On the construction of efficient estimators in semiparametric models

Root-n-consistent and efficient estimation in semiparametric additive regression models

IntroductionRandomized controlled trial (RCT) data are analyzed by two challengeable adjusted and non-adjusted approaches. Performing appropriate adjusted analysis leads to a more interpretable and efficient estimation of treatment effects. Semiparametric adjustment approach modifies the estimating equations solved by the marginal treatment effect estimator by adding an augmentation function, which makes use of the baseline covariates and estimate the unbiased marginal treatment effect with improved precision. The effect of the intervention obtained using the semi-parametric adjustment method, similar to the unadjusted method and contrary to the adjusted parametric method, is marginal, resulting in better interpretability. Moreover, due to leveraging baseline covariates, it is more efficient compared to the unadjusted models. This study aimed to estimate the effect of beractant (Beraksurf™, Tekzima Company), compared with the Poractant alfa (Curosurf®, Chiesi Pharmaceuticals), as surfactant replacement therapy, on the need for Intermittent Positive Pressure Ventilation (IPPV) in Neonatal Respiratory Distress Syndrome (NRDS) more precisely by fitting a semi-parametric efficient model adjusted for appropriate covariates.MethodThis study is secondary and we re-analyzing data of a published RCT. This RCT was conducted in the NICU of Alzahra Hospital in Tabriz, Iran for eight months, and 200 infants were assigned to two groups receiving either 100 mg/kg BeraksurfTM (n = 99) or 200 mg/kg Curosurf® (n = 101). The effect of the treatments was evaluated regarding the need for IPPV by fitting semi-parametric logistic regression models, adjusted for the best subset of covariates selected by the forward variable selection algorithm and confounders identified by the expert panel. IPPV in our study was administered via an endotracheal tube, as per the protocol followed in the primary trial. The need for IPPV was determined based on the clinical judgment of neonatologists, considering the infants' respiratory distress levels, oxygen saturation, and arterial blood gas measurements. The decision was made within the first 72 h after surfactant administration.ResultsThe proportions of the required IPPV outcome were 29.3% and 59.4% in the BeraksurfTM group and Curosurf®, respectively. While the unadjusted comparison between the two treatments was significant (OR = .283, 95% CI: (.157, .509), P-value < .001), adjusted OR in semi-parametric logistic regression by adjusting for the best subset of covariates selected by forward method including steroids, Apgar score at min1, and initial Fio2 wasn’t significant (OR = .751, 95% CI: (.510, 1.111), P-value = .151). The efficacy of this semi-parametric model over the unadjusted model was 1.81. The results of the expert-based adjusted model, adjusting for the gestational age, birth weight, and initial FiO2, were consistent with those derived from the R2-based selection, supporting the robustness of our findings (OR = .685, 95% CI: (.449, 1.529), P-value = .078).ConclusionFitting a semi-parametric model adjusted for the baseline covariates resulted in a marginal, unbiased, more efficient and interpretable estimation of BeraksurfTM versus Curosurf® effects. Although the crude model showed that BeraksurfTM was more effective than Curosurf®, the results of the efficient semi-parametric model with adjustment for the best subset of covariates revealed no statistically significant difference between the two drugs regarding their effects. We hope that the use of this method and its findings will contribute to a better understanding of covariate adjustment.

In this paper, we consider a semiparametric regression model where the error follows a scale mixture of Gaussian distributions. The purpose is to estimate the target function which is assumed to belong to some class of functions using the EM algorithm and approximations via P-splines and B-splines. We illustrate the proposed methodology through several simulation studies. Other forms of function approximation are also studied, namely Fourier and wavelet expansions.

Bounded influence functions are used for robust estimation in semiparametric models. In this paper, we generalize Hampel's variational problem to semiparametric models and define the optimal B-robust influence function as the one solving the variational problem. We identify the lowest bounds for influence functions and establish the existence and uniqueness of the optimal influence functions in general semiparametric models. Explicit optimal influence functions are given for a special case. Examples are provided to illustrate the procedures for calculating the optimal influence functions and for constructing the corresponding optimal estimators.

