Estimation of Adjusted risk ratio of confounding factors determining heart disease among elderly: LASI data analysis

The cause-and-effect relation is measured through Odds ratio in epidemiological studies. When the risk of outcome is low odds ratio statistics to be adjusted. Further to estimate the influence of confounding factors to determine the influence of cause factor on effect, it is necessary to calculate cured and adjusted risk ratio. Cochran (1954), Mental and Haenszel (MH) (1959) suggested extension of chi square test to estimate stratum specific crude and adjusted risk ratio for categorical variables. The MH statistics results generate “residual confounder” when the continuous data set is grouped in to categories. To overcome this error, generalize linear regression model or multinominal regression models have been suggested. Present paper aims to estimate adjusted risk ratio of confounding factors determining Heart disease among elderly by using generalized linear regression model. To achieve the objective, data were collected from Longitudinal Ageing study of India (LASI). Age of elderly (>45), sex, Hypertension, ever diagnosed diabetes, ever diagnosed heart disease are the variables collected to estimate crude, adjusted risk ratio of the confounding factors on effect of heart disease. Age of elderly has been considered as continuous to overcome “residual of confounder. The results revealed that elder person who had hypertension is 4.69 times at higher risk than who did not had hypertension. When hypertension considered as confounding variable influencing heart disease through diabetes the adjusted risk ratio declined to 1.996. The adjusted risk ratio increased to 3.069 when Sex, hypertension as confounding factors on heart disease through diabetics. Further when age factor is added as confounder to sex, hypertension the adjusted risk ratio declined to 0.660. These variations were discussed in the results.

1. Estimation of Adjusted risk of confounding factors determining heart disease among Elderly: LASI Data Analysis by Prof. C. P. PRAKASAM Former Professor International Institute for Population Sciences, Mumbai [email protected]

2. RISK ESTIMATES Odds ratio is the basic measure to establish the risk of cause and effect in epidemiological studies. The odds ratio (OR) is the odds of an event in experimental group compared to that in control group. Odds ratio= ad / bc Limitations Odds ratios lack the property of collapsibility . That is over all odds ratio does not equal to the weighted average of stratum specific odds ratio. Hence to measure the risk of confounding variables on cause and effect, relative risk and risk difference is suggested.

3. Risk estimates Adjusted odds ratio Adjusted relative risk or Adjusted risk ratio (ARR). Adjusted risk difference (ARD) . The relative risk or the risk ratio (RR) is the ratio of the probability of an outcome in exposed group to the probability of an unexposed group. Hence RR measures the association between the exposed and outcome. The RR is comparable derived by each confounding variable on effect though cause is comparable.

4. Objectives 1.To identify the confounding risk factors influencing chronic heart disease among elderly 2.To estimate the risk of chronic heart disease caused by confounding factors among elderly

5. DATA source and Variables Source : Longitudinal ageing study of elderly (LASI) Wave I (IIPS, 2019) Variables Selected : CAUSE Ever diagnosed diabetes DI YES/NO EFFECT Ever diagnosed Chronic heart disease HEART YES/NO CONFOUNDING FACTORS Ever diagnosed hypertension Sex Age Group of Elderly Or Age of Elderly (continuous) HT SEX RAGE AGE YES/NO MALE/FEMALE 45-60 years 61-80 years 80+ years 45 and above single year

6. Confounding variable or a confounder is an external factor that affects independent variable and dependent variable. A Confounder introduces an error or bias that affects actual relationship between the variables (dependent and independent variables) under study. HEART SEX RAGE HT DI Confounders Cause Effect DATA structure

7. METHODOLOGY Mantel–Haenszel and inverse-variance stratified methods for categorical data : SEX—RAGE---HT—DI—HEART Age of elderly considered as group data. Formula for MH test: mhodds HEART DI, by (SEX RAGE HT) pool and cs HEART DI, by (SEX RAGE HT) Magnitude of confounding= (Crude OR – Adjusted OR) Crude OR STATA 16/1 VERSION

8. MH-test analysis To identify the influence of confounding variable through cause (DI) on effect (HEART) variables, one by one confounding variable added to DI x HEART and estimated adjusted odds ratio and its magnitude influencing HEART through DI is given in Table 1. The odds ratio is around 3.3

9. Risk estimates by MH-test: TABLE : 1 Cause and effect and confounding variables Crude Odds Ratio* Adjusted Odds Ratio MH test Magnitude of confounding (MC) DI x HEART 3.31215 --------   HT x DI x HEART 3.31203 1.998287 39.67% RAGE x HT x DI x HEART 3.31216 1.934177 88.54% SEX x RAGE x HT x DI x HEART 3.31215 1.888391 42.99% RAGE x DI x HEART 3.31215 3.068502 7.36% SEX x DI x HEART 3.31215 3.297116 0.45% SEX x RAGE x DT x HEART 3.31215 3.051595 7.87% mhodds HEART DI, by (SEX RAGE HT), *base odds ratio considered

