Researchers conducting randomized clinical trials with two treatment groups sometimes wish to determine whether biomarkers are predictive and/or prognostic. They can use regression models with interaction terms to ass...Researchers conducting randomized clinical trials with two treatment groups sometimes wish to determine whether biomarkers are predictive and/or prognostic. They can use regression models with interaction terms to assess the role of the biomarker of interest. However, although the interaction term is undoubtedly a suitable measure for prediction, the optimal way to measure prognosis is less clear. In this article, we define causal measures that can be used for prognosis and prediction based on biomarkers. The causal measure for prognosis is defined as the average of two differences in status between biomarker-positive and -negative subjects under treatment and control conditions. The causal measure for prediction is defined as the difference between the causal effect of the treatment for biomarker-positive and biomarker-negative subjects. We also explain the relationship between the proposed measures and the regression parameters. The causal measure for prognosis corresponds to the terms for the biomarker in a regression model, where the values of the dummy variables representing the explanatory variables are -1/2 or 1/2. The causal measure for prediction is simply the causal effect of the interaction term in a regression model. In addition, for a binary outcome, we express the causal measures in terms of four response types: always-responder, complier, non-complier, and never-responder. The causal measure for prognosis can be expressed as a function of always- and never-responders, and the causal measure for prediction as a function of compliers and non-compliers. This enables us to demonstrate that the proposed measures are plausible in the case of a binary outcome. Our causal measures should be used to assess whether a biomarker is prognostic and/or predictive.展开更多
The main purpose in many randomized trials is to make an inference about the average causal effect of a treatment. Therefore, on a binary outcome, the null hypothesis for the hypothesis test should be that the causal ...The main purpose in many randomized trials is to make an inference about the average causal effect of a treatment. Therefore, on a binary outcome, the null hypothesis for the hypothesis test should be that the causal risks are equal in the two groups. This null hypothesis is referred to as the weak causal null hypothesis. Nevertheless, at present, hypothesis tests applied in actual randomized trials are not for this null hypothesis;Fisher’s exact test is a test for the sharp causal null hypothesis that the causal effect of treatment is the same for all subjects. In general, the rejection of the sharp causal null hypothesis does not mean that the weak causal null hypothesis is rejected. Recently, Chiba developed new exact tests for the weak causal null hypothesis: a conditional exact test, which requires that a marginal total is fixed, and an unconditional exact test, which does not require that a marginal total is fixed and depends rather on the ratio of random assignment. To apply these exact tests in actual randomized trials, it is inevitable that the sample size calculation must be performed during the study design. In this paper, we present a sample size calculation procedure for these exact tests. Given the sample size, the procedure can derive the exact test power, because it examines all the patterns that can be obtained as observed data under the alternative hypothesis without large sample theories and any assumptions.展开更多
This paper discusses the relationship among the total causal effect and local causal effects in a causal chain and identifiability of causal effects. We show a transmission relationship of causal effects in a causal c...This paper discusses the relationship among the total causal effect and local causal effects in a causal chain and identifiability of causal effects. We show a transmission relationship of causal effects in a causal chain. According to the relationship, we give an approach to eliminating confounding bias through controlling for intermediate variables in a causal chain.展开更多
Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser s...Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser six cognitive functions and provide new perspectives on which a lot of extensions and particularlly flexible Lmser are proposed.Interestingly,either or two of these dualities actually takes an important role in recent models such as U-net,ResNet,and Dense Net.The second thread is about bidirectional learning principles unified by best yIng-yAng(IA)harmony in BYY system.After getting insights on deep bidirectional learning from a bird-viewing on existing typical learning principles from one or both of the inward and outward directions,maximum likelihood,variational principle,and several other learning principles are summarised as exemplars of the BYY learning,with new perspectives on advanced topics.The third thread further proceeds to deep bidirectional intelligence,driven by long term dynamics(LTD)for parameter learning and short term dynamics(STD)for image thinking and rational thinking in harmony.Image thinking deals with information flow of continuously valued arrays and especially image sequence,as if thinking was displayed in the real world,exemplified by the flow from inward encoding/cognition to outward reconstruction/transformation performed in Lmser learning and BYY learning.In contrast,rational thinking handles symbolic strings or discretely valued vectors,performing uncertainty reasoning and problem solving.In particular,a general thesis is proposed for bidirectional intelligence,featured by BYY intelligence potential theory(BYY-IPT)and nine essential dualities in architecture,fundamentals,and implementation,respectively.Then,problems of combinatorial solving and uncertainty reasoning are investigated from this BYY IPT perspective.First,variants and extensions are suggested for AlphaGoZero like searching tasks,such as traveling salesman problem(TSP)and attributed graph matching(AGM)that ar展开更多
