Operational research in Indian defence

The paper gives an outline of the areas of Operational Research (OR) where work in the Defence Department in India has been successful, even though it has not been fully implemented due to certain reservations on the part of the users and some limitations of OR scientists. There is an ad hoc quality in the decision making of the customer, and no large scale OR models are available which give a total effect of defence spending on social measures and human resources development. OR would be able to contribute to a balanced spending on defence in developing countries, if effort were made to analyse defence problems in the wider context. The author was formerly Director of Scientific Evaluation, Ministry of Defence, India.     

Mathematical models and their applications in medicine and health

Mathematical models have great potentialities as regards their utility in different disciplines of medicine and health. This paper attempts to elucidate their uses in the field. A brief mention of some models has also been made. Mathematical models are useful in epidemiologic research, planning and evaluation of preventive and control programmes, clinical trials, measurement of health, cost-benefit analysis, diagnosis of patients and in maximizing effectiveness of operations aimed at attaining specified goals within existing resources.     

On-line control procedures for integrated moving average process of order one

A commonly used model in process adjustment is the integrated moving average (IMA) process of order one. When the disturbances are normally distributed, this problem has been considered by Box and Jenkins (1963, 1976), Kramer (1989), Srivastava and Wu (1992), Box and Kramer (1992) and Srivastava (1996). Box and Lucefio (1994) extended the above model to any disturbance that is symmetrically distributed. However, their solution involves Fred holm integral equation which must be solved by numerical methods. In this paper, we follow the approach of Srivastava and Wu (1992, 1996) and provide the optimum control limit explicitly in terms of the first moment of the randomly stopped random sum of independent and identically distributed observations. These results are also used to study the robustness of the normal model. It is shown that the procedure is robust for small to moderate departure from normality.     

Regression analysis of multivariate recurrent event data with a dependent terminal event

Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data, 2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest (Ghosh and Lin, Biometrics 56:554–562, 2000; Wang et al., J Am Stat Assoc 96:1057–1065, 2001; Huang and Wang, J Am Stat Assoc 99:1153–1165, 2004; Ye et al., Biometrics 63:78–87, 2007). In addition, sometimes there may exist more than one type of recurrent events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics 5:129–143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of leukemia patients.     

Stein-rule estimator under inclusion of superfluous variables in linear regression models

Stein-rule estimation is a well-known method to improve the unbiased OLSE in the sense of smaller Mean-Square-Error. The paper is investigating the behaviour of this efficiency relation in case of misspecification of the linear model caused by inclusion of superfluous variables     

A second order approximation to taguchps online control procedure

In this paper, a second order approximation of the average loss function for on-line control procedure is developed under a Brownian motion model. The approximation depends on whether the ratio of the adjustment cost to the inspection cost is small or large. Both cases are dealt with. Simple formulae for the optimal parameters are given for both cases. These approximations are shown to be better than the ones given by Taguchi et al.(1989) and Adams and WoodaU(1989).     

Maximum likelihood estimation for the proportional odds model with mixed interval-censored failure time data

This article discusses regression analysis of mixed interval-censored failure time data. Such data frequently occur across a variety of settings, including clinical trials, epidemiologic investigations, and many other biomedical studies with a follow-up component. For example, mixed failure times are commonly found in the two largest studies of long-term survivorship after childhood cancer, the datasets that motivated this work. However, most existing methods for failure time data consider only right-censored or only interval-censored failure times, not the more general case where times may be mixed. Additionally, among regression models developed for mixed interval-censored failure times, the proportional hazards formulation is generally assumed. It is well-known that the proportional hazards model may be inappropriate in certain situations, and alternatives are needed to analyze mixed failure time data in such cases. To fill this need, we develop a maximum likelihood estimation procedure for the proportional odds regression model with mixed interval-censored data. We show that the resulting estimators are consistent and asymptotically Gaussian. An extensive simulation study is performed to assess the finite-sample properties of the method, and this investigation indicates that the proposed method works well for many practical situations. We then apply our approach to examine the impact of age at cranial radiation therapy on risk of growth hormone deficiency in long-term survivors of childhood cancer.     

Weighted modified first order regression procedures for estimation in linear models with missingX-observations

This paper considers the estimation of coefficients in a linear regression model with missing observations in the independent variables and introduces a modification of the standard first order regression method for imputation of missing values. The modification provides stochastic values for imputation and, as an extension, makes use of the principle of weighted mixed regression. The proposed procedures are compared with two popular procedures—one which utilizes only the complete observations and the other which employs the standard first order regression imputation method for missing values. A simulation experiment to evaluate the gain in efficiency and to examine interesting issues like the impact of varying degree of multicollinearity in explanatory variables is proceeded. Some work on the case of discrete regressor variables is in progress and will be reported in a future article to follow.     

Amputation versus imputation of missing values through ratio method in sample surveys

In this article, we consider the estimation of a population mean when some observations on the study characteristic are missing in the bivariate sample data. In all, five estimators are presented and their efficiency properties are discussed. One estimator arises from the the amputation of incomplete observations while the remaining four estimators are formulated using imputed values obtained by the ratio method of estimation. This work was carried out before Professor V.K. Srivastava passed away in 2001.