Since carbon price volatility is critical to the risk management of the CO2 emissions trading market, research has focused on energy prices and macroeconomic drivers which cause changes in carbon prices and make the carbon market more volatile than other markets. However, they have ignored whether the impact of carbon price determinants changes when the carbon price is at different levels. To fill this gap, this paper applies a semiparametric quantile regression model to explore the effects of energy prices and macroeconomic drivers on carbon prices at different quantiles. The model combines the advantages of parameter estimation, nonparametric estimation and quantile regression to describe the nonlinear relationship between carbon price and its fundamentals, which do not need to make any assumptions about the random error. Carbon prices are high–tailed and exhibit higher kurtosis, the traditional models which tend to assume that data are normally distributed can’t perform well. Furthermore, the semiparametric model doesn’t need to assume that the data are normally distributed. Therefore, the semiparametric model can effectively model the data. Some new evidence from China’s emission trading scheme (ETS) pilots shows that energy prices and macroeconomic drivers have different effects on carbon prices at high or low quantiles. First, the negative impact of coal prices on carbon prices was greater at the lower quantile of carbon prices in the Shenzhen ETS pilot. However, the effects of coal prices were positive in the Beijing ETS pilot, which may be attributed to great demand for coal. Second, oil prices had greater negative effects on carbon prices at higher quantiles in Beijing and Hubei ETS pilots. This can be attributed to the fact that businesses use less oil when carbon prices are high. For the Shenzhen ETS pilot, the effects of oil prices were positive. Third, natural gas prices have a stronger effect on carbon prices as quantiles increased in the Beijing and Hubei ETS pilots. Lastly, the effects of macroeconomic drivers on carbon prices at low quantiles were stronger in the Shenzhen ETS pilots and higher at the medium quantiles in Beijing and Hubei ETS pilots. These findings suggest that the impact of determinants on the carbon prices at different levels is not constant. Ignoring this issue will lead to a missed warning about the risks of the carbon market. This study will be of positive significance for China’s emission trading scheme (ETS) pilots, in order to accurately monitor the effects of carbon prices determinants and effectively avoid carbon market risks.

In this lecture and the next lecture we discuss empirical processes. Our main focus is the application of empirical processes to the derivation of asymptotic properties of estimators in semiparametric models. In this first lecture we discuss entropy numbers, Glivenko—Cantelli classes and their application to proving consistency of M- and Z-estimators.

Hodges and Lehmann proposed using rank test statistics evaluated at inversely transformed data to construct estimating equations. This paper reframes the resulting estimates in terms of a rank likelihood. In the context of a model of the form Y = h( e; z, β), where Y is a response, z a vector of predictors and e is a random error, this approach corresponds to computing the inverse e = g( Y, z; β) by solving Y = h( e; z, β) for e and using the distribution of the ranks of independent e’s as a likelihood. The properties of the resulting estimators have been developed in many important contexts. This paper will review and extend asymptotic optimality properties of Hodges Lehmann estimators in semiparametric models. In particular, the paper will establish semiparametric optimality of the estimate obtained from a Gaussian linear model. Moreover, it will be shown that the Hodges-Lehmann estimate obtained from the exponential likelihood is asymptotically minimax for the semiparametric accelerated failure time model with increasing hazard rates, and it will be shown that a uniform (Wilcoxon) score estimate applied to log Yi, 1 ≤ i ≤ n, is asymptotically minimax for an accelerated failure time model with increasing logit rate. References to recently developed software in R is provided.

Summary We propose goodness-of-fit tests for testing generalized linear models and semiparametric regression models against smooth alternatives. The focus is on models having both continous and factorial covariates. As a smooth extension of a parametric or semiparametric model we use generalized varying-coefficient models as proposed by Hastie and Tibshirani. A likelihood ratio statistic is used for testing. Asymptotic expansions allow us to write the estimates as linear smoothers which in turn guarantees simple and fast bootstrapping of the test statistic. The test is shown to have √n-power, but in contrast with parametric tests it is powerful against smooth alternatives in general.

SUMMARY When there are covariate effects to be considered, multi-state survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox's (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox's model in a general finite-state Markov process setting. We shall look at two alternative models, Aalen's (1989) nonparametric additive hazards model and Lin & Ying's (1994) semiparametric additive hazards model. The former allows the effects of covariates to vary freely over time, while the latter assumes that the regression coefficients are constant over time. With the basic tools of the product integral and the functional delta-method, we present an estimator of the transition probability matrix and develop the large-sample theory for the estimator under each of these two models. Data on 1459 HLA identical sibling transplants for acute leukaemia from the International Bone Marrow Transplant Registry serve as illustration.

