Sequential Comparisons Research Articles

Restricted time win ratio: from estimands to estimation

The win ratio is a novel approach to analyzing prioritized composite endpoints in clinical trials. The win ratio has grown increasingly popular and has been applied in many ongoing cardiovascular clinical trials. Despite the intuitive interpretation of win ratio statistics, the traditionally used win ratio estimands are heavily influenced by the pattern of censoring. Treating missing values or censored data as ties is generally not a reliable way of handling missing values even in the estimation procedure. To avoid this complication, we propose the restricted time win ratio, which is the win ratio at a pre-specified time point τ and can be written in terms of the expectations of potential outcomes. To estimate the proposed estimand, we develop an approximately fully conditional specification algorithm which imputes the missing data of longitudinal and clinical outcomes jointly up to τ . The imputation algorithm can be easily revised to adjust a different hierarchical structure of the sequential comparisons specified by the users. Simulation studies in realistic settings show that the proposed imputation algorithm provides an unbiased and robust estimation of the restricted time win ratio. Finally, real data from a cardiovascular clinical trial are used to illustrate the proposed method.

Developmental Trajectory of Anticipation: Insights from Sequential Comparative Judgments.

Reaction time (RT) is a critical measure of performance, and studying its distribution at the group or individual level provides useful information on the cognitive processes or strategies used to perform a task. In a previous study measuring RT in children and adults asked to compare two successive stimuli (quantities or words), we discovered that the group RT distribution was bimodal, with some subjects responding with a mean RT of around 1100 ms and others with a mean RT of around 500 ms. This bimodal distribution suggested two distinct response strategies, one reactive, the other anticipatory. In the present study, we tested whether subjects' segregation into fast and slow responders (1) extended to other sequential comparative judgments (2) evolved from age 8 to adulthood, (3) could be linked to anticipation as assessed using computer modeling (4) stemmed from individual-specific strategies amenable to instruction. To test the first three predictions, we conducted a distributional and theoretical analysis of the RT of 158 subjects tested earlier using four different sequential comparative judgment tasks (numerosity, phonological, multiplication, subtraction). Group RT distributions were bimodal in all tasks, with the two strategies differing in speed and sometimes accuracy too. The fast strategy, which was rare or absent in 8- to 9-year-olds, steadily increased through childhood. Its frequency in adolescence remained, however, lower than in adulthood. A mixture model confirmed this developmental evolution, while a diffusion model corroborated the idea that the difference between the two strategies concerns anticipatory processes preceding decision processes. To test the fourth prediction, we conducted an online experiment where 236 participants made numerosity comparisons before and after an instruction favoring either reactive or anticipatory responses. The results provide out-of-the-lab evidence of the bimodal RT distribution associated with sequential comparisons and demonstrated that the proportions of fast vs. slow responders can be modulated simply by asking subjects to anticipate or not the future result of the comparison. Although anticipation of the future is as important for cognition as memory of the past, its evolution after the first year of life is much more poorly known. The present study is a step toward meeting this challenge. It also illustrates how analyzing individual RT distributions in addition to group RT distributions and using computational models can improve the assessment of decision making cognitive processes.