We start where we use an inflaton value due to use of a scale factor . Also we use as the variation of the time component of the metric tensor in Pre-Planckian space-time. Our objective is to find an effective magneti...We start where we use an inflaton value due to use of a scale factor . Also we use as the variation of the time component of the metric tensor in Pre-Planckian space-time. Our objective is to find an effective magnetic field, to obtain the minimum scale factor in line with Non Linear Electrodynamics as given by Camara, et al., 2004. Our suggestion is based upon a new procedure for an effective current based upon an inflaton time exp (i times (frequency) times (cosmological time)) factor as a new rescaled inflaton which is then placed right into a Noether Current scalar field expression as given by Peskins, 1995. This is before the Causal surface with which is, right next to a quantum bounce, determined by , with the next shift in the Hubble parameter as set up to be then . And is an initial degree of freedom value of about 110. Upon calculation of the current, and a resulting magnetic field, for the space time bubble, we then next obtain a shift in energy, leading to a transition from too. We argue then that the delineation of the term is a precursor to filling in information as to the Weyl Tensor for near singularity measurements of starting space-time. Furthermore, as evidenced in Equations ((26) and (27)) of this document, we focus upon a “first order” that checks into if a cosmological “constant” would be invariant in time, or would be along the trajectory of the time, varying Quinessence models. We close this document, with Maxwell equations as to Post Newtonian theory, for Gravity, with our candidates as to a magnetic field included in, with what we think this pertains to, as far as Gravo Electric and Gravo Magnetic fields, and then make suggestions as to a quantum version of this methodology for future gravitational wave physics research. This is Appendix G, this last topic, and deliberately set up future works paradigm which will be investigated in the coming year. It is based upon a Gravo Electric potential, and we make suggestions as to its upgrade in our future works, in early universe cosmolog展开更多
文摘Researchers conducting randomized clinical trials with two treatment groups sometimes wish to determine whether biomarkers are predictive and/or prognostic. They can use regression models with interaction terms to assess the role of the biomarker of interest. However, although the interaction term is undoubtedly a suitable measure for prediction, the optimal way to measure prognosis is less clear. In this article, we define causal measures that can be used for prognosis and prediction based on biomarkers. The causal measure for prognosis is defined as the average of two differences in status between biomarker-positive and -negative subjects under treatment and control conditions. The causal measure for prediction is defined as the difference between the causal effect of the treatment for biomarker-positive and biomarker-negative subjects. We also explain the relationship between the proposed measures and the regression parameters. The causal measure for prognosis corresponds to the terms for the biomarker in a regression model, where the values of the dummy variables representing the explanatory variables are -1/2 or 1/2. The causal measure for prediction is simply the causal effect of the interaction term in a regression model. In addition, for a binary outcome, we express the causal measures in terms of four response types: always-responder, complier, non-complier, and never-responder. The causal measure for prognosis can be expressed as a function of always- and never-responders, and the causal measure for prediction as a function of compliers and non-compliers. This enables us to demonstrate that the proposed measures are plausible in the case of a binary outcome. Our causal measures should be used to assess whether a biomarker is prognostic and/or predictive.
文摘The main purpose in many randomized trials is to make an inference about the average causal effect of a treatment. Therefore, on a binary outcome, the null hypothesis for the hypothesis test should be that the causal risks are equal in the two groups. This null hypothesis is referred to as the weak causal null hypothesis. Nevertheless, at present, hypothesis tests applied in actual randomized trials are not for this null hypothesis;Fisher’s exact test is a test for the sharp causal null hypothesis that the causal effect of treatment is the same for all subjects. In general, the rejection of the sharp causal null hypothesis does not mean that the weak causal null hypothesis is rejected. Recently, Chiba developed new exact tests for the weak causal null hypothesis: a conditional exact test, which requires that a marginal total is fixed, and an unconditional exact test, which does not require that a marginal total is fixed and depends rather on the ratio of random assignment. To apply these exact tests in actual randomized trials, it is inevitable that the sample size calculation must be performed during the study design. In this paper, we present a sample size calculation procedure for these exact tests. Given the sample size, the procedure can derive the exact test power, because it examines all the patterns that can be obtained as observed data under the alternative hypothesis without large sample theories and any assumptions.
