Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our...Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our previous studies, we have shown that the use of a polytomous logistic model for estimating cumulative odds ratios when the outcome (response) variable is ordinal (in addition to being polytomous) under matched pairs case-control design. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cutpoint level as compared to less than equal to that level. In this paper we propose an alternative method of estimating the cumulative odds ratios and reanalyze the Los Angeles Endometrial Cancer data in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer under the matched pair case-control design. Methods: In the present study, the cumulative logit model is fitted using a single multinomial logit model for the data. For this, the full maximum likelihood estimation procedure is adopted. A test for equality of the cumulative odds ratios across the exposure levels is proposed. Results: The analysis revealed that there is a strong evidence of risk for developing endometrial cancer due to oestrogen exposure above each of the three dose level as compared to less than equal to that level. The estimated values at the three cutpoint levels were found to be 6.17, 3.60 and 5.16 respectively. Conclusions: The odds of developing endometrial cancer are very high for the users of any amount of oestrogen, even if it is the least dose, as compared to the non-users.展开更多
The paper addresses the problem of reconciling the modern control paradigm developed by R. Kalman in the sixties of the past century, and the centenary error-based design of the proportional, integrative and derivati...The paper addresses the problem of reconciling the modern control paradigm developed by R. Kalman in the sixties of the past century, and the centenary error-based design of the proportional, integrative and derivative （PID） controllers. This is done with the help of the error loop whose stability is proved to be necessary and sufficient for the close-loop plant stability. The error loop is built by cascading the uncertain plant-to-model discrepancies （causal, parametric, initial state, neglected dynamics）, which are driven by the design model output and by arbitrary bounded signals, with the control unit transfer functions. The embedded model control takes advantage of the error loop and its equations to design appropriate algorithms of the modern control theory （state predictor, control law, reference generator）, which guarantee the error loop stability and performance. A simulated multivariate case study shows modeling and control design steps and the coherence of the predicted and simulated performance.展开更多
文摘Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our previous studies, we have shown that the use of a polytomous logistic model for estimating cumulative odds ratios when the outcome (response) variable is ordinal (in addition to being polytomous) under matched pairs case-control design. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cutpoint level as compared to less than equal to that level. In this paper we propose an alternative method of estimating the cumulative odds ratios and reanalyze the Los Angeles Endometrial Cancer data in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer under the matched pair case-control design. Methods: In the present study, the cumulative logit model is fitted using a single multinomial logit model for the data. For this, the full maximum likelihood estimation procedure is adopted. A test for equality of the cumulative odds ratios across the exposure levels is proposed. Results: The analysis revealed that there is a strong evidence of risk for developing endometrial cancer due to oestrogen exposure above each of the three dose level as compared to less than equal to that level. The estimated values at the three cutpoint levels were found to be 6.17, 3.60 and 5.16 respectively. Conclusions: The odds of developing endometrial cancer are very high for the users of any amount of oestrogen, even if it is the least dose, as compared to the non-users.
文摘The paper addresses the problem of reconciling the modern control paradigm developed by R. Kalman in the sixties of the past century, and the centenary error-based design of the proportional, integrative and derivative （PID） controllers. This is done with the help of the error loop whose stability is proved to be necessary and sufficient for the close-loop plant stability. The error loop is built by cascading the uncertain plant-to-model discrepancies （causal, parametric, initial state, neglected dynamics）, which are driven by the design model output and by arbitrary bounded signals, with the control unit transfer functions. The embedded model control takes advantage of the error loop and its equations to design appropriate algorithms of the modern control theory （state predictor, control law, reference generator）, which guarantee the error loop stability and performance. A simulated multivariate case study shows modeling and control design steps and the coherence of the predicted and simulated performance.
