| Objective: This study aims to systematically assess the applicability of intrinsic estimator(IE)based on different design matrices to the analysis of age-period-cohort(APC)data with different effect structures.Based on boundary analysis,Bayesian method,and orthogonal polynomial coding matrices,this study intends to construct a more general and flexible model that provides a methodological support for APC analysis.Methods:(1)This study simulated thirty-two types of APC effect structure data,constructed nine design matrices based on different classification variable coding systems,and then obtained the corresponding IEs by using Moore-Penrose generalized inverse.The accuracy of effect estimation of different IEs on age,period,and cohort was compared under each APC effect structure,and sensitivity analysis was conducted by adjusting the relative effects of age,period,and cohort to evaluate the applicable scenarios of IE.(2)Goodness-of-fit test was used to determine the independent effects of age,period,and cohort.The inadequacy of graphical methods in the identification of APC effect structure was evaluated based on simulated data.This study optimized the identification process of APC effect structure with external information(Factor characteristics).(3)Within the Bayesian framework,an APC model(B-LAPC)was constructed by using orthogonal polynomial coding matrices,in which identifiable nonlinear effects and unidentifiable linear effects were separately modelled,and the parameters of the prior distribution were obtained by the boundary analysis.The applicability of the B-LAPC model to the analysis of different APC effects structural data was evaluated by the simulation study.(4)The accuracy of estimation was assessed by means of estimated value,mean square error(MSE),and standard error of MSE(SEMSE).The convergence of Markov chains was checked by trace plot and Gelman-Rubin trend plot.This study verified the correctness of the simulation research conclusions by using instance data as well as the Best Substantive Solution based on theoretical knowledge.The data were collected from homicide rate data in the United States from 1965 to 2010 and related researches.(5)The alcohol use disorder(AUD)incidence and mortality rates in China were collected from the data released by Global Burden of Disease(GBD)in 2019.Goodnessof-fit test was used to select either B-LAPC model or the omitted variable model to estimate the age,period,and cohort effects of the incidence and mortality risk of AUD in Chinese men and women aged 15-79 years from 1994 to 2019.This study also explored the underlying physiological,social,cultural,and other factors which affected AUD incidence and mortality.Results:(1)The simulation study showed that when the linear effects of age and cohort were in the same direction,or when age had a strong nonlinear effect and the directions of the linear effects of period and cohort were opposite,estimates obtained from different IEs showed considerable difference from the true parameters(0.1<MSE<1.0).When the linear effect of age and period were in opposite directions to the cohort,the estimation effect of IE based on orthogonal polynomial coding matrix(OE)was the best(MSE<0.015).When the linear effect of age was in opposite directions to the period and cohort,the IE based on Helmert coding matrix(HE)showed the best estimation effect,and MSE could be controlled within 0.015 well;When age showed strong nonlinear effect and the directions of period and cohort linear effect were the same,the estimation effect of IE based on differential coding matrix(DE)is the best(MSE<0.015).The results of sensitivity analysis also showed that the optimal choices of IE in the above scenarios were reliable.(2)The simulation study showed that the goodness-of-fit test could determine whether the effects of the three dimensions exist or not,but it cannot reflect the specific changing trends of the effects;The graphical methods can reflect the effect trends of age and period,but often cannot identify the cohort effect trends.In homicide rate data,the cohort characteristic factor(Nonmarital births)could explain the 87.30% of the specific variance of the cohort variable,and its linear coefficient was 0.57(P<0.001).The cohort characteristic factor could indicate that the cohort effect showed a strong linear upward trend,which identified the correct cohort trends.(3)The B-LAPC model based on boundary analysis could be more flexible and fully use the external information to impose more explicit and effective constraints on parameters.In scenarios when IE was not applicable,the simulation study showed that he B-LAPC model performed slightly worse(MSE=0.048)when the age effect increased monotonically,the period effect showed a downward trend and the cohort effect showed an upward trend.Apart from this scenario,B-LAPC model could accurately estimate the parameter(MSE<0.015);In the scenarios where OE,HE,or DE were the optimal choices,the simulation study showed that the B-LAPC model performed slightly worse(MSE=0.034)when the age effect increased monotonically,and the period and cohort effects showed a downward trend.Besides this,B-LAPC model had good accuracy in the estimation of parameters in other scenarios(MSE<0.015).(4)Under the APC effect structure of homicide rate data,OE showed the best estimation effect compared to other IEs(MSE=0.011),but it was still worse than the BLAPC model(MSE=0.006),which is consistent with the results from the simulation study.(5)The results of the goodness of fit test showed that age,period,and cohort all had an impact on the risk of AUD incidence and death in males,while period had no significant effect on the incidence and mortality risk of AUD in females.The B-LAPC model was used to analyze the mortality and incidence of AUD in males,and the age-cohort model was used to analyze AUD in females.The results showed that the age effect of AUD incidence risk increased briefly and then decreased gradually in both males and females.Compared with the lowest risk group,men aged 25～29 and women aged 30～34 had the highest risk of incidence(OR=34.124,95%CI: 25.110～46.373;OR=4.728,95%CI: 3.856～5.796).The period effect on the risk of AUD in men gradually and sligthtly increased.The cohort effect on the risk of AUD in men showed a gradual downward trend,with the lowest risk of AUD in the most recent cohort(2000～2004),which was about 38 times lower than that in the earliest born cohort(1915～1919).The cohort effect of AUD incidence risk in women showed a trend of decreasing at first and then rising with fluctuations.Compared with the lowest risk group,the odds ratio of AUD incidence in the most recent birth cohort was 1.694(95%CI: 1.227～2.339).(6)The age effect of male AUD mortality risk showed a trend of increasing at first and then slightly decreasing.Compared with the lowest risk group,the mortality risk of 50～54years old male was the highest(OR=40.488,95%CI: 29.339～55.873).The age effect of female AUD mortality risk showed a temporal trend of increasing at first and then decreasing,with the highest mortality risk among females aged 30～34,which was approximately 2.5 times of the lowest-risk group(OR=2.467,95% CI: 2.092～2.910).The period effect of male AUD mortality risk showed an overall fluctuating upward trend with little increase.The cohort effect of AUD death risk for both male and female showed a downward trend in general,but there was a small increase in the recent birth cohort(2000～2004).Compared with the lowest risk group,the most recent birth cohort in male and female AUD The odd ratio of mortality were 2.100(95% CI: 1.522～2.899)and 1.266(95% CI: 0.954～1.681),respectively.Conclusions:(1)The APC effect structure is critical for using IE correctly.Combined with external information,the effect structure of APC data can be more accurately identified,which can avoid the abuse of IE and improve the accuracy of effect estimation.(2)B-LAPC model based on boundary analysis can obtain relatively accurate parameter estimation under different effect structures.This approach can be applied to a variety of scenarios and thus provides a solid methodological support for APC analysis.(3)Young and middle-aged people are the high-risk groups for AUD in China.The gender difference in AUD incidence among young people keeps narrowing,and the risk of AUD incidence among recent-born women increased.Therefore,health education on drinking behavior of young and middle-aged people,especially female juveniles,should be strengthened to prevent the occurrence of AUD.Young and middle-aged women as well as middle-aged and elderly men are high-risk groups for AUD mortality,so it is necessary to strengthen AUD screening and improve treatment compliance in these groups to reduce the harm of AUD. |
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