group mean difference for the pretest, and the correlation between pretest and posttest true scores. It revealed a concerning consequence of ignoring measurement errors in pretest scores: treatment effects could be overestimated or underestimated, and positive treatment effects can be estimated as negative effects in certain conditions. A simulation study was also conducted to verify the derived bias formula.

Increasing Precision without Altering Treatment Effects: Repeated Measures Designs in Survey Experiments

2021 ◽  
pp. 1-18
Author(s):  
SCOTT CLIFFORD ◽  
GEOFFREY SHEAGLEY ◽  
SPENCER PISTON
Keyword(s):  
Treatment Effect ◽  
Repeated Measures ◽  
Treatment Effects ◽  
Repeated Measurements ◽  
Experimental Designs ◽  
Treatment Effect Size ◽  
Standard Design ◽  
Survey Experiments ◽  
Repeated Measures Designs ◽  
Alternative Designs

The use of survey experiments has surged in political science. The most common design is the between-subjects design in which the outcome is only measured posttreatment. This design relies heavily on recruiting a large number of subjects to precisely estimate treatment effects. Alternative designs that involve repeated measurements of the dependent variable promise greater precision, but they are rarely used out of fears that these designs will yield different results than a standard design (e.g., due to consistency pressures). Across six studies, we assess this conventional wisdom by testing experimental designs against each other. Contrary to common fears, repeated measures designs tend to yield the same results as more common designs while substantially increasing precision. These designs also offer new insights into treatment effect size and heterogeneity. We conclude by encouraging researchers to adopt repeated measures designs and providing guidelines for when and how to use them.

scholarly journals Estimating and reporting treatment effects in clinical trials for weight management: using estimands to interpret effects of intercurrent events and missing data

2021 ◽  
Author(s):  
Sean Wharton ◽  
Arne Astrup ◽  
Lars Endahl ◽  
Michael E. J. Lean ◽  
Altynai Satylganova ◽  
...  
Keyword(s):  
Clinical Trials ◽  
Missing Data ◽  
Weight Management ◽  
Treatment Effect ◽  
Repeated Measures ◽  
Treatment Effects ◽  
Randomized Clinical Trials ◽  
Weight Losses ◽  
The Difference ◽  
Treatment Of Obesity

AbstractIn the approval process for new weight management therapies, regulators typically require estimates of effect size. Usually, as with other drug evaluations, the placebo-adjusted treatment effect (i.e., the difference between weight losses with pharmacotherapy and placebo, when given as an adjunct to lifestyle intervention) is provided from data in randomized clinical trials (RCTs). At first glance, this may seem appropriate and straightforward. However, weight loss is not a simple direct drug effect, but is also mediated by other factors such as changes in diet and physical activity. Interpreting observed differences between treatment arms in weight management RCTs can be challenging; intercurrent events that occur after treatment initiation may affect the interpretation of results at the end of treatment. Utilizing estimands helps to address these uncertainties and improve transparency in clinical trial reporting by better matching the treatment-effect estimates to the scientific and/or clinical questions of interest. Estimands aim to provide an indication of trial outcomes that might be expected in the same patients under different conditions. This article reviews how intercurrent events during weight management trials can influence placebo-adjusted treatment effects, depending on how they are accounted for and how missing data are handled. The most appropriate method for statistical analysis is also discussed, including assessment of the last observation carried forward approach, and more recent methods, such as multiple imputation and mixed models for repeated measures. The use of each of these approaches, and that of estimands, is discussed in the context of the SCALE phase 3a and 3b RCTs evaluating the effect of liraglutide 3.0 mg for the treatment of obesity.

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.

Inference for treatment effect parameters in potentially misspecified high-dimensional models

Biometrika ◽  
2020 ◽  
Author(s):  
Oliver Dukes ◽  
Stijn Vansteelandt
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Treatment Effect ◽  
Observational Studies ◽  
Treatment Effects ◽  
Treatment Selection ◽  
High Dimensional ◽  
Selection Mechanism ◽  
Dimensional Models ◽  
Effect Parameter

Summary Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators, such as the lasso, or other regularization approaches. Naïve use of such estimators yields confidence intervals for the conditional treatment effect parameter that are not uniformly valid. Moreover, as the number of covariates grows with the sample size, correctly specifying a model for the outcome is nontrivial. In this article we deal with both of these concerns simultaneously, obtaining confidence intervals for conditional treatment effects that are uniformly valid, regardless of whether the outcome model is correct. This is done by incorporating an additional model for the treatment selection mechanism. When both models are correctly specified, we can weaken the standard conditions on model sparsity. Our procedure extends to multivariate treatment effect parameters and complex longitudinal settings.

