Jason Hilton, Erengul Dodd, J. Forster, Peter W. F. Smith
Abstract Mortality rates differ across countries and years, and the country with the lowest observed mortality has changed over time. However, the classic Science paper by Oeppen and Vaupel (2002) identified a persistent linear trend over time in maximum national life expectancy. In this article, we look to exploit similar regularities in age-specific mortality by considering for any given year a hypothetical mortality ‘frontier’, which we define as the lower limit of the force of mortality at each age across all countries. Change in this frontier reflects incremental advances across the wide range of social, institutional and scientific dimensions that influence mortality. We jointly estimate frontier mortality as well as mortality rates for individual countries. Generalised additive models are used to estimate a smooth set of baseline frontier mortality rates and mortality improvements, and country-level mortality is modelled as a set of smooth, positive deviations from this, forcing the mortality estimates for individual countries to lie above the frontier. This model is fitted to data for a selection of countries from the Human Mortality Database (2019). The efficacy of the model in forecasting over a ten-year horizon is compared to a similar model fitted to each country separately.
{"title":"Modelling Frontier Mortality Using Bayesian Generalised Additive Models","authors":"Jason Hilton, Erengul Dodd, J. Forster, Peter W. F. Smith","doi":"10.2478/jos-2021-0026","DOIUrl":"https://doi.org/10.2478/jos-2021-0026","url":null,"abstract":"Abstract Mortality rates differ across countries and years, and the country with the lowest observed mortality has changed over time. However, the classic Science paper by Oeppen and Vaupel (2002) identified a persistent linear trend over time in maximum national life expectancy. In this article, we look to exploit similar regularities in age-specific mortality by considering for any given year a hypothetical mortality ‘frontier’, which we define as the lower limit of the force of mortality at each age across all countries. Change in this frontier reflects incremental advances across the wide range of social, institutional and scientific dimensions that influence mortality. We jointly estimate frontier mortality as well as mortality rates for individual countries. Generalised additive models are used to estimate a smooth set of baseline frontier mortality rates and mortality improvements, and country-level mortality is modelled as a set of smooth, positive deviations from this, forcing the mortality estimates for individual countries to lie above the frontier. This model is fitted to data for a selection of countries from the Human Mortality Database (2019). The efficacy of the model in forecasting over a ten-year horizon is compared to a similar model fitted to each country separately.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"569 - 589"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48259460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Righi, P. D. Falorsi, Stefano Daddi, Epifania Fiorello, P. Massoli, M. Terribili
Abstract For the first time in 2018 the Italian Institute of Statistics (Istat) implemented the annual Permanent Population Census which relies on the Population Base Register (PBR) and the Population Coverage Survey (PCS). This article provides a general overview of the PCS sampling design, which makes use of the PBR to correct population counts with the extended dual system estimator (Nirel and Glickman 2009). The sample allocation, proven optimal under a set of precision constraints, is based on preliminary estimates of individual probabilities of over-coverage and under-coverage. It defines the expected sample size in terms of individuals, and it oversamples the sub-populations subject to the risk of under/over coverage. Finally, the article introduces a sample selection method, which to the greatest extent possible satisfies the planned allocation of persons in terms of socio-demographic characteristics. Under acceptable assumptions, the article also shows that the sampling strategy enhances the precision of the estimates.
{"title":"Optimal Sampling for the Population Coverage Survey of the New Italian Register Based Census","authors":"P. Righi, P. D. Falorsi, Stefano Daddi, Epifania Fiorello, P. Massoli, M. Terribili","doi":"10.2478/jos-2021-0029","DOIUrl":"https://doi.org/10.2478/jos-2021-0029","url":null,"abstract":"Abstract For the first time in 2018 the Italian Institute of Statistics (Istat) implemented the annual Permanent Population Census which relies on the Population Base Register (PBR) and the Population Coverage Survey (PCS). This article provides a general overview of the PCS sampling design, which makes use of the PBR to correct population counts with the extended dual system estimator (Nirel and Glickman 2009). The sample allocation, proven optimal under a set of precision constraints, is based on preliminary estimates of individual probabilities of over-coverage and under-coverage. It defines the expected sample size in terms of individuals, and it oversamples the sub-populations subject to the risk of under/over coverage. Finally, the article introduces a sample selection method, which to the greatest extent possible satisfies the planned allocation of persons in terms of socio-demographic characteristics. Under acceptable assumptions, the article also shows that the sampling strategy enhances the precision of the estimates.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"655 - 671"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42111492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jairo Fúquene-Patiño, C. Cristancho, Mariana Ospina, Domingo Morales González
Abstract This article proposes a new methodology for estimating the proportions of households that had experience of international migration at the municipal level in Colombia. The Colombian National Statistical Office usually produces estimations of internal migration based on the results of population censuses, but there is a lack of disaggregated information about the main small areas of origin of the population that emigrates from Colombia. The proposed methodology uses frequentist and Bayesian approaches based on a Fay-Herriot model and is illustrated by one example with a dependent variable from the Demographic and Health Survey 2015 and covariables available from the population census 2005. The proposed alternative produces proportion estimates that are consistent with sample sizes and the main internal immigration trends in Colombia. Additionally, the estimated coefficients of variation are lower than 20% for municipalities for both frequentist and Bayesian approaches and large demographically-relevant capital cities and therefore estimates may be considered to be reliable. Finally, we illustrate how the proposed alternative leads to important reductions of the estimated coefficients of variations for the areas with very small sample sizes.
