The paper aims to discuss three interesting issues of statistical inferences for a common risk ratio (RR) in sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator encounters a number of problem...The paper aims to discuss three interesting issues of statistical inferences for a common risk ratio (RR) in sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator encounters a number of problems when the number of events in the experimental or control group is zero in sparse data of a 2 × 2 table. The adjusted log-risk ratio estimator with the continuity correction points based upon the minimum Bayes risk with respect to the uniform prior density over (0, 1) and the Euclidean loss function is proposed. Secondly, the interest is to find the optimal weights of the pooled estimate that minimize the mean square error (MSE) of subject to the constraint on where , , . Finally, the performance of this minimum MSE weighted estimator adjusted with various values of points is investigated to compare with other popular estimators, such as the Mantel-Haenszel (MH) estimator and the weighted least squares (WLS) estimator (also equivalently known as the inverse-variance weighted estimator) in senses of point estimation and hypothesis testing via simulation studies. The results of estimation illustrate that regardless of the true values of RR, the MH estimator achieves the best performance with the smallest MSE when the study size is rather large and the sample sizes within each study are small. The MSE of WLS estimator and the proposed-weight estimator adjusted by , or , or are close together and they are the best when the sample sizes are moderate to large (and) while the study size is rather small.展开更多
It is difficult to measure the sizes of illegal drug user populations directly by using the survey method because of many “hidden drug addicts” and the difficulty of receiving a true response. Systematic and routine...It is difficult to measure the sizes of illegal drug user populations directly by using the survey method because of many “hidden drug addicts” and the difficulty of receiving a true response. Systematic and routine information on treatment episodes of drug users is adopted to estimate the population size in this study. Mixture models of zero-truncated Poisson distributions using the nonparametric maximum likelihood estimators (NPMLE) by means of capture-recapture repeated count data were used to project the number of drug users. The method was applied to surveillance data of drug users identified by treatment episodes in over 1140 health treatment centers in Thailand from the Bureau of Health Service System Development, Ministry of Public Health. We presented how this mixture model could be utilized to construct the unobserved frequency of drug users with no treatment episode and further estimated the total population size of drug users in the country from 2005 to 2007. The result of simulation was confirmed that mixture model is suitable when population is large. By means of mixture models, the estimations for the number of drug users were fitted with excellent goodness-of-fit values and we were also compared to the conventional Chao estimates. The NPMLE for the total number of drug users in Thailand 2005, 2006, and 2007 were 184,045 (95% CI: 181,297-86,793), 230,665 (95% CI: 226,611-234,719), 299,670 (95% CI: 294,217-305,123), respectively, also 125,265 (95% CI: 123,092-127,142), 166,287 (95% CI: 163,222-169,352), 228,898 (95% CI: 224,766 - 233,030) for the number of methamphetamine (Yaba) users, and 11,559 (95% CI: 10,234-12,884), 11,333 (95% CI: 9276-13,390), 8953 (95% CI: 7878-10,028) for the number of heroin users, respectively. The numbers of marijuana, kratom-plant, opium, and inhalant users were underestimated because their symptoms were mild and not severe enough to remedy in health treatment centers which led to the smaller size of the total number of drug users. The well-estimated sizes of heroin and methamphetamine addicts are high reliable because they are based on clearly evident count with a severe addiction problem to health treatment centers. The estimation by means of mixture models can be recommended to monitor drug demand trend and drug health service routinely;it is easy to calculate via the available programs MIXTP based on request.展开更多
文摘The paper aims to discuss three interesting issues of statistical inferences for a common risk ratio (RR) in sparse meta-analysis data. Firstly, the conventional log-risk ratio estimator encounters a number of problems when the number of events in the experimental or control group is zero in sparse data of a 2 × 2 table. The adjusted log-risk ratio estimator with the continuity correction points based upon the minimum Bayes risk with respect to the uniform prior density over (0, 1) and the Euclidean loss function is proposed. Secondly, the interest is to find the optimal weights of the pooled estimate that minimize the mean square error (MSE) of subject to the constraint on where , , . Finally, the performance of this minimum MSE weighted estimator adjusted with various values of points is investigated to compare with other popular estimators, such as the Mantel-Haenszel (MH) estimator and the weighted least squares (WLS) estimator (also equivalently known as the inverse-variance weighted estimator) in senses of point estimation and hypothesis testing via simulation studies. The results of estimation illustrate that regardless of the true values of RR, the MH estimator achieves the best performance with the smallest MSE when the study size is rather large and the sample sizes within each study are small. The MSE of WLS estimator and the proposed-weight estimator adjusted by , or , or are close together and they are the best when the sample sizes are moderate to large (and) while the study size is rather small.
文摘It is difficult to measure the sizes of illegal drug user populations directly by using the survey method because of many “hidden drug addicts” and the difficulty of receiving a true response. Systematic and routine information on treatment episodes of drug users is adopted to estimate the population size in this study. Mixture models of zero-truncated Poisson distributions using the nonparametric maximum likelihood estimators (NPMLE) by means of capture-recapture repeated count data were used to project the number of drug users. The method was applied to surveillance data of drug users identified by treatment episodes in over 1140 health treatment centers in Thailand from the Bureau of Health Service System Development, Ministry of Public Health. We presented how this mixture model could be utilized to construct the unobserved frequency of drug users with no treatment episode and further estimated the total population size of drug users in the country from 2005 to 2007. The result of simulation was confirmed that mixture model is suitable when population is large. By means of mixture models, the estimations for the number of drug users were fitted with excellent goodness-of-fit values and we were also compared to the conventional Chao estimates. The NPMLE for the total number of drug users in Thailand 2005, 2006, and 2007 were 184,045 (95% CI: 181,297-86,793), 230,665 (95% CI: 226,611-234,719), 299,670 (95% CI: 294,217-305,123), respectively, also 125,265 (95% CI: 123,092-127,142), 166,287 (95% CI: 163,222-169,352), 228,898 (95% CI: 224,766 - 233,030) for the number of methamphetamine (Yaba) users, and 11,559 (95% CI: 10,234-12,884), 11,333 (95% CI: 9276-13,390), 8953 (95% CI: 7878-10,028) for the number of heroin users, respectively. The numbers of marijuana, kratom-plant, opium, and inhalant users were underestimated because their symptoms were mild and not severe enough to remedy in health treatment centers which led to the smaller size of the total number of drug users. The well-estimated sizes of heroin and methamphetamine addicts are high reliable because they are based on clearly evident count with a severe addiction problem to health treatment centers. The estimation by means of mixture models can be recommended to monitor drug demand trend and drug health service routinely;it is easy to calculate via the available programs MIXTP based on request.