OCTOPUS – Optical coherence tomography plaque and stent analysis software

Background and objectiveCompared with other imaging modalities, intravascular optical coherence tomography (IVOCT) has significant advantages for guiding percutaneous coronary interventions, assessing their outcomes, and characterizing plaque components. To aid IVOCT research studies, we developed the Optical Coherence TOmography PlaqUe and Stent (OCTOPUS) analysis software, which provides highly automated, comprehensive analysis of coronary plaques and stents in IVOCT images. MethodsUser specifications for OCTOPUS were obtained from detailed, iterative discussions with IVOCT analysts in the Cardiovascular Imaging Core Laboratory at University Hospitals Cleveland Medical Center, a leading laboratory for IVOCT image analysis. To automate image analysis results, the software includes several important algorithmic steps: pre-processing, deep learning plaque segmentation, machine learning identification of stent struts, and registration of pullbacks for sequential comparisons. Intuitive, interactive visualization and manual editing of segmentations were included in the software. Quantifications include stent deployment characteristics (e.g., stent area and stent strut malapposition), strut level analysis, calcium angle, and calcium thickness measurements. Interactive visualizations include (x,y) anatomical, en face, and longitudinal views with optional overlays (e.g., segmented calcifications). To compare images over time, linked visualizations were enabled to display up to four registered vessel segments at a time. ResultsOCTOPUS has been deployed for nearly 1 year and is currently being used in multiple IVOCT studies. Underlying plaque segmentation algorithm yielded excellent pixel-wise results (86.2% sensitivity and 0.781 F1 score). Using OCTOPUS on 34 new pullbacks, we determined that following automated segmentation, only 13% and 23% of frames needed any manual touch up for detailed lumen and calcification labeling, respectively. Only up to 3.8% of plaque pixels were modified, leading to an average editing time of only 7.5 s/frame, an approximately 80% reduction compared to manual analysis. Regarding stent analysis, sensitivity and precision were both greater than 90%, and each strut was successfully classified as either covered or uncovered with high sensitivity (94%) and specificity (90%). We demonstrated use cases for sequential analysis. To analyze plaque progression, we loaded multiple pullbacks acquired at different points (e.g., pre-stent, 3-month follow-up, and 18-month follow-up) and evaluated frame-level development of in-stent neo-atherosclerosis. In ex vivo cadaver experiments, the OCTOPUS software enabled visualization and quantitative evaluation of irregular stent deployment in the presence of calcifications identified in pre-stent images. ConclusionsWe introduced and evaluated the clinical application of a highly automated software package, OCTOPUS, for quantitative plaque and stent analysis in IVOCT images. The software is currently used as an offline tool for research purposes; however, the software's embedded algorithms may also be useful for real-time treatment planning.

Cost-aware sequential diagnostics

A simple search problem is studied in which a binary n-tuple is to be found in a list, by sequential bit comparisons with cost. The problem can be solved (for small n) using dynamic programming. We show how the “bottom up” part of the algorithm can be organized by means of Formal Concept Analysis.

Longitudinal measurement properties of the Montreal Cognitive Assessment

ABSTRACT Introduction The Montreal Cognitive Assessment (MoCA) has started to be used in longitudinal investigations to measure cognition trends but its measurement properties over time are largely unknown. This study aimed to examine the longitudinal measurement invariance of individual MoCA items. Method We used four waves of data collected between 2014 and 2017 from a cohort study on health and well-being of older adults from twelve public housing estates in Hong Kong. We identified people aged 65 years or older at baseline who answered the MoCA items across all time points and had a valid indicator of educational level. A total of 1028 participants were included. We applied confirmatory factor analysis of ordinal variables to examine measurement invariance of the Chinese (Cantonese) MoCA (version 7.0) items across four time points, stratified by educational level, where invariant items were identified by sequential model comparisons. Results Four items exhibited a lack of measurement invariance across the four time points in both education groups (Clock Hand, abstraction, Delayed Recall, and Orientation). The items Cube and Sentence Repetition lacked longitudinal measurement invariance only in the “some education” group and the items Clock Shape and Clock Number only in the “no education” group. However, accounting for the lack of measurement invariance did not substantially affect classification properties for major neurocognitive disorder and mild cognitive impairment. Conclusions Our findings support using MoCA to assess changes in cognition over time in the study population while calling for future research in other populations.

Longitudinal Measurement Properties of the Montreal Cognitive Assessment

Background: The Montreal Cognitive Assessment (MoCA) has started to be widely used in longitudinal investigations to measure changes in cognition. However, the longitudinal measurement properties of MoCA have not been investigated. We aimed to examine the measurement invariance of individual MoCA items across four time points. Methods: We used longitudinal data collected between 2014 and 2017 from a cohort study on health and well-being of older adults in Hong Kong. The Cantonese version of the MoCA was used. We applied multiple group confirmatory factor analysis of ordinal variables to examine measurement invariance by educational level and across time points. Invariant items were identified by sequential model comparisons. Results: We included 1029 participants that answered MoCA items across all time points. We found that items Cube, Clock Hand and Clock Number had significantly different item parameters between participants with and without formal education at all time points. The selected model (RMSEA=0.031; SRMR=0.064) indicated that eight items (Trail, Cube, Clock Shape, Clock Number, Clock Hand, ion, Short-term Memory, and Orientation) did not exhibit measurement invariance over time. However, the differences in item parameter estimate over time were marginal. Accounting for the lack of measurement invariance did not substantially affect classification properties based on cutoff values at the 2nd ( major neurocognitive disorder) and 7th (mild cognitive impairment) percentile. Conclusion: Our findings support using MoCA to assess changes in cognition over time in the study population. Future research should examine the longitudinal measurement properties of the test in other populations with different characteristics.