Permutation Tests for Common Locations Among Samples With Unequal Variances

1994 ◽  
Vol 19 (3) ◽  
pp. 217-236 ◽  
Author(s):  
Paul W. Mielke ◽  
Kenneth J. Berry
Keyword(s):  
Null Hypothesis ◽  
Treatment Effects ◽  
Alternative Hypothesis ◽  
Permutation Tests ◽  
Experimental Designs ◽  
Bivariate Distributions ◽  
Unequal Variances ◽  
Trace Test ◽  
Location Shift ◽  
Power Comparisons

In completely randomized experimental designs where population variances are equal under the null hypothesis, it is not uncommon to have multiplicative treatment effects that produce unequal variances under the alternative hypothesis. Permutation procedures are presented to test for (a) median location and scale shifts, (b) scale shifts only, and (c) mean location shifts only. Corresponding multivariate extensions are provided. Location-shift power comparisons between the parametric Bartlett-Nanda-Pillai trace test and three alternative multivariate permutation tests for five bivariate distributions are included.

scholarly journals Blinding, sham, and treatment effects in randomized controlled trials for back pain in 2000–2019: A review and meta-analytic approach

2021 ◽  
pp. 174077452098487
Author(s):  
Brian Freed ◽  
Brian Williams ◽  
Xiaolu Situ ◽  
Victoria Landsman ◽  
Jeehyoung Kim ◽  
...  
Keyword(s):  
Back Pain ◽  
Active Treatment ◽  
Treatment Effect ◽  
Effect Size ◽  
Treatment Effects ◽  
Effect Sizes ◽  
Controlled Trials ◽  
Sham Treatment ◽  
Randomized Controlled ◽  
Random Guess

Background: Blinding aims to minimize biases from what participants and investigators know or believe. Randomized controlled trials, despite being the gold standard to evaluate treatment effect, do not generally assess the success of blinding. We investigated the extent of blinding in back pain trials and the associations between participant guesses and treatment effects. Methods: We did a review with PubMed/OvidMedline, 2000–2019. Eligibility criteria were back pain trials with data available on treatment effect and participants’ guess of treatment. For blinding, blinding index was used as chance-corrected measure of excessive correct guess (0 for random guess). For treatment effects, within- or between-arm effect sizes were used. Analyses of investigators’ guess/blinding or by treatment modality were performed exploratorily. Results: Forty trials (3899 participants) were included. Active and sham treatment groups had mean blinding index of 0.26 (95% confidence interval: 0.12, 0.41) and 0.01 (−0.11, 0.14), respectively, meaning 26% of participants in active treatment believed they received active treatment, whereas only 1% in sham believed they received sham treatment, beyond chance, that is, random guess. A greater belief of receiving active treatment was associated with a larger within-arm effect size in both arms, and ideal blinding (namely, “random guess,” and “wishful thinking” that signifies both groups believing they received active treatment) showed smaller effect sizes, with correlation of effect size and summary blinding indexes of 0.35 ( p = 0.028) for between-arm comparison. We observed uniformly large sham treatment effects for all modalities, and larger correlation for investigator’s (un)blinding, 0.53 ( p = 0.046). Conclusion: Participants in active treatments in back pain trials guessed treatment identity more correctly, while those in sham treatments tended to display successful blinding. Excessive correct guesses (that could reflect weaker blinding and/or noticeable effects) by participants and investigators demonstrated larger effect sizes. Blinding and sham treatment effects on back pain need due consideration in individual trials and meta-analyses.

The Effect of Extension Services and Credit on Agricultural Production in Bolivia, Peru, and Colombia

2021 ◽  
Author(s):  
Mateus C. R. Neves ◽  
Felipe De Figueiredo Silva ◽  
Carlos Otávio Freitas
Keyword(s):  
Travel Time ◽  
Treatment Effect ◽  
Agricultural Production ◽  
Treatment Effects ◽  
Geographic Information ◽  
Average Treatment Effect ◽  
Extension Services ◽  
Average Treatment ◽  
Andean Countries ◽  
Average Treatment Effects

In this paper we estimate the average treatment effect from access to extension services and credit on agricultural production in selected Andean countries (Bolivia, Peru, and Colombia). More specifically, we want to identify the effect of accessibility, here represented as travel time to the nearest area with 1,500 or more inhabitants per square kilometer or at least 50,000 inhabitants, on the likelihood of accessing extension and credit. To estimate the treatment effect and identify the effect of accessibility on these variables, we use data from the Colombian and Bolivian Agricultural Censuses of 2013 and 2014, respectively; a national agricultural survey from 2017 for Peru; and geographic information on travel time. We find that the average treatment effect for extension is higher compared to that of credit for farms in Bolivia and Peru, and lower for Colombia. The average treatment effects of extension and credit for Peruvian farms are $2,387.45 and $3,583.42 respectively. The average treatment effect for extension and credit are $941.92 and $668.69, respectively, while in Colombia are $1,365.98 and $1,192.51, respectively. We also find that accessibility and the likelihood of accessing these services are nonlinearly related. Results indicate that higher likelihood is associated with lower travel time, especially in the analysis of credit.