10. The odds ratio is around 3.3 (Table 1) T he magnitude of confounding factors found to be high with RAGE and HT (88.54%) indicates that elderly who have reported “ever had hypertension (HT)” influences “ever diagnosed Chronic heart disease (HEART)” with diabetes (DI). When SEX (Gender) as a confounder is added to age and hypertension to find out the influence of Diabetics (DI) on Chronic heart disease (HEART) then the magnitude of confounding reduces to half of the earlier influence (42.99%). magnitude of confounding found to be less than 8% when RAGE and SEX are considered as confounders in estimating risk of Chronic heart disease (HEART) among elderly with diabetics (DI) with out HT

11. Risk Ratios, ARR, ARD On the basis of these magnitude of confounding values, one can notice that RAGE and HT are the prime risk factors in influencing heart disease among those elderly with Diabetics (DI). Therefore, risk ratio, adjusted risk ratio (ARR) and adjusted risk deference (ARD) has been calculated to understand the risk by different age groups and the results are given in Table 2. STATA code: cs HEART DI, by (RAGE HT) pool ,

12. Crude and Adjusted Risk Ratio Table 2: Estimation of Crude and Adjusted risk ratio by Mantel and Haenszel test by confounding factors Age (RAGE) and Hypertension (HT) influencing Chronic Heart disease (HEART) through Diabetics (DI) confounding Variable         Age (RAGE)* Hypertension (HT) Risk ratio 95% Conf. Interval M-H weight 45 – 60 years Yes 1.040313 1.02568 1.055154 1482.513   No 1.026527 1.017197 1.035942 1630.832 61-80 years Yes 1.048825 1.031798 1.066134 1644.864   No 1.046710 1.031742 1.061895 1153.174 81+ Yes 1.101006 1.04116 1.164291 173.1001   No 1.039858 .9927062 1.089249 110.1913             Crude   1.065851 1.058629 1.073123   Pooled (direct)   1.037072 1.030699 1.043484   M-H combined   1.041822 1.03473 1.048964   cs HEART DI, by (RAGE HT) pool, *Grouped data

13. MH-test analysis shows: Adjusted risk ratio (ARR ) is the ratio that measures the increase in risk from exposure to a factor (DI), while taking into account of other confounders The crude RR found to be 1.065851 and ARR 1.041822. The pooled risk ratio is 1.037072 which is obtained by using MH- inverse-variance method. E lderly aged 45-60 years with hypertension and diagnosed Diabetics (DI) are 1.040 (4.0%) times at higher risk of “chronic heart disease” than those who are not reported Diabetics with confounding factors RAGE and Hypertension (HT). 61-80: 1.048 (4.8%) and 80 and above 1.101 (10.1%) at risk Risk ratio shows no difference between elderly in the age group 61-80 years who had hypertension comparing with no hypertension as confounding factor influencing heart disease through Diabetics.

14. MH-test-Limitation MH-test: It identifies Strata adjusted odds ratio ARD, ARR and odds due to confounding factors. MH method is more suitable for categorical data set To estimate OR, ARR , ARD for continuous data set, Generalized linear model Applying GLM with family as gaussian and link log, the data could not converge to show the results. Cummins (2009) suggested binreg to overcome the convergence

15. Regression Models (GLM): Table 3: Estimated odds ratio by regression method introducing confounding factors. Cause and effect and confounding variables ** Odds Ratio of confounding variables   DI HT Age* SEX Constant# DI x HEART 3.31215 - - - 10.29893 HT x DI x HEART 2.038842 3.957502 - - 7.123766 AGE x HT x DI x HEART 2.003608 3.655305 0.973359 - 39.98432 SEX x AGE x HT x DI x HEART 1.957312 3.826935 0.9742423 1.501738 30.64197 * Age is a continuous variable. # _constant estimates baseline odds ** binreg HEART x confounding variable/s, or or glm HEART DI HT dm005 SEX, fam(bin) nolog eform Overall odds ratio is same as observed in the MH method . GLM regression method gives the odds ratio for each confounding factor entered in to regression. Elderly who reported hypertension and diabetes had chronic heart disease (HEART) 3.96 times at higher risk than who have ever had HT and DI.