A decision-making model with sequential incomplete additive pairwise comparisons

A sequential modelling of pairwise comparisons exhibits the capability to effectively cope with some complexity in a decision making process. When the complexity of decision making problems leads to incomplete pairwise comparisons, a feasible approach to optimal solutions is worth investigations. In this paper, we propose the idea that a missing value is mainly dependent on the neighbour ones in a sequential of comparisons; and develop a decision making model. First, additive pairwise comparisons with missing values are captured by proposing a sequential model and some properties are studied. Second, an optimization model for completing an incomplete additive reciprocal matrix (ARM) is recalled. Based on the sequential model, the missing values of incomplete ARMs are estimated using particle swarm optimization (PSO). Different with the previous studies, the permutations of alternatives are considered to give various estimations of a missing value. Third, a granularity-based method is proposed to improve additive consistency of a completed ARM; and the best granularity level is chosen. Finally, a decision-making algorithm is established, where the opinions of decision makers (DMs) are expressed as incomplete ARMs. Some cases are studied to illustrate the finding that multi-optimal solutions could exist in a decision making problem. The novel phenomenon is in agreement with the case that different orders of comparing alternatives may yield different results due to the inconsistency of human-originated information.

Adaptive group sequential survival comparisons based on log-rank and pointwise test statistics.

Whereas the theory of confirmatory adaptive designs is well understood for uncensored data, implementation of adaptive designs in the context of survival trials remains challenging. Commonly used adaptive survival tests are based on the independent increments structure of the log-rank statistic. This implies some relevant limitations: On the one hand, essentially only the interim log-rank statistic may be used for design modifications (such as data-dependent sample size recalculation). Furthermore, the treatment arm allocation ratio in these classical methods is assumed to be constant throughout the trial period. Here, we propose an extension of the independent increments approach to adaptive survival tests that addresses some of these limitations. We present a confirmatory adaptive two-sample log-rank test that allows rejection regions and sample size recalculation rules to be based not only on the interim log-rank statistic, but also on point-wise survival rate estimates, simultaneously. In addition, the possibility is opened to adapt the treatment arm allocation ratio after each interim analysis in a data-dependent way. The ability to include point-wise survival rate estimators in the rejection region of a test for comparing survival curves might be attractive, e.g., for seamless phase II/III designs. Data-dependent adaptation of the allocation ratio could be helpful in multi-arm trials in order to successively steer recruitment into the study arms with the greatest chances of success. The methodology is motivated by the LOGGIC Europe Trial from pediatric oncology. Distributional properties are derived using martingale techniques in the large sample limit. Small sample properties are studied by simulation.

A Channel Classification Scheme Accounting for Nakagami-m Shadowing and FTR Model

In this letter, we address the problem of channel classification. Specifically, we consider five channel models also accounting for the incoming fifth generation mobile communication network (5G). The classification problem is formulated in terms of a multiple hypothesis testing problem and solved through a heuristic decision logic relying on sequential binary comparisons. This choice is dictated by the mathematical intractability of probability density functions (PDFs) under some hypotheses which contain transcendental functions. As a consequence, decision rules raising from well-known design criteria based upon data distribution might suffer numerical instability related to the routines used to implement such PDFs. The performance analysis is conducted on simulated data and shows the effectiveness of the proposed strategy in channel classification.

Group decision support model based on sequential additive complementary pairwise comparisons

In group decision support systems, it is important on how to process and manage individual decision information. In the paper, a sequential model is proposed to manage individual judgements with additively reciprocal property over paired alternatives. The process of realizing additive complementary pairwise comparisons (ACPCs) is captured. A real-time feedback mechanism is constructed to address the irrational behavior of individuals. An optimization model is established and solved by using the particle swarm optimization (PSO) algorithm, such that the consistency of individual judgements can be improved fast yet effectively. For the aggregation of individual decision information in group decision making (GDM), the weighted averaging operator is used. It is found that when all individual judgements are acceptably additively consistent, the collective matrix is with acceptable additive consistency. Under the control of individual consistency degrees, the approach of reaching consensus in GDM is further proposed. By comparing with some existing models, the observations reveal that the sequential model of originating additive complementary pairwise comparisons possesses the ability to rationally manage individual decision information.