Crash risk analysis for Shanghai urban expressways: A Bayesian semi-parametric modeling approach

Understanding the distribution and propagation of train delay is crucial for railway management. This paper combines the interpretability of logistic regression models with the robustness and accuracy of Random Forest models to create a combined model which was applied to predict punctuality. The data consists of relative timetable deviation of train movement for all stations, as well as punctuality observations at destination stations. The data was recorded for both passenger and freight trains in Sweden between year 2017 and 2018.The data consists of many policy and categorical variables such as train operator which are known to indirectly effect delay risk, but are labeled as insignificant in classical regression making their coefficients unstable and difficult to interpret. For this reason, the study has applied logistic regression model with the variables of interest such as train type as well as first registered delay (relative deviation compared with timetable) along with "bagging" of Random Forest capturing indirect or/and sensitive predictors. This semi-parametric logistic regression model was trained using 2017 data and was accurate and robust when tested using the 2018 data. It has shown to be capable of handling the delays caused by unforeseen disruptions such as abnormal weather in the test year. In this paper we show that the semi-parametric model has significantly better prediction performance than linear models, Weibull distributions, Binomial logistic regression and Random Forest alone. Furthermore, the semiparametric model maintains its interpretability whilst producing accurate predictions with new data.

In the May 15, 1997, issue of Transplantation (1997; 63[9]: 1257), Dr. Shield and co-workers (1) reported on an analysis of the United Network for Organ Sharing to compare results in renal transplant recipients treated with and without antilymphocyte products. We agree that the use of this very large database offers an important opportunity to elucidate the critical issues in this controversial area. However, after carefully reviewing this article, we are left with a number of important questions about the data. Are we correct in assuming that only patients whose data was validated (84% of the total) were used in this study? There is a comment regarding validation of data with respect to the antilymphocyte product and the duration of its administration. Was there any attempt to validate data relating to rejection episodes, graft survival, and the other data that were used in the study? We believe (without having seen data) that most U.S. centers will have definite policies regarding the use of antilymphocyte products. We would appreciate comments by the authors on this issue. A potential beneficial effect of antilymphocyte products is to reduce the rejection rate. Table 3 gives rejection episodes up to the time of discharge from hospital, but no information is given on rejection episodes that recurred after this time. Is this data available? A listing of the variables that were entered into the Cox regimen analysis would be helpful. For example, in the entire group of patients, was delayed graft function an independent risk factor or was it a dependent variable interacting with the presence or absence of an antilymphocyte product? Furthermore, was the complete absence of the use of an antilymphocyte product associated with an increase in relative risk (data not given in Table 6)? Additional information on the panel-reactive antibody as a dependent or independent risk factor for delayed graft function and graft outcome would be helpful to interpret the results. Since one of the main findings of the study seems to be that if graft loss during the first week is excluded, there is no difference in outcomes among the three groups, we believe that an analysis of the causes of graft loss in the three groups, including an analysis of the causes of graft loss within the first week separately, would be useful. Finally, we are confused by Table 8, in that data are shown for patients not receiving an antilymphocyte product based on the number of days of induction. Is this also used to indicate the day after transplant on which the events occurred in this group? Jolanta Karpinski Carl Cardella Edward Cole1 Renal Transplant Program; University of Toronto; Toronto, Ontario, Canada

Recurrent event data are often encountered in biomedical research, for example, recurrent infections or recurrent hospitalizations for patients after renal transplant. In many studies, there are more than one type of events of interest. Cai and Schaubel (2004) advocated a proportional marginal rate model for multiple type recurrent event data. In this paper, we propose a general additive marginal rate regression model. Estimating equations approach is used to obtain the estimators of regression coefficients and baseline rate function. We prove the consistency and asymptotic normality of the proposed estimators. The finite sample properties of our estimators are demonstrated by simulations. The proposed methods are applied to the India renal transplant study to examine risk factors for bacterial, fungal and viral infections.

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the covariates increases. We propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern. Consistency of the method is proved for parametric and semiparametric regression models. A bootstrap implementation is also discussed. Simulation comparisons with several existing methods are made, suggesting that the proposed methods are more efficient than the existing methods when the dimension increases. Air pollution data from Chicago are used to illustrate the procedure.

This article investigates modeling and calibration issues that are associated with inertially stabilized platforms to achieve accurate pointing. In modeling part, the Denavit–Hartenberg notation is used to perform an error analysis of the kinematics of inertially stabilized platforms. A physical model is then established to illustrate the effects of geometric errors that are caused by imprecision in the manufacturing and assembly processes on the pointing accuracy of inertially stabilized platforms. In the calibration part, an improved hybrid model denoted as the semi-parametric regression model is developed to compensate for remaining nonlinear errors. With applications to a two-degree-of-freedom miniature inertially stabilized platform, semi-parametric regression model is shown to outperform physical model substantially in all cases. The experimental results also indicate that the proposed semi-parametric regression model eliminates both the geometric and nonlinear errors, and that the pointing accuracy of miniature inertially stabilized platform significantly improves after compensation.