16. Table 4: Estimated risk ratio by regression method introducing confounding variables Cause and effect and confounding variables ** Risk Ratio of confounding variables   DI HT Age* SEX Constant# DI x HEART 1.065851 --- --- --- .911496 HT x DI x HEART 1.041524 1.057961 --- --- .8931936 AGE x HT x DI x HEART 1.039213 1.054135 .9992674 --- .9373735 SEX x AGE x HT x DI x HEART 1.038761 1.054636 .9993589 1.007643 .928499 *Age is a continuous variable. # _constant estimates baseline risk ** binreg HEART x confounding variable/s, rr The calculated ARR shows (Table 4) that 6.5 percent (Risk ratio=1.065851) increase in the “ever had chronic heart disease” with Diabetes than who do not. Similarly, elderly who reported ever had hypertension (HT) and DI had an increase in 5.7 percent risk in reporting HEART. Risk ratio shows less than “one” for Age variable (Risk ratio .9993) reveals that a decrease in the likelihood of Outcome (HEART) with AGE included as confounding variable.

17. Regression model results: R isk difference of elderly who ever diagnosed diabetes with ever diagnosed chronic heart disease are 6 percent higher risk than those who are not with diabetes. H igher risk difference values indicate higher risk of the exposed group to the disease. Hypertension (HT) as a confounding variable along with DI, HEART shows higher value of risk difference (more than 5 percent) reveals that HT is an important risk factor among elderly with diabetes causing heart disease. AGE and SEX of elderly shows low risk difference indicates that the difference between exposed and unexposed group is more or less same and hence the influence of confounding factor AGE and SEX are minimal.

18. ADJUSTED RISK DIFFERENCE: TABLE 5 Table 5: Estimated Adjusted risk difference by regression method introducing confounding variables Cause and effect and confounding variables ** Adjusted Risk difference of confounding variables   DI HT Age* SEX Constant# DI x HEART .060023 -- -- -- .911496 HT x DI x HEART .040030 .054022 --- --- .890461 AGE x HT x DI x HEART .038977 .051052 -.000953 ---- .950448 SEX x AGE x HT x DI x HEART .038226 .052589 -.000925 .014003 .940813 *Age is a continuous variable. # _constant estimates baseline odds ** glm HEART DI HT dm005 SEX, family(gaussian) link(identity) robust Note: the coefficients derived are risk difference values Hypertension (HT) as a confounding variable along with DI, HEART shows higher value of risk difference (more than 5 percent) reveals that HT is an important risk factor among elderly with diabetes causing heart disease.

19. Findings: Elderly who had Diabetes likely 3.3 times at higher risk of chronic heart disease and the risk increases with HT as confounding factor. T he magnitude of confounding factors found to be high with RAGE and HT (88.54%) Age and Sex as independent confounders with out HT shows less effect on heart disease among elderly with DI. R isk ratio was high in the age group 45-60 and 81+ than 61-80 who reported “yes” to HT, DI and HEART. Risk of chronic heart disease with hypertension at lower ages may be due to early onset of HT .

20. Continued…. Research studies also reveal that Adults with diabetes are nearly twice as likely to have heart disease or stroke as adults without diabetes . P eople with HT, diabetes tend to develop heart disease at a younger age than people without diabetes Hence HT is a risk factor as confounder and AGE is a risk factor directly influencing heart disease than as a confounder, based on the age at onset of diabetes. Cause for Hypertension and Diabetes should be suitably explored to reduce Chronic heart disease among elderly.

21. METHODOLOGICAL ISSUES Limitation of odds ratio is that the stratum odds ratios ate not additive ( COLLAPSIBLE). Adjusted risk ratio and Risk Difference calculated. Mantel–Haenszel and inverse-variance stratified methods is a powerful tool for estimating the pool odds ratio, adjusted relative risk and risk difference. But suitable only for categorical dataset . To overcome residual error due to age group data set , Generalized linear model (GLM) has been used which is suitable for continuous as well as categorical data set. Convergence in GLM failed due to the estimated risk is close to 1 in stratum data set. Hence binreg command used to modify the convergence which will give the results in 0-1 range.

22. Selected references Barrett-Connor E, Wingard D, Wong N, Goldberg R.: Chapter 18: Heart disease and diabetes (PDF, 1.07 MB) . In: Cowie CC, Casagrande SS, Menke A, et al, eds.  Diabetes in America , 3rd ed. 2008, NIH Pub No. 17-1468. National Institutes of Health; :18.1–18.30 Cummings, P : “Methods for estimating adjusted risk ratios”, The STATA Journal , 2009, 9, Number 2, pp. 175–19 Greenland, S. : Interpretation and choice of effect measures in epidemiologic analyses. American Journal of Epidemiology , 1987,125: 761–768 Greenland, S., and P. W. Holland. : Estimating standardized risk differences from odds ratios. Biometrics , 1991,47: 319–322 DATA SOURCE : IIPS : National Programme for Health care of Elderly (LASI), I nternational Institute for Population Sciences (IIPS), NPHCE, MOHFW, Harvard T. H. Chan School of Public Health (HSPH) and the University of Southern California (USC): “Longitudinal ageing study in India (LASI) Wave I, 2017-18”, 2020, IIPS, Mumbai. 

23. THANK YOU C.P.PRAKASAM [email protected]