Minimally invasive radical trachelectomy: Considerations on surgical approach

Current evidence supports that radical trachelectomy is a safe and feasible alternative to patients with early-stage cervical cancer who wish to preserve fertility. In addition, published retrospective literature supports that oncologic outcomes are equivalent to those of radical hysterectomy. First published as a vaginal approach, a number of other approaches have been reported including laparotomic, laparoscopic, and robotic. In 2018, the first ever prospective randomized trial (LACC) comparing open vs. minimally invasive radical hysterectomy showed worse disease-free and overall survival for the minimally invasive (both laparoscopic and robotic) approach than the open approach. This landmark publication raised concerns regarding the oncologic safety of minimally invasive radical trachelectomy. In the United States, minimally invasive became the dominant approach by 2011 for radical trachelectomy. Given that radical trachelectomy is an infrequent performed procedure, only small retrospective studies, systematic reviews, and large database studies have been published. These studies are limited by their retrospective nature, small sample size, patient selection bias, unbalanced groups, and sequential surgical approach comparisons. However, the available evidence thus far shows that oncologic outcomes for both open and minimally invasive radical trachelectomy are equivalent. Given the rarity of the procedure and the low recurrence and death rates of patients with early-stage cervical cancer undergoing radical trachelectomy, a prospective randomized trial seems unlikely. A multi-institutional international registry study (International Radical Trachelectomy Assessment - IRTA - study) has been recently completed evaluating open vs. minimally invasive radical trachelectomy. There are three ongoing prospective studies evaluating the possibility of less radical surgery in a low-risk early-stage cervical cancer population, ConCerv, SHAPE, and GOG 278. We look forward to the final results of these studies that will hopefully shed light on the optimal treatment option for patients with early-stage cervical cancer wishing to preserve fertility. This article will review the most impacting publications comparing open vs. minimally invasive radical trachelectomy and analyze the limitations of the current available literature.

Impact of SARS-CoV-2 Pandemic on "Stroke Code" Imaging Utilization and Yield.

Indirect consequences of the Severe Acute Respiratory Syndrome coronavirus 2 (SARS-CoV-2) pandemic include those related to failure of patients to seek or receive timely medical attention for seemingly unrelated disease. We report our experience with stroke code imaging during the early pandemic months of 2020. Retrospective review of stroke codes during the 2020 pandemic and both 2020 and matched 2019 prepandemic months was performed. Patient variables were age, sex, hospital location, and severity of symptoms based on the NIHSS. We reviewed the results of CT of the head, CTA, CTP, and MR imaging examinations and classified a case as imaging-positive if any of the imaging studies yielded a result that related to the clinical indication for the study. Both year-to-year and sequential comparisons were performed between pandemic and prepandemic months. A statistically significant decrease was observed in monthly stroke code volumes accompanied by a statistically significant increased proportion of positive imaging findings during the pandemic compared with the same months in the prior year (P < .001) and prepandemic months in the same year (P < .001). We also observed statistically significant increases in average NIHSS scores (P = .045 and P = .03) and the proportion of inpatient stroke codes (P = .003 and P = .03). During our pandemic period, there was a significantly decreased number of stroke codes but simultaneous increases in positivity rates, symptom severity, and inpatient codes. We postulate that this finding reflects the documented reluctance of patients to seek medical care during the pandemic, with the shift toward a greater proportion of inpatient stroke codes potentially reflecting the neurologic complications of the virus itself.

Ethnomathematics Vs Ethomodeling: how does cigugur traditional community determines the direction of the wind to seek fortune based on month

This study discusses the way of Cigugur indigenous communityin predicting the direction ins seeking fortunes. It uses a phenomenological approach with a realist ethnographic design through observation techniques, in-depth interviews, documentation, and field notes. The findings of this study indicate that the system of knowledge and livelihood which are included in the universal element of culture are implemented by the community using formal mathematical principles. Ethnomathematics as a research genre tries to reveal the dimensions of basic universal mathematical activities, while ethnomodeling as a methodology is used to represent the ideas and practices of community mathematics into academic mathematics through ethical, emic and dialctical approaches. The combination of naktu weton lahir, naktu pasaran, naktu tahun and naktu bulan, the time of one’s birth month can be used to predict a good direction in seeking fortune. Based on the study of ethnomathematics, the community determines the direction in seeking fortune, the mathematical concept used by the traditional Cigugur community is the concept of sequential pairs, relations, summations, and comparisons. Meanwhile, based on ethnomodeling, the community uses the concept of modulo and congruence. Ethnomatematics and ethnomodeling provide a different perspective on the conceptual mathematics that is inherent with the universal element of holistic culture.