基金This work was supported by the National Natural Science Foundation of China(Grant No.90209010)NBRP2003CB715900.
文摘This paper discusses the relationship among the total causal effect and local causal effects in a causal chain and identifiability of causal effects. We show a transmission relationship of causal effects in a causal chain. According to the relationship, we give an approach to eliminating confounding bias through controlling for intermediate variables in a causal chain.
基金supported by the Zhi-Yuan Chair Professorship Start-up Grant (WF220103010) from Shanghai Jiao Tong University
文摘Advances on bidirectional intelligence are overviewed along three threads,with extensions and new perspectives.The first thread is about bidirectional learning architecture,exploring five dualities that enable Lmser six cognitive functions and provide new perspectives on which a lot of extensions and particularlly flexible Lmser are proposed.Interestingly,either or two of these dualities actually takes an important role in recent models such as U-net,ResNet,and Dense Net.The second thread is about bidirectional learning principles unified by best yIng-yAng(IA)harmony in BYY system.After getting insights on deep bidirectional learning from a bird-viewing on existing typical learning principles from one or both of the inward and outward directions,maximum likelihood,variational principle,and several other learning principles are summarised as exemplars of the BYY learning,with new perspectives on advanced topics.The third thread further proceeds to deep bidirectional intelligence,driven by long term dynamics(LTD)for parameter learning and short term dynamics(STD)for image thinking and rational thinking in harmony.Image thinking deals with information flow of continuously valued arrays and especially image sequence,as if thinking was displayed in the real world,exemplified by the flow from inward encoding/cognition to outward reconstruction/transformation performed in Lmser learning and BYY learning.In contrast,rational thinking handles symbolic strings or discretely valued vectors,performing uncertainty reasoning and problem solving.In particular,a general thesis is proposed for bidirectional intelligence,featured by BYY intelligence potential theory(BYY-IPT)and nine essential dualities in architecture,fundamentals,and implementation,respectively.Then,problems of combinatorial solving and uncertainty reasoning are investigated from this BYY IPT perspective.First,variants and extensions are suggested for AlphaGoZero like searching tasks,such as traveling salesman problem(TSP)and attributed graph matching(AGM)that ar
文摘We start where we use an inflaton value due to use of a scale factor . Also we use as the variation of the time component of the metric tensor in Pre-Planckian space-time. Our objective is to find an effective magnetic field, to obtain the minimum scale factor in line with Non Linear Electrodynamics as given by Camara, et al., 2004. Our suggestion is based upon a new procedure for an effective current based upon an inflaton time exp (i times (frequency) times (cosmological time)) factor as a new rescaled inflaton which is then placed right into a Noether Current scalar field expression as given by Peskins, 1995. This is before the Causal surface with which is, right next to a quantum bounce, determined by , with the next shift in the Hubble parameter as set up to be then . And is an initial degree of freedom value of about 110. Upon calculation of the current, and a resulting magnetic field, for the space time bubble, we then next obtain a shift in energy, leading to a transition from too. We argue then that the delineation of the term is a precursor to filling in information as to the Weyl Tensor for near singularity measurements of starting space-time. Furthermore, as evidenced in Equations ((26) and (27)) of this document, we focus upon a “first order” that checks into if a cosmological “constant” would be invariant in time, or would be along the trajectory of the time, varying Quinessence models. We close this document, with Maxwell equations as to Post Newtonian theory, for Gravity, with our candidates as to a magnetic field included in, with what we think this pertains to, as far as Gravo Electric and Gravo Magnetic fields, and then make suggestions as to a quantum version of this methodology for future gravitational wave physics research. This is Appendix G, this last topic, and deliberately set up future works paradigm which will be investigated in the coming year. It is based upon a Gravo Electric potential, and we make suggestions as to its upgrade in our future works, in early universe cosmolog