Bounding Treatment Effects with Contaminated and Censored Data: Assessing the Impact of Early Childbearing on Children

2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Charles H Mullin
Keyword(s):  
Censored Data ◽  
Treatment Effect ◽  
Instrumental Variable ◽  
Treatment Effects ◽  
Child Outcomes ◽  
Well Being ◽  
Teenage Mothers ◽  
Age At First Birth ◽  
First Birth ◽  
The Impact

AbstractEmpirical researchers commonly invoke instrumental variable (IV) assumptions to identify treatment effects. This paper considers what can be learned under two specific violations of those assumptions: contaminated and corrupted data. Either of these violations prevents point identification, but sharp bounds of the treatment effect remain feasible. In an applied example, random miscarriages are an IV for women’s age at first birth. However, the inability to separate random miscarriages from behaviorally induced miscarriages (those caused by smoking and drinking) results in a contaminated sample. Furthermore, censored child outcomes produce a corrupted sample. Despite these limitations, the bounds demonstrate that delaying the age at first birth for the current population of non-black teenage mothers reduces their first-born child’s well-being.

scholarly journals Spatial allocation effects within a potentization basic research model – evidence for field-like effects of homeopathic preparations?

2021 ◽  
Vol 13 (47) ◽  
pp. 86-87
Author(s):  
Stephan Baumgartner ◽  
Lucietta Betti ◽  
Mascha Binder ◽  
Peter Heusser ◽  
Ursula Wolf
Keyword(s):  
Treatment Effect ◽  
Mode Of Action ◽  
Treatment Effects ◽  
False Negative ◽  
Shoot Length ◽  
Spatial Position ◽  
Cross Contamination ◽  
Water Control ◽  
Wheat Seedlings ◽  
Wheat Shoot

Background: The mode of action of ultramolecular homeopathic preparations is still unknown. Interactions between objects or entities can be grouped in four main general scientific categories: material, force-/field-like, entanglement-like or informational. Should homeopathic preparations have a field-like mode of action, there is greater probability of cross-contamination as long as the means to “shield” objects from each other is unknown. A field-like interaction would also lead to treatment at a distance effects that are distance-dependent. Aims: We analysed a set of experiments with Arsenicum album 45x treated wheat seedlings regarding a possible distance-dependent cross-contamination. Materials and Methods: We performed an a posteriori analysis of a set of 17 independent experiments [1,2] with wheat seedlings pre-treated with 1‰ arsenic. Three treatments were applied (Arsenicum album 45x, water 45x, or unpotentized water) with 150 seedlings in each treatment group per experiment. Seedlings were arranged in hanging plastic bags side-by-side in identically treated blocks of 10 seedlings. The 3x15 blocks were coded and randomly allocated to the three treatments. Wheat shoot length was measured after 7 days. Treatment effects were analysed as function of the position (1–10) within the blocks of 10 seedlings. Results: Analyzing all data, Arsenicum album 45x exerted an inhibiting effect (–3.2%, p=0.01) compared to both water and water 45x. When restricting the analysis to the outermost seedlings of all subgroups (pos. 1, 10), the treatment effect vanished (0.3%, p=0.92). In contrast, the innermost seedlings of all subgroups (pos. 5, 6) showed a treatment effect of –5.6% (p=0.02). Intermediate pairs of positions (pos. 2–4, 7–9) showed intermediate effects. Regarding shoot length, dependency on spatial position was observed for the plants of the water control groups, but not for the plants treated with Arsenicum album 45x. Conclusions: Whilst the effect of Arsenicum album 45x on wheat-shoot growth was not dependent on the spatial position within the subgroup, the water-control plants became smaller the closer they were to Arsenicum album 45x-treated seedlings. This observation is compatible with the existence of a field-like effect of homeopathic dilutions. Another possible explanation that cannot be ruled out by the present experiments, is contamination through the gas-phase. Future investigations of ultramolecular homeopathic preparations should control any such effects since they may mask treatment effects, leading to false-negative results. Closer investigation of the nature of this distance-dependent effect might contribute to identification of the mode of action of ultramolecular homeopathic preparations.

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