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• Beyond the edge of statistical analysis
  Wenbin Liang
  Published on: 27 April 2016
• Findings from the back of the regression model: re-analysing data from the article
  Wenbin Liang
  Published on: 27 April 2016

• Published on: 27 April 2016

  Beyond the edge of statistical analysis

  • Wenbin Liang, taking master of public health

  Dear Editor,

  The mortalities of the 56 sub-cohorts in the study are not randomly chosen from a defined population.[1] However the validity of many statistical analysis methods including regression analysis are based on the condition that samples are random drawn.[2] Therefore the regression model fitted this set of data, in my point of view would be better taken as a description of this set of data rather than pr...

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  Dear Editor,

  The mortalities of the 56 sub-cohorts in the study are not randomly chosen from a defined population.[1] However the validity of many statistical analysis methods including regression analysis are based on the condition that samples are random drawn.[2] Therefore the regression model fitted this set of data, in my point of view would be better taken as a description of this set of data rather than predicting the relationship between middle age mortality and old age mortality of other populations chosen from other countries or chosen from the future.

  The changes of mortality are greatly affected by the development of technology, improvement of medical services, changes in people’s life style, and many other unknown determinants, which may rise in the future, while it’s impossible to use statistical methods to control such factors, which are unknown, moreover it would not be possible to draw samples from the future.

  Obviously it is necessary to have a well classification and clear understanding of the determinants on an observed relationship from this kind of vital statistics data, before any prediction can be made.

  Reference

  1. Janssen, F., Peeters, A, Mackenbach P J, Kunst A E for NEDCOM, Relation between trends in late middle age mortality and trends in old age mortality—is there evidence for mortality selection? J Epidemiol Community Health, 2005. 59.

  2. Afifi, A.A., Computer-aided multivariate analysis. 4th ed. 2004: Chapman & Hall/CRC.

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  Conflict of Interest:
  None declared.

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• Published on: 27 April 2016

  Findings from the back of the regression model: re-analysing data from the article

  • Wenbin Liang, taking master of public health

  Dear Editor,

  Mortality data are obtained from table 1a and 1b in the article[1], and SPSS version 11 is used for analysis. There are total 56 “subjects”: 4 (different centralize birth cohort)*7 (different cou...

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  Dear Editor,

  Mortality data are obtained from table 1a and 1b in the article[1], and SPSS version 11 is used for analysis. There are total 56 “subjects”: 4 (different centralize birth cohort)*7 (different countries)*2(sex type). Each “subject” with five variables, 3 categorical variables: year according to which they were centralized, country, and sex.; 2 continuous variables: mortality rate(*10000) at age 55-69, and mortality rate(*10000) at age 80-89.

  Findings:

  1) The assumptions of the regression model or the analysis of correlation between mortalities in late middle age and mortalities in old age for all sub-cohorts (N=56) do not hold. Thus the validity of the regression model needs to be evaluated, and the correlation coefficients may be meaningless.

  2) The associations between mortality in two different age groups for all male sub-cohorts (N=28) seems to be great different between sub- cohorts with early mortality rate (*10000) <240 and sub-cohorts with early mortality rate (*10000) >240.

  3) The strong association between mortalities in two different age for both sex of all sub-cohorts (N=56) or sub-cohorts from different countries are likely to be confounded by sex.

  Explanation:

  1) The assumptions of the regression model—Normal distribution of dependent variable, Normal distribution of residuals, equal variance of residuals, and independence of residuals[2] are tested. Normality test: Shapiro-Wilk are conducted for both dependent and independent variables: mortality rate(*10000) in 55-69 age, and mortality rate(*10000) in 80-89 age, results for both of them are significant at 0.01 level, therefore it would be more than 95% confident to say the two variables are not Normal distributed.

  Then two regressions analysis are preformed a) Mortality in 80-89 age set as independent variable while Mortality in 55-69 age set as dependent variable, b) Mortality in 80-89 age set as dependent variable while Mortality in 55-56 age set as independent variable. Standardized residuals are saved for analysis. Normality test :Shapiro-Wilk again are conducted for the two residuals showing that residuals of the first model is significant at 0.01:assumption of Normality does not hold. Though the test for the residuals of the second model is not statistical significant. In the third step, two scatterplots are constructed by plotting residuals against dependent variable for the above two models, and both of the scatterplots shows patterns indicating that residuals are likely lack of randomness. Based on these, it may not be suitable that using regression models or correlation to describe the relationship between mortalities in two different age for all sub-cohorts (N=56) directly.

  2) Two scatterplots are constructed by plotting mortality in 55-69 age groups against mortality in 80-89 age groups for men (N=28) and for Women (N=28). Among men sub-cohorts the patterns of plots are great different between sub-cohorts with early mortality rate(*10000) lower than 240 and sub-cohorts with early mortality rate(*10000)higher than 240. Two regression models are conducted by choosing men cohorts with mortality in 55-69 age higher than 240 (*10000) or lower than that. Only among men cohorts with middle age mortality higher than 240, the regression model is significant with R=0.716. While assumptions for the model are found to be able to assumed.

  3) Two-block regression model(old age mortality as dependent variable, block one including sex as independent variable, block two includes both sex and middle age mortality) is constructed to determine the impact of sex on the “relation” between middle age mortality and old age mortality among all sub-cohorts N=56, cohorts from different countries N=8, (7 groups). The results show that among all countries, R increase less than 12% when middle age mortality is added into the model given that sex is already in the model. Though the assumption of the models are not hold, it is still likely that sex is a great confounder.

  References

  1. Janssen, F., Peeters, A, Mackenbach P J, Kunst A E for NEDCOM, Relation between trends in late middle age mortality and trends in old age mortality—is there evidence for mortality selection? J Epidemiol Community Health, 2005. 59.

  2. Afifi, A.A., Computer-aided multivariate analysis. 4th ed. 2004: Chapman & Hall/CRC.

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  Conflict of Interest:
  None declared.

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