scholarly journals Nonparametric inference for interventional effects with multiple mediators

2021 ◽  
Vol 9 (1) ◽  
pp. 172-189
Author(s):  
David Benkeser ◽  
Jialu Ran
Keyword(s):  
Interval Estimation ◽  
Small Sample ◽  
Parametric Models ◽  
Nonparametric Bootstrap ◽  
Mediation Effects ◽  
Specific Effects ◽  
Convergence Results ◽  
Large Sample Theory ◽  
Scientific Goal ◽  
Statistical Learning Techniques

Abstract Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway-specific effects. Interventional direct and indirect effects provide one such decomposition. Existing estimators of these effects are based on parametric models with confidence interval estimation facilitated via the nonparametric bootstrap. We provide theory that allows for more flexible, possibly machine learning-based, estimation techniques to be considered. In particular, we establish weak convergence results that facilitate the construction of closed-form confidence intervals and hypothesis tests and prove multiple robustness properties of the proposed estimators. Simulations show that inference based on large-sample theory has adequate small-sample performance. Our work thus provides a means of leveraging modern statistical learning techniques in estimation of interventional mediation effects.

scholarly journals Improved Confidence Interval Estimation for Oscillometric Blood Pressure Measurement by Combining Bootstrap-After-Jackknife Function with Non-Gaussian Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Soojeong Lee
Keyword(s):  
Blood Pressure ◽  
Blood Pressure Measurement ◽  
Interval Estimation ◽  
Maximum Amplitude ◽  
Small Sample ◽  
Nonparametric Bootstrap ◽  
Gaussian Models ◽  
Distribution Method ◽  
Non Gaussian ◽  
Oscillometric Blood Pressure Measurement

Confidence intervals (CIs) are generally not provided along with estimated systolic blood pressure (SBP) and diastolic blood pressure (DBP) measured using oscillometric blood pressure devices. No criteria exist to determine the CI from a small sample set of oscillometric blood pressure measurements. We provide an extended methodology to improve estimation of CIs of SBP and DBP based on a nonparametric bootstrap-after-jackknife function and a Bayesian approach. We use the nonparametric bootstrap-after-jackknife function to reduce maximum amplitude outliers. Improved pseudomaximum amplitudes (PMAs) and pseudoenvelopes (PEs) are derived from the pseudomeasurements. Moreover, the proposed algorithm uses an unfixed ratio obtained by employing non-Gaussian models based on the Bayesian technique to estimate the SBP and DBP ratios for individual subjects. The CIs obtained through our proposed approach are narrower than those obtained using the traditional Studentt-distribution method. The mean difference (MD) and standard deviation (SD) of the SBP and DBP estimates using our proposed approach are better than the estimates obtained by conventional fixed ratios based on the PMA and PE (PMAE).

scholarly journals Conditional or Pseudo Exact Tests with an Application in the Context of Modeling Response Times

Psych ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 198-208
Author(s):  
Clemens Draxler ◽  
Stephan Dahm
Keyword(s):  
Power Function ◽  
Rasch Model ◽  
Power Analysis ◽  
Response Times ◽  
Real Data ◽  
Small Sample ◽  
Chi Square ◽  
Research Context ◽  
Large Sample Theory ◽  
The Rasch Model

This paper treats a so called pseudo exact or conditional approach of testing assumptions of a psychometric model known as the Rasch model. Draxler and Zessin derived the power function of such tests. They provide an alternative to asymptotic or large sample theory, i.e., chi square tests, since they are also valid in small sample scenarios. This paper suggests an extension and applies it in a research context of investigating the effects of response times. In particular, the interest lies in the examination of the influence of response times on the unidimensionality assumption of the model. A real data example is provided which illustrates its application, including a power analysis of the test, and points to possible drawbacks.