{"title":"Fay-Herriot Model-Based Prediction Alternatives for Estimating Households with Emigrated Members","authors":"Jairo Fúquene-Patiño, C. Cristancho, Mariana Ospina, Domingo Morales González","doi":"10.2478/jos-2021-0034","DOIUrl":"https://doi.org/10.2478/jos-2021-0034","url":null,"abstract":"Abstract This article proposes a new methodology for estimating the proportions of households that had experience of international migration at the municipal level in Colombia. The Colombian National Statistical Office usually produces estimations of internal migration based on the results of population censuses, but there is a lack of disaggregated information about the main small areas of origin of the population that emigrates from Colombia. The proposed methodology uses frequentist and Bayesian approaches based on a Fay-Herriot model and is illustrated by one example with a dependent variable from the Demographic and Health Survey 2015 and covariables available from the population census 2005. The proposed alternative produces proportion estimates that are consistent with sample sizes and the main internal immigration trends in Colombia. Additionally, the estimated coefficients of variation are lower than 20% for municipalities for both frequentist and Bayesian approaches and large demographically-relevant capital cities and therefore estimates may be considered to be reliable. Finally, we illustrate how the proposed alternative leads to important reductions of the estimated coefficients of variations for the areas with very small sample sizes.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"771 - 789"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43225302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In 2017, Pakistan implemented a long-awaited population census since the last one conducted in 1998. However, several experts are contesting the validity of the census data at the sub-national level, particularly in the absence of a post-enumeration survey. We propose in this article to use demographic analysis to assess the results of the 2017 census at the sub-national level, using data from the 1998 census, from all available intercensal surveys, including three rounds of Demographic and Health Survey. Applying the cohort-component method of population projection, we subject each five first-level subnational entities to estimates regarding the level of fertility, mortality, international, and internal migration derived from the analysis of the existing data. We arrive at approximately similar results as the census at the national level: an estimated 210 million (95% CI: 203.4–218.9) compared to 207.8 million counted (1.1% difference). However, we found substantial sub-national variations. While there are too many uncertainties in the data used for the reconstruction to be fully confident about them, this analysis should prompt the national and the international community to ensure that a post-enumeration survey and demographic analysis are regular features of census operations of Pakistan in particular, and in developing countries with deficient data as a whole.
{"title":"Exploratory Assessment of the Census of Pakistan Using Demographic Analysis","authors":"A. Wazir, A. Goujon","doi":"10.2478/jos-2021-0032","DOIUrl":"https://doi.org/10.2478/jos-2021-0032","url":null,"abstract":"Abstract In 2017, Pakistan implemented a long-awaited population census since the last one conducted in 1998. However, several experts are contesting the validity of the census data at the sub-national level, particularly in the absence of a post-enumeration survey. We propose in this article to use demographic analysis to assess the results of the 2017 census at the sub-national level, using data from the 1998 census, from all available intercensal surveys, including three rounds of Demographic and Health Survey. Applying the cohort-component method of population projection, we subject each five first-level subnational entities to estimates regarding the level of fertility, mortality, international, and internal migration derived from the analysis of the existing data. We arrive at approximately similar results as the census at the national level: an estimated 210 million (95% CI: 203.4–218.9) compared to 207.8 million counted (1.1% difference). However, we found substantial sub-national variations. While there are too many uncertainties in the data used for the reconstruction to be fully confident about them, this analysis should prompt the national and the international community to ensure that a post-enumeration survey and demographic analysis are regular features of census operations of Pakistan in particular, and in developing countries with deficient data as a whole.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"719 - 750"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41779700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Projection studies have often focused on mortality and, more recently, migration. Fertility is less studied, although even small changes can have significant repercussions for the size and age structure of future populations. Across Europe, there is no consensus on how fertility is best projected. In this article, we identify different approaches used to project fertility among statistical agencies in Europe and provide an assessment of the different approaches according to the producers themselves. Data were collected using a mixed-method approach. First, European statistical agencies answered a questionnaire regarding fertility projection practices. Second, an in-depth review of select countries was performed. Most agencies combine formal models with expert opinion. While many attempt to maximise the use of relevant inputs, there is more variation in the detail of outputs, with some agencies unable to account for changing age patterns. In a context of limited resources, most are satisfied with their approaches, though some are assessing alternative methodologies to improve accuracy and increase transparency. This study highlights the diversity of approaches used in fertility projections across Europe. Such knowledge may be useful to statistical agencies as they consider, test and implement different approaches, perhaps in collaboration with other agencies and the wider scientific community.