Complex Time-Dependent ERP Hemispheric Asymmetries during Word Matching in Phonological, Semantic and Orthographical Matching Judgment Tasks

Language-induced asymmetry to single word reading has been well investigated in past research. Less known are the complex processes and related asymmetries occurring when a word is compared with the previous one, according to specific tasks. To this end, we used a paradigm based on 80 sequential word pair comparisons and three blocked tasks: phonological, semantic and orthographical matching judgment. Participants had to decide whether the target word (W2) did or did not match the prime word (W1), presented 2 sec before, according to the task. The event-related potentials (ERPs) evoked by W2 in 20 participants have been analyzed. The first negative wave, the Recognition Potential (RP), peaking at about 120 ms over parietal sites, showed greater amplitude at left sites in all tasks, thus revealing the typical left-lateralization. At frontal sites, only the phonological task showed left lateralization. The following N400 (300–450 ms) showed an interesting interaction: Match trials elicited greater left asymmetry on frontal regions to phonological than to semantic than to visual-perceptual tasks, whereas mismatch trials induced an inverted asymmetry, marked by greater amplitude over right frontal sites, regardless of the task. Concerning the late N400 (450–600 ms), phonological and semantic tasks showed an overlapping pattern, with left lateralization in match and right lateralization in mismatch conditions. Results point to complex task- and time-dependent hemispheric asymmetries in word matching.

Artificial Intelligence Aids Cardiac Image Quality Assessment for Improving Precision in Strain Measurements

ObjectivesThe aim of this study was to develop an artificial intelligence tool to assess echocardiographic image quality objectively. BackgroundLeft ventricular global longitudinal strain (LVGLS) has recently been used to monitor cancer therapeutics−related cardiac dysfunction (CTRCD) but image quality limits its reliability. MethodsA DenseNet-121 convolutional neural network was developed for view identification from an athlete’s echocardiographic dataset. To prove the concept that classification confidence (CC) can serve as a quality marker, values of longitudinal strain derived from feature tracking of cardiac magnetic resonance (CMR) imaging and strain analysis of echocardiography were compared. The CC was then applied to patients with breast cancer free from CTRCD to investigate the effects of image quality on the reliability of strain analysis. ResultsCC of the apical 4-chamber view (A4C) was significantly correlated with the endocardial border delineation index. CC of A4C >900 significantly predicted a <15% relative difference in longitudinal strain between CMR feature tracking and automated echocardiographic analysis. Echocardiographic studies (n =752) of 102 patients with breast cancer without CTRCD were investigated. The strain analysis showed higher parallel forms, inter-rater, and test-retest reliabilities in patients with CC of A4C >900. During sequential comparisons of automated LVGLS in individual patients, those with CC of A4C >900 had a lower false positive detection rate of CTRCD. ConclusionsCC of A4C was associated with the reliability of automated LVGLS and could also potentially be used as a filter to select comparable images from sequential echocardiographic studies in individual patients and reduce the false positive detection rate of CTRCD.

The Evaluation of Joint Mobilization Dosage on Ankle Range of Motion in Individuals With Decreased Dorsiflexion and a History of Ankle Sprain.

Mulligan's Mobilization with Movement (MWM) is a common intervention used to address dorsiflexion range of motion (DFROM) impairments. However, the treatment dosage of MWMs varies within the literature. The aim of this study was to examine the effect of serial MWM application on DFROM. Repeated-measures cohort. A Midwestern University and the surrounding community. A total of 18 adults (13 females; age = 29 [12.87]y; DFROM = 30.26° [4.60°]) with decrease dorsiflexion (<40°) participated. Inclusion criteria consisted of a history of ≥1 ankle sprain, ≥18 years old, no lower-extremity injury in the last 6months, and no history of foot/ankle surgery. Participants completed a single data collection session consisting of 10 individual sets of MWMs. DFROM was taken at baseline and immediately after each intervention set (post 1, post 2, … post 10). DFROM was measured with a digital inclinometer on the anterior aspect of the tibia during the weight-bearing lunge test with the knee straight and knee bent. Analysis of variances examined DFROM changes over time. Post hoc analysis evaluated sequential pairwise comparisons and changes from baseline at each time point. Analysis of variance results indicated a significant time main effect for weight-bearing lunge test with knee bent (P < .001) and a nonsignificant effect for weight-bearing lunge test with knee straight (P < .924). Post hoc analysis indicated improvements in the weight-bearing lunge test with knee bent at each timepoint compared with baseline (P < .005). Post 2 improved compared with post 1 (P = .027). No other pairwise sequential comparisons were significant (P > .417). MWMs significantly improved acute knee bent DFROM and indicated that after 2 sets of MWMs, no further DFROM improvements were identified. Future research should investigate the lasting effects of DFROM improvements with variable MWM dosages.