scholarly journals Causal Mediation Analysis

2011 ◽  
Vol 11 (4) ◽  
pp. 605-619 ◽  
Author(s):  
Raymond Hicks ◽  
Dustin Tingley
Keyword(s):  
Mediation Analysis ◽  
Parametric Models ◽  
Sensitivity Analyses ◽  
Statistical Methodology ◽  
Mediation Effects ◽  
Explanatory Variables ◽  
Causal Mediation ◽  
Different Types ◽  
Recent Developments ◽  
Causal Mediation Analysis

Estimating the mechanisms that connect explanatory variables with the explained variable, also known as “mediation analysis,” is central to a variety of social-science fields, especially psychology, and increasingly to fields like epidemiology. Recent work on the statistical methodology behind mediation analysis points to limitations in earlier methods. We implement in Stata computational approaches based on recent developments in the statistical methodology of mediation analysis. In particular, we provide functions for the correct calculation of causal mediation effects using several different types of parametric models, as well as the calculation of sensitivity analyses for violations to the key identifying assumption required for interpreting mediation results causally.

scholarly journals Performance on verbal fluency tasks depends on the given category/letter: Preliminary data from a multivariable analysis

2022 ◽  
Author(s):  
Petar Gabrić ◽  
Mija Vandek
Keyword(s):  
Verbal Fluency ◽  
Response Times ◽  
Small Sample Size ◽  
Multivariable Analysis ◽  
Small Sample ◽  
Corpus Analysis ◽  
Response Latencies ◽  
Specific Effects ◽  
First Response ◽  
The Given

Verbal fluency tasks are often used in neuropsychological research and may have predictive and diagnostic utility in psychiatry and neurology. However, researchers using verbal fluency have uncritically assumed that there are no category- or phoneme-specific effects on verbal fluency performance. We recruited 16 young adult subjects and administered two semantic (animals, trees) and phonemic (K, M) fluency tasks. Because of the small sample size, results should be regarded as preliminary. On the animal compared to the tree task, subjects produced significantly more legal words, had a significantly lower intrusion rate, significantly shorter first-response latencies and final silence periods, as well as significantly shorter between-cluster response latencies. These differences may be explained by differences in the category sizes, integrity of the categories' borders, and efficiency of the functional connectivity between subcategories. On the K compared to the M task, subjects produced significantly more legal words and had significantly shorter between-cluster response times. Counterintuitively, a corpus analysis revealed there are more words starting with m compared to k in the experimental language. Our results have important implications for research utilizing verbal fluency, including decreased reproducibility, unreliability of diagnostic and predictive tools based on verbal fluency, and decreased knowledge accumulation.

Understanding the impact of family routines and rituals in relative in kinship families

2017 ◽  
Author(s):  
◽  
Karen B. Traylor-Adolph
Keyword(s):  
Problem Behaviors ◽  
Family Cohesion ◽  
Small Sample Size ◽  
Small Sample ◽  
Emotional Symptoms ◽  
Mediation Effects ◽  
Family Types ◽  
The Impact ◽  
Home And School ◽  
At Home

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Fiese and colleagues (2002) describe routines and rituals as naturally occurring behaviors creating a sense of predictability and stability via the underpinnings of communication, commitment, and continuity in a family unit. Although traditionally studied in intact families, these simple but profound parenting strategies are malleable and impact all family types. In this study, 65 relative and kinship legal guardians and 33 teachers were surveyed, extending the scope of routine and ritual research to "grandfamilies." Measures of routines and rituals, family cohesion and adaptability, youth behaviors at home and school, as well as open-ended descriptions of unique routines and rituals were employed. Findings reveal grandfamilies incorporate unique routines and rituals while navigating obstacles such as incarceration, scattered family members, and biological parent instability. On formal measures, routines and rituals were associated with more prosocial behaviors and less problem behaviors at home and school, as well as significantly correlated with cohesion and adaptability. Rituals were correlated with less teacher-rated emotional symptoms. Additionally, regarding cohesion and adaptability in grandfamilies, caregivers reported having strict, yet enmeshed family types. Lastly, results unexpectedly suggest that relationships of routines and rituals to youth and family outcomes become less strong when demographics and conditions of placement are factored. Small sample size prohibited evaluation of mediation effects. Further research to operationalize unique routines and rituals for examination with a broader canvas of community outcomes and including informal grandfamilies is recommended.