{"title":"Fertility Projections in a European Context: A Survey of Current Practices among Statistical Agencies","authors":"R. Gleditsch, A. Syse, Michael J Thomas","doi":"10.2478/jos-2021-0025","DOIUrl":"https://doi.org/10.2478/jos-2021-0025","url":null,"abstract":"Abstract Projection studies have often focused on mortality and, more recently, migration. Fertility is less studied, although even small changes can have significant repercussions for the size and age structure of future populations. Across Europe, there is no consensus on how fertility is best projected. In this article, we identify different approaches used to project fertility among statistical agencies in Europe and provide an assessment of the different approaches according to the producers themselves. Data were collected using a mixed-method approach. First, European statistical agencies answered a questionnaire regarding fertility projection practices. Second, an in-depth review of select countries was performed. Most agencies combine formal models with expert opinion. While many attempt to maximise the use of relevant inputs, there is more variation in the detail of outputs, with some agencies unable to account for changing age patterns. In a context of limited resources, most are satisfied with their approaches, though some are assessing alternative methodologies to improve accuracy and increase transparency. This study highlights the diversity of approaches used in fertility projections across Europe. Such knowledge may be useful to statistical agencies as they consider, test and implement different approaches, perhaps in collaboration with other agencies and the wider scientific community.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"547 - 568"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45309639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bernard Baffour, James J. Brown, Peter W. F. Smith
Abstract Estimation of the unknown population size using capture-recapture techniques relies on the key assumption that the capture probabilities are homogeneous across individuals in the population. This is usually accomplished via post-stratification by some key covariates believed to influence individual catchability. Another issue that arises in population estimation from data collected from multiple sources is list dependence, where an individual’s catchability on one list is related to that of another list. The earlier models for population estimation heavily relied upon list independence. However, there are methods available that can adjust the population estimates to account for dependence among lists. In this article, we propose the use of latent class analysis through log-linear modelling to estimate the population size in the presence of both heterogeneity and list dependence. The proposed approach is illustrated using data from the 1988 US census dress rehearsal.
{"title":"Latent Class Analysis for Estimating an Unknown Population Size – with Application to Censuses","authors":"Bernard Baffour, James J. Brown, Peter W. F. Smith","doi":"10.2478/jos-2021-0030","DOIUrl":"https://doi.org/10.2478/jos-2021-0030","url":null,"abstract":"Abstract Estimation of the unknown population size using capture-recapture techniques relies on the key assumption that the capture probabilities are homogeneous across individuals in the population. This is usually accomplished via post-stratification by some key covariates believed to influence individual catchability. Another issue that arises in population estimation from data collected from multiple sources is list dependence, where an individual’s catchability on one list is related to that of another list. The earlier models for population estimation heavily relied upon list independence. However, there are methods available that can adjust the population estimates to account for dependence among lists. In this article, we propose the use of latent class analysis through log-linear modelling to estimate the population size in the presence of both heterogeneity and list dependence. The proposed approach is illustrated using data from the 1988 US census dress rehearsal.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"673 - 697"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42900380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Bijak, John B. Bryant, Elżbieta Gołata, Steve Smallwood
{"title":"Preface","authors":"J. Bijak, John B. Bryant, Elżbieta Gołata, Steve Smallwood","doi":"10.2478/jos-2021-0023","DOIUrl":"https://doi.org/10.2478/jos-2021-0023","url":null,"abstract":"","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"533 - 541"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48358309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Letter to the Editors","authors":"G. Lanzieri","doi":"10.2478/jos-2021-0024","DOIUrl":"https://doi.org/10.2478/jos-2021-0024","url":null,"abstract":"","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"543 - 545"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42374399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-01Epub Date: 2021-09-12DOI: 10.2478/jos-2021-0033
Philip S Boonstra, Roderick J A Little, Brady T West, Rebecca R Andridge, Fernanda Alvarado-Leiton
A non-probability sampling mechanism arising from non-response or non-selection is likely to bias estimates of parameters with respect to a target population of interest. This bias poses a unique challenge when selection is 'non-ignorable', i.e. dependent upon the unobserved outcome of interest, since it is then undetectable and thus cannot be ameliorated. We extend a simulation study by Nishimura et al. [International Statistical Review, 84, 43-62 (2016)], adding two recently published statistics: the so-called 'standardized measure of unadjusted bias (SMUB)' and 'standardized measure of adjusted bias (SMAB)', which explicitly quantify the extent of bias (in the case of SMUB) or non-ignorable bias (in the case of SMAB) under the assumption that a specified amount of non-ignorable selection exists. Our findings suggest that this new sensitivity diagnostic is more correlated with, and more predictive of, the true, unknown extent of selection bias than other diagnostics, even when the underlying assumed level of non-ignorability is incorrect.
