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Objective To predict preterm birth in nulliparous women using logistic regression and machine learning. Design Population-based retrospective cohort. Participants Nulliparous women (N = 112,963) with a singleton gestation who gave birth between 20–42 weeks gestation in Ontario hospitals from April 1, 2012 to March 31, 2014. Methods We used data during the first and second trimesters to build logistic regression and machine learning models in a “training” sample to predict overall and spontaneous preterm birth. We assessed model performance using various measures of accuracy including sensitivity, specificity, positive predictive value, negative predictive value, and area under the receiver operating characteristic curve (AUC) in an independent “validation” sample. Results During the first trimester, logistic regression identified 13 variables associated with preterm birth, of which the strongest predictors were diabetes (Type I: adjusted odds ratio (AOR): 4.21; 95% confidence interval (CI): 3.23–5.42; Type II: AOR: 2.68; 95% CI: 2.05–3.46) and abnormal pregnancy-associated plasma protein A concentration (AOR: 2.04; 95% CI: 1.80–2.30). During the first trimester, the maximum AUC was 60% (95% CI: 58–62%) with artificial neural networks in the validation sample. During the second trimester, 17 variables were significantly associated with preterm birth, among which complications during pregnancy had the highest AOR (13.03; 95% CI: 12.21–13.90). During the second trimester, the AUC increased to 65% (95% CI: 63–66%) with artificial neural networks in the validation sample. Including complications during the pregnancy yielded an AUC of 80% (95% CI: 79–81%) with artificial neural networks. All models yielded 94–97% negative predictive values for spontaneous PTB during the first and second trimesters. Conclusion Although artificial neural networks provided slightly higher AUC than logistic regression, prediction of preterm birth in the first trimester remained elusive. However, including data from the second trimester improved prediction to a moderate level by both logistic regression and machine learning approaches.

Funding information Natural Sciences and Engineering Research Council (NSERC) of CanadaGamma regression is applied in several areas such as life testing, forecasting cancer incidences, genomics, rainfall prediction, experimental designs, and quality control. Gamma regression models allow for a monotone and no constant hazard in survival models. Owing to the broad applicability of gamma regression, we propose some novel and improved methods to estimate the coefficients of gamma regression model. We combine the unrestricted maximum likelihood (ML) estimators and the estimators that are restricted by linear hypothesis, and we present Stein-type shrinkage estimators (SEs). We then develop an asymptotic theory for SEs and obtain their asymptotic quadratic risks. In addition, we conduct Monte Carlo simulations to study the performance of the estimators in terms of their simulated relative efficiencies. It is evident from our studies that the proposed SEs outperform the usual ML estimators. Furthermore, some tabular and graphical representations are given as proofs of our assertions. This study is finally ended by appraising the performance of our estimators for a real prostate cancer data. KEYWORDS asymptotic quadratic risk, gamma regression, positive-part Stein-type shrinkage estimator, prostate cancer, relative efficiency, Stein-type shrinkage estimator 4310

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observed under type-II censoring. We obtain maximum likelihood estimates and associated interval estimates under a classical approach, and Bayes estimates using various loss functions and associated highest posterior density interval estimates. Maximum likelihood estimates are obtained using the Newton-Raphson method and Expectation Maximization (EM) algorithm, and Bayes estimates are computed using importance sampling and Lindley approximation. We also compute shrinkage preliminary test estimates based on maximum likelihood and Bayes estimates. Further, we provide inference on the censored observations by making use of best unbiased and condition median predictors under a classical approach, and predictive estimates under the Bayesian paradigm using importance sampling. The associated predictive interval estimates are also obtained using different methods. Finally, we conduct a simulation study to compare the performance of all the proposed methods of estimation and prediction, and analyze a real data set for illustration purpose.

In this paper some different sorts of estimators are proposed based on record breaking observations in the Burr type XII model. We define Bayes as well as empirical Bayes preliminary test estimators in the same fashion as in the ordinary preliminary test estimator using relevant combinations of uniformly minimum variance unbiased (UMVU) and Bayes estimators. Exact and asymptotic bias and mean square error (MSE) expressions for the proposed estimators are derived under two different conditions of knowing the shape parameters. We compare the MSEs and obtain the confidence interval for the parameter of interest in which the preliminary test type estimators outperform the UMVU, Bayes and empirical Bayes estimators.An application of the ordinary preliminary test estimator is also considered. We conclude this approach by a useful discussion for practical purposes and a summary.

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