Analysis

The International Tobacco Control (ITC) Policy Evaluation China Survey uses a multi-stage unequal probability sampling design with upper level clusters selected by the randomized systematic PPS sampling method. A difficulty arises in the execution of the survey: several selected upper level clusters refuse to participate in the survey and have to be replaced by substitute units, selected from units not included in the initial sample and once again using the randomized systematic PPS sampling method. Under such a scenario the first order inclusion probabilities of the final selected units are very difficult to calculate and the second order inclusion probabilities become virtually intractable. In this paper we develop a simulation-based approach for computing the first and the second order inclusion probabilities when direct calculation is prohibitive or impossible. The efficiency and feasibility of the proposed approach are demonstrated through both theoretical considerations and numerical examples. Several R/S-PLUS functions and codes for the proposed procedure are included. The approach can be extended to handle more complex refusal/substitution scenarios one may encounter in practice.

In this paper, we consider the effect of the interval censoring of cessation time on intensity parameter estimation with regard to smoking cessation and pregnancy. The three waves of the National Population Health Survey allow the methodology of event history analysis to be applied to smoking initiation, cessation and relapse. One issue of interest is the relationship between smoking cessation and pregnancy. If a longitudinal respondent who is a smoker at the first cycle ceases smoking by the second cycle, we know the cessation time to within an interval of length at most a year, since the respondent is asked for the age at which she stopped smoking, and her date of birth is known. We also know whether she is pregnant at the time of the second cycle, and whether she has given birth since the time of the first cycle. For many such subjects, we know the date of conception to within a relatively small interval. If we knew the time of smoking cessation and pregnancy period exactly for each member who experienced one or other of these events between cycles, we could model their temporal relationship through their joint intensities.

Godambe and Thompson consider the problem of confidence intervals in survey sampling. They first review the use of estimating functions to obtain model robust pivotal quantities and associated confidence intervals, and then discuss the adaptation of this approach to the survey sampling context. Details are worked out for some more specific types of models, and an empirical comparison of this approach with more conventional methods is presented.

Using the optimal estimating functions for survey sampling estimation (Godambe and Thompson 1986), we obtain some optimality results for nonresponse situations in survey sampling.

The International Tobacco Control (ITC) Policy Evaluation China Survey uses a multi-stage unequal probability sampling design with upper level clusters selected by the randomized systematic PPS sampling method. A difficulty arises in the execution of the survey: several selected upper level clusters refuse to participate in the survey and have to be replaced by substitute units, selected from units not included in the initial sample and once again using the randomized systematic PPS sampling method. Under such a scenario the first order inclusion probabilities of the final selected units are very difficult to calculate and the second order inclusion probabilities become virtually intractable. In this paper we develop a simulation-based approach for computing the first and the second order inclusion probabilities when direct calculation is prohibitive or impossible. The efficiency and feasibility of the proposed approach are demonstrated through both theoretical considerations and numerical examples. Several R/S-PLUS functions and codes for the proposed procedure are included. The approach can be extended to handle more complex refusal/substitution scenarios one may encounter in practice.

In this paper, we consider the effect of the interval censoring of cessation time on intensity parameter estimation with regard to smoking cessation and pregnancy. The three waves of the National Population Health Survey allow the methodology of event history analysis to be applied to smoking initiation, cessation and relapse. One issue of interest is the relationship between smoking cessation and pregnancy. If a longitudinal respondent who is a smoker at the first cycle ceases smoking by the second cycle, we know the cessation time to within an interval of length at most a year, since the respondent is asked for the age at which she stopped smoking, and her date of birth is known. We also know whether she is pregnant at the time of the second cycle, and whether she has given birth since the time of the first cycle. For many such subjects, we know the date of conception to within a relatively small interval. If we knew the time of smoking cessation and pregnancy period exactly for each member who experienced one or other of these events between cycles, we could model their temporal relationship through their joint intensities.

Godambe and Thompson consider the problem of confidence intervals in survey sampling. They first review the use of estimating functions to obtain model robust pivotal quantities and associated confidence intervals, and then discuss the adaptation of this approach to the survey sampling context. Details are worked out for some more specific types of models, and an empirical comparison of this approach with more conventional methods is presented.

Using the optimal estimating functions for survey sampling estimation (Godambe and Thompson 1986), we obtain some optimality results for nonresponse situations in survey sampling.