The impact of measurement error and omitting confounders on statistical inference of mediation effects and tools for sensitivity analysis

Periodontal Health and Its Relationship with Psychological Stress: A Cross-Sectional Study

Background: Studies suggest that chronic psychological stress can lead to oral health deterioration, alter the immune response, and possibly contribute to increased inflammation, which can impact the physiological healing of periodontal tissues. This cross-sectional study seeks to assess and improve clinical understanding regarding the relationship between perceived stress, mindfulness, and periodontal health. Methods: A total of 203 people were analyzed from December 2022 to June 2023. The Periodontal Screening and Recording (PSR) score and Gingival Bleeding Index (GBI), and Plaque Control Record (PCR) of every patient were registered. Subsequently, participants completed the Sheldon Cohen Perceived Stress Scale (PSS) and the Mindfulness Awareness Attention Scale (MAAS) questionnaires. The collected data underwent statistical analysis, encompassing the evaluation of correlations and dependencies. Applying Welch's t-test to assess the relationship between MAAS and the variable indicating the presence or absence of periodontitis, a noteworthy p-value of 0.004265 was obtained. Results: This underscores a significant distinction in MAAS scores between patients affected by periodontitis and those unaffected by the condition. Additionally, Pearson correlations were computed for GBI and perceived stress, PCR and perceived stress, PCR and MAAS. The resulting p-values of 2.2-16, 3.925-8, and 2.468-8, respectively, indicate a statistically significant correlation in each instance. Conclusions: These findings contribute valuable insights into the interconnectedness of these variables, emphasizing the significance of their associations in the study context. Despite the limitations, the findings of this study suggest a significant relationship between psychological stress, mindfulness, and periodontal tissue health. Clinical trials are necessary to incorporate the assessment of a patient's psychological status as a new valuable tool in the management of periodontal health.

A sensitivity analysis for temporal bias in cross-sectional mediation

For over three decades, methodologists have cautioned against the use of cross-sectional mediation analyses because they yield biased parameter estimates. Yet, cross-sectional mediation models persist in practice and sometimes represent the only analytic option. We propose a sensitivity analysis procedure to encourage a more principled use of cross-sectional mediation analysis, drawing inspiration from Gollob and Reichardt (1987, 1991). The procedure is based on the two-wave longitudinal mediation model and uses phantom variables for the baseline data. After a researcher provides ranges of possible values for cross-lagged, autoregressive, and baseline Y and M correlations among the phantom and observed variables, they can use the sensitivity analysis to identify longitudinal conditions in which conclusions from a cross-sectional model would differ most from a longitudinal model. To support the procedure, we first show that differences in sign and effect size of the b-path occur most often when the cross-sectional effect size of the b-path is small and the cross-lagged and the autoregressive correlations are equal or similar in magnitude. We then apply the procedure to cross-sectional analyses from real studies and compare the sensitivity analysis results to actual results from a longitudinal mediation analysis. While no statistical procedure can replace longitudinal data, these examples demonstrate that the sensitivity analysis can recover the effect that was actually observed in the longitudinal data if provided with the correct input information. Implications of the routine application of sensitivity analysis to temporal bias are discussed. R code for the procedure is provided in the online supplementary materials. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Adjusting for Baseline Measurements of the Mediators and Outcome as a First Step Toward Eliminating Confounding Biases in Mediation Analysis

Mediation analysis prevails for researchers probing the etiological mechanisms through which treatment affects an outcome. A central challenge of mediation analysis is justifying sufficient baseline covariates that meet the causal assumption of no unmeasured confounding. But current practices routinely overlook this assumption. In this article, we suggest a relatively easy way to mitigate the risks of incorrect inferences resulting from unmeasured confounding: include pretreatment measurements of the mediator(s) and the outcome as baseline covariates. We explain why adjusting for pretreatment baseline measurements is a necessary first step toward eliminating confounding biases. We hope that such a practice can encourage explication, justification, and reflection of the causal assumptions underpinning mediation analysis toward improving the validity of causal inferences in psychology research.

Accommodating a Latent XM Interaction in Statistical Mediation Analysis

Statistical mediation analysis is used in the social sciences and public health to uncover potential mechanisms, known as mediators, by which a treatment led to a change in an outcome. Recently, the estimation of the treatment-by-mediator interaction (i.e., the XM interaction) has been shown to play a pivotal role in understanding the equivalence between the traditional mediation effects in linear models and the causal mediation effects in the potential outcomes framework. However, there is limited guidance on how to estimate the XM interaction when the mediator is latent. In this article, we discuss eight methods to accommodate latent XM interactions in statistical mediation analysis, which fall in two categories: using structural models (e.g., latent moderated structural equations, Bayesian mediation, unconstrained product indicator method, multiple-group models) or scoring the mediator prior to estimating the XM interaction (e.g., summed scores and factor scores, with and without attenuation correction). Simulation results suggest that finite-sample bias is low, type 1 error rates and coverage of percentile bootstrap confidence intervals and Bayesian credible intervals are close to the nominal values, and statistical power is similar across approaches. The methods are demonstrated with an applied example, syntax is provided for their implementation, and general considerations are discussed.