POSSIBILITY OF USING ELEMENTS OF MATHEMATICAL LIBRARY FOR A PARALLEL LANGUAGE IN CONSTRUCTION MATRIX PROGRAMS

Today, due to problems in improving computing performance, parallel programming continues to evolve. There are many different languages in which you can write parallel programs. One of them is the functional-threading parallel programming language Pifagor, which in turn is very specific and allows you to write a program with maximum parallelism, as well as it is designed to solve the portability problem of parallel programs. Tools and a library of functions continue to be developed for this language. This study is devoted to the development of elements of the mathematical library and the search for the most effective mathematical parallel algorithms. The following methods are considered and used in the work: sequential, recursive (left and right recursion), factorization, and pairwise comparisons. As a result of the study, a number of mathematical functions were developed, and a study was made of the possibility of using these functions in the development of programs for multiplying large-dimensional matrices. The work demonstrates the effectiveness of using the developed simple functions implemented by different methods in matrix multiplication programs. The prospects of further work in this direction are noted, having in mind the analysis of the possibility of using artificial intelligence methods to increase efficiency and facilitate the development of parallel programs with large-sized matrices.

Enhancing the promiscuity of a member of the Caspase protease family by rational design.

The N‐terminal cleavage of fusion tags to restore the native N‐terminus of recombinant proteins is a challenging task and up to today, protocols need to be optimized for different proteins individually. Within this work, we present a novel protease that was designed in‐silico to yield enhanced promiscuity toward different N‐terminal amino acids. Two mutations in the active‐site amino acids of human Caspase‐2 were determined to increase the recognition of branched amino‐acids, which show only poor binding capabilities in the unmutated protease. These mutations were determined by sequential and structural comparisons of Caspase‐2 and Caspase‐3 and their effect was additionally predicted using free‐energy calculations. The two mutants proposed in the in‐silico studies were expressed and in‐vitro experiments confirmed the simulation results. Both mutants showed not only enhanced activities toward branched amino acids, but also smaller, unbranched amino acids. We believe that the created mutants constitute an important step toward generalized procedures to restore original N‐termini of recombinant fusion proteins.

Group sequential tests for treatment effect on survival and cumulative incidence at a fixed time point.

Medical research frequently involves comparing an event time of interest between treatment groups. Rather than comparing the entire survival or cumulative incidence curves, it is sometimes preferable to evaluate these probabilities at a fixed point in time. Performing a covariate adjusted analysis can improve efficiency, even in randomized clinical trials, but no currently available group sequential test for fixed point analysis provides this adjustment. This paper introduces covariate adjusted group sequential pointwise comparisons of survival and cumulative incidence probabilities. Their test statistics have an asymptotic distribution with independent increments, permitting use of common stopping boundary specification methods. These tests are demonstrated through a redesign of BMT CTN 0402, a clinical trial that evaluated a prophylactic treatment for adverse outcomes following blood and marrow transplantation. A simulation study demonstrates that these tests maintain the type I error rate and power at nominal levels under a variety of settings involving influential covariates.

Centro-parietal EEG potentials index subjective evidence and confidence during perceptual decision making

Recent studies suggest that a centro-parietal positivity (CPP) in the EEG signal tracks the absolute (unsigned) strength of accumulated evidence for choices that require the integration of noisy sensory input. Here, we investigated whether the CPP might also reflect the evidence for decisions based on a quantitative comparison between two sequentially presented stimuli (a signed quantity). We recorded EEG while participants decided whether the latter of two vibrotactile frequencies was higher or lower than the former in six variants of this task (n = 116). To account for biases in sequential comparisons, we applied a behavioral model based on Bayesian inference that estimated subjectively perceived frequency differences. Immediately after the second stimulus, parietal ERPs reflected the signed value of subjectively perceived differences and afterwards their absolute value. Strikingly, the modulation by signed difference was evident in trials without any objective evidence for either choice and correlated with choice-selective premotor beta band amplitudes. Modulations by the absolute strength of subjectively perceived evidence – a direct indicator of task difficulty - exhibited all features of statistical decision confidence. Together, our data suggest that parietal EEG signals first index subjective evidence, and later include a measure of confidence in the context of perceptual decision making.