{"title":"A simulation study of diagnostics for selection bias.","authors":"Philip S Boonstra, Roderick J A Little, Brady T West, Rebecca R Andridge, Fernanda Alvarado-Leiton","doi":"10.2478/jos-2021-0033","DOIUrl":"https://doi.org/10.2478/jos-2021-0033","url":null,"abstract":"<p><p>A non-probability sampling mechanism arising from non-response or non-selection is likely to bias estimates of parameters with respect to a target population of interest. This bias poses a unique challenge when selection is 'non-ignorable', i.e. dependent upon the unobserved outcome of interest, since it is then undetectable and thus cannot be ameliorated. We extend a simulation study by Nishimura et al. [<i>International Statistical Review</i>, 84, 43-62 (2016)], adding two recently published statistics: the so-called 'standardized measure of unadjusted bias (SMUB)' and 'standardized measure of adjusted bias (SMAB)', which explicitly quantify the extent of bias (in the case of SMUB) or non-ignorable bias (in the case of SMAB) under the assumption that a specified amount of non-ignorable selection exists. Our findings suggest that this new sensitivity diagnostic is more correlated with, and more predictive of, the true, unknown extent of selection bias than other diagnostics, even when the underlying assumed level of non-ignorability is incorrect.</p>","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 3","pages":"751-769"},"PeriodicalIF":1.1,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8460089/pdf/nihms-1654085.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39450929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The occurrence of relaunches of consumer goods at the barcode (GTIN) level is a well-known phenomenon in transaction data of consumer purchases. GTINs of disappearing and reintroduced items have to be linked in order to capture possible price changes. This article presents a method that groups GTINs into strata (‘products’) by balancing two measures: an explained variance (R squared) measure for the ‘homogeneity’ of GTINs within products, while the second expresses the degree to which products can be ‘matched’ over time with respect to a comparison period. The resulting product ‘match adjusted R squared’ (MARS) combines explained variance in product prices with product match over time, so that different stratification schemes can be ranked according to the combined measure. MARS has been applied to a broad range of product types. Individual GTINs are suitable as products for food and beverages, but not for product types with higher rates of churn, such as clothing, pharmacy products and electronics. In these cases, products are defined as combinations of characteristics, so that GTINs with the same characteristics are grouped into the same product. Future research focuses on further developments of MARS, such as attribute selection when data sets contain large numbers of variables.
{"title":"A Product Match Adjusted R Squared Method for Defining Products with Transaction Data","authors":"A. Chessa","doi":"10.2478/jos-2021-0018","DOIUrl":"https://doi.org/10.2478/jos-2021-0018","url":null,"abstract":"Abstract The occurrence of relaunches of consumer goods at the barcode (GTIN) level is a well-known phenomenon in transaction data of consumer purchases. GTINs of disappearing and reintroduced items have to be linked in order to capture possible price changes. This article presents a method that groups GTINs into strata (‘products’) by balancing two measures: an explained variance (R squared) measure for the ‘homogeneity’ of GTINs within products, while the second expresses the degree to which products can be ‘matched’ over time with respect to a comparison period. The resulting product ‘match adjusted R squared’ (MARS) combines explained variance in product prices with product match over time, so that different stratification schemes can be ranked according to the combined measure. MARS has been applied to a broad range of product types. Individual GTINs are suitable as products for food and beverages, but not for product types with higher rates of churn, such as clothing, pharmacy products and electronics. In these cases, products are defined as combinations of characteristics, so that GTINs with the same characteristics are grouped into the same product. Future research focuses on further developments of MARS, such as attribute selection when data sets contain large numbers of variables.","PeriodicalId":51092,"journal":{"name":"Journal of Official Statistics","volume":"37 1","pages":"411 - 432"},"PeriodicalIF":1.1,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44044946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：