The impact of omitting confounders in parallel process latent growth curve mediation models: Three sensitivity analysis approaches

Parallel process latent growth curve mediation models (PP-LGCMMs) are frequently used to longitudinally investigate the mediation effects of treatment on the level and change of outcome through the level and change of mediator. An important but often violated assumption in empirical PP-LGCMM analysis is the absence of omitted confounders of the relationships among treatment, mediator, and outcome. In this study, we analytically examined how omitting pretreatment confounders impacts the inference of mediation from the PP-LGCMM. Using the analytical results, we developed three sensitivity analysis approaches for the PP-LGCMM, including the frequentist, Bayesian, and Monte Carlo approaches. The three approaches help investigate different questions regarding the robustness of mediation results from the PP-LGCMM, and handle the uncertainty in the sensitivity parameters differently. Applications of the three sensitivity analyses are illustrated using a real-data example. A user-friendly Shiny web application is developed to conduct the sensitivity analyses.

Quantitative bias analysis in practice: review of software for regression with unmeasured confounding

BACKGROUND

Failure to appropriately account for unmeasured confounding may lead to erroneous conclusions. Quantitative bias analysis (QBA) can be used to quantify the potential impact of unmeasured confounding or how much unmeasured confounding would be needed to change a study's conclusions. Currently, QBA methods are not routinely implemented, partly due to a lack of knowledge about accessible software. Also, comparisons of QBA methods have focused on analyses with a binary outcome.

METHODS

We conducted a systematic review of the latest developments in QBA software published between 2011 and 2021. Our inclusion criteria were software that did not require adaption (i.e., code changes) before application, was still available in 2022, and accompanied by documentation. Key properties of each software tool were identified. We provide a detailed description of programs applicable for a linear regression analysis, illustrate their application using two data examples and provide code to assist researchers in future use of these programs.

RESULTS

Our review identified 21 programs with [Formula: see text] created post 2016. All are implementations of a deterministic QBA with [Formula: see text] available in the free software R. There are programs applicable when the analysis of interest is a regression of binary, continuous or survival outcomes, and for matched and mediation analyses. We identified five programs implementing differing QBAs for a continuous outcome: treatSens, causalsens, sensemakr, EValue, and konfound. When applied to one of our illustrative examples, causalsens incorrectly indicated sensitivity to unmeasured confounding whereas the other four programs indicated robustness. sensemakr performs the most detailed QBA and includes a benchmarking feature for multiple unmeasured confounders.

CONCLUSIONS

Software is now available to implement a QBA for a range of different analyses. However, the diversity of methods, even for the same analysis of interest, presents challenges to their widespread uptake. Provision of detailed QBA guidelines would be highly beneficial.

The trouble with triples: Examining the impact of measurement error in mediation analysis

Mediation analysis is used in genetic mapping studies to identify candidate gene mediators of quantitative trait loci (QTL). We consider genetic mediation analysis of triplets-sets of three variables consisting of a target trait, the genotype at a QTL for the target trait, and a candidate mediator that is the abundance of a transcript or protein whose coding gene co-locates with the QTL. We show that, in the presence of measurement error, mediation analysis can infer partial mediation even in the absence of a causal relationship between the candidate mediator and the target. We describe a measurement error model and a corresponding latent variable model with estimable parameters that are combinations of the causal effects and measurement errors across all three variables. The relative magnitudes of the latent variable correlations determine whether or not mediation analysis will tend to infer the correct causal relationship in large samples. We examine case studies that illustrate the common failure modes of genetic mediation analysis and demonstrate how to evaluate the effects of measurement error. While genetic mediation analysis is a powerful tool for identifying candidate genes, we recommend caution when interpreting mediation analysis findings.

Estimating latent baseline-by-treatment interactions in statistical mediation analysis

Statistical mediation analysis is used to uncover intermediate variables, known as mediators [ M ], that explain how a treatment [ X ] changes an outcome [Y ]. Often, researchers examine whether baseline levels of M and Y moderate the effect of X on posttest M or Y . However, there is limited guidance on how to estimate baseline-by-treatment interaction (BTI) effects when M and Y are latent variables, which entails the estimation of latent interaction effects. In this paper, we discuss two general approaches for estimating latent BTI effects in mediation analysis: using structural models or scoring latent variables prior to estimating observed BTIs and correcting for unreliability. We present simulation results describing bias, power, type 1 error rates, and interval coverage of the latent BTIs and mediated effects estimated using these approaches. These methods are also illustrated with an applied example. R and Mplus syntax are provided to facilitate the implementation of these approaches.

Causal mediation effects in single case experimental designs

Single case experimental designs (SCEDs) are used to test treatment effects in a wide range of fields and consist of repeated measurements for a single case throughout one or more baseline phases and throughout one or more treatment phases. Recently, mediation analysis has been applied to SCEDs. Mediation analysis decomposes the total treatment-outcome effect into a direct and indirect effect, and therefore aims to unravel the causal processes underlying treatment-outcome effects. The most recent methodological advancement for mediation analysis is the development of causal mediation analysis methodology which clarifies the necessary causal assumptions for mediation analysis. The goal of this article is to derive the causal mediation effects and corresponding standard errors based on piecewise linear regression models for the mediator and outcome and to evaluate the performance of these regression estimators and standard errors. Whereas previous studies estimated the direct and indirect effects as either the change in level or change in trend, we showed that the causal direct and indirect effects incorporate both the change in level and change in trend. Based on our simulation study we showed that for the causal indirect effects, Monte Carlo confidence intervals provided accurate (i.e., p = .05) Type I error rates and higher statistical power than normal theory confidence intervals. For the causal direct effects and total effect, normal theory confidence intervals provided accurate Type I error rates and higher statistical power than the Monte Carlo confidence intervals. Limitations and future directions are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).