scholarly journals On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding

Biometrika ◽  
2019 ◽  
Author(s):  
C H Miles ◽  
I Shpitser ◽  
P Kanki ◽  
S Meloni ◽  
E J Tchetgen Tchetgen
Keyword(s):  
Broad Class ◽  
Specific Effect ◽  
Parametric Models ◽  
Finite Sample ◽  
Semiparametric Inference ◽  
Mediated Effects ◽  
Specific Effects ◽  
Causal Pathways ◽  
Finite Sample Properties ◽  
Intermediate Variables

Summary Path-specific effects constitute a broad class of mediated effects from an exposure to an outcome via one or more causal pathways along a set of intermediate variables. Most of the literature concerning estimation of mediated effects has focused on parametric models, with stringent assumptions regarding unmeasured confounding. We consider semiparametric inference of a path-specific effect when these assumptions are relaxed. In particular, we develop a suite of semiparametric estimators for the effect along a pathway through a mediator, but not through an exposure-induced confounder of that mediator. These estimators have different robustness properties, as each depends on different parts of the likelihood of the observed data. One estimator is locally semiparametric efficient and multiply robust. The latter property implies that machine learning can be used to estimate nuisance functions. We demonstrate these properties, as well as finite-sample properties of all the estimators, in a simulation study. We apply our method to an HIV study, in which we estimate the effect comparing two drug treatments on a patient’s average log CD4 count mediated by the patient’s level of adherence, but not by previous experience of toxicity, which is clearly affected by which treatment the patient is assigned to and may confound the effect of the patient’s level of adherence on their virologic outcome.

Two Reduced-Bias Autocorrelation Estimators: rF1 and rF2

1994 ◽  
Vol 78 (1) ◽  
pp. 323-330 ◽  
Author(s):  
Bradley E. Huitema ◽  
Joseph W. McKean
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Error Variance ◽  
Small Sample ◽  
Monte Carlo Experiment ◽  
Advantages And Disadvantages ◽  
Large Sample Theory ◽  
Absolute Bias ◽  
Sample Case ◽  
Major Reduction

Among the problems associated with the application of time-series analysis to typical psychological data are difficulties in parameter estimation. For example, estimates of autocorrelation coefficients are known to be biased in the small-sample case. Previous work by the present authors has shown that, in the case of conventional autocorrelation estimators of ρ1 the degree of bias is more severe than is predicted by formulas that are based on large-sample theory. Two new autocorrelation estimators, rF1 and rF2, were proposed; a Monte Carlo experiment was carried out to evaluate the properties of these statistics. The results demonstrate that both estimators provide major reduction of bias. The average absolute bias of rF2 is somewhat smaller than that of rF1 at all sample sizes, but both are far less biased than is the conventional estimator found in most time-series software. The reduction in bias comes at the price of an increase in error variance. A comparison of the properties of these estimators with those of other estimators suggested in 1991 shows advantages and disadvantages for each. It is recommended that the choice among autocorrelation estimators be based upon the nature of the application. The new estimator rF2 is especially appropriate when pooling estimates from several samples.

scholarly journals Conditional Inference in Small Sample Scenarios Using a Resampling Approach

Stats ◽  
2021 ◽  
Vol 4 (4) ◽  
pp. 837-849
Author(s):  
Clemens Draxler ◽  
Andreas Kurz
Keyword(s):  
Power Function ◽  
Small Sample Size ◽  
R Package ◽  
Small Sample ◽  
Conditional Inference ◽  
Test Statistics ◽  
Chi Square ◽  
Large Sample Theory ◽  
Chi Square Test ◽  
True Values

This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.

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