Age

Fig.1 Plot of Age distribution across Groups

The Dodged bar chart above represents individual counts representing frequency of age_grp categories 50-60,40-50,60-70,30-40,70-80 and 10-20 in categories AECOPD<=2 and AECOPD>=3 belonging to group Group. Subgroup 50-60 has highest percentage 17/42 ( 40.48 % ) in group AECOPD<=2 . Subgroup 50-60 has highest percentage 19/48 ( 39.58 % ) in group AECOPD>=3 . To formally check for association between groups we performed pearson chi-square test .

we found a Significant association between age_grp and Group. The chi-square statistic was 11.23 . The degree of freedom was 5 and P value was 0.05 .Contingency and Proportion table are shown below

Table 3

Table 4

Gender

Figure 2 Sex Distribution in Our Population

The Dodged bar chart above represents individual counts representing frequency of Sex categories Male and Female in categories AECOPD<=2 and AECOPD>=3 belonging to group Group. Subgroup Male has highest percentage 35/42 ( 83.33 % ) in group AECOPD<=2 . Subgroup Male has highest percentage 43/48 ( 89.58 % ) in group AECOPD>=3 . To formally check for association between groups we performed pearson chi-square test .

we found a Non-significant association between Sex and Group. The chi-square statistic was 0.31 . The degree of freedom was 1 and P value was 0.58 .Contingency and Proportion table are shown below

Table 5

Table 6

Smoker

Figure 3 Distribution Of smokers in Our Population

The Dodged bar chart above represents individual counts representing frequency of Smoker categories Ex-Smoker,Smoker and Non-smoker in categories AECOPD<=2 and AECOPD>=3 belonging to group Group. Subgroup Ex-Smoker has highest percentage 30/42 ( 71.43 % ) in group AECOPD<=2 . Subgroup Ex-Smoker has highest percentage 35/48 ( 72.92 % ) in group AECOPD>=3 . To formally check for association between groups we performed pearson chi-square test .

we found a Non-significant association between Smoker and Group. The chi-square statistic was 0.35 . The degree of freedom was 2 and P value was 0.84 .Contingency and Proportion table are shown below

Table 7

Table 8

ANTHONISEN TYPE

Figure 4 Distribution Of Anthonisen Classification in Our Population

The Dodged bar chart above represents individual counts representing frequency of Anthonisen_Type categories Type 1,Type 3 and Type 2 in categories AECOPD<=2 and AECOPD>=3 belonging to group Group. Subgroup Type 1 has highest percentage 34/42 ( 80.95 % ) in group AECOPD<=2 . Subgroup Type 1 has highest percentage 26/48 ( 54.17 % ) in group AECOPD>=3 . To formally check for association between groups we performed pearson chi-square test .

we found a Non-significant association between Smoker and Group. The chi-square statistic was 0.35 . The degree of freedom was 2 and P value was 0.84 .Contingency and Proportion table are shown below

Table 9

Table 10

COPD STAGE

Figure 5 Distribution Of COPD Stage according to GOLD Criteria in Our Population

The Dodged bar chart above represents individual counts representing frequency of COPD_Stage categories Moderate,Severe and Very Severe in categories AECOPD<=2 and AECOPD>=3 belonging to group Group. Subgroup Moderate has highest percentage 31/42 ( 73.81 % ) in group AECOPD<=2 . Subgroup Severe has highest percentage 33/48 ( 68.75 % ) in group AECOPD>=3 . To formally check for association between groups we performed pearson chi-square test .

twe found a Significant association between COPD_Stage and Group. The chi-square statistic was 20.05 . The degree of freedom was 2 and P value was <0.001 .Contingency and Proportion table are shown below

Table 11

Table 12

Magnesium

Figure 6 Boxplot Of Distribution Of LDL in our Population

In this Figure we see Box plot of Magnesium in 2 sub-groups of Group : AECOPD<=2 and AECOPD>=3 respectively .The individual jittered data points of Magnesium are overlaid over transparent Boxplot for better visualisation. We see distribution of data in individual sub-groups of Group based on these box-plots. The lower edge of box plot represents -first quartile (Q1), Horizontal bar represents the median, Upper edge represnts third quartile (Q3), Two black lines (whiskers) emanating from box-plots signify range of non-outlier data for the particular sub-group. Lower whisker represents minimum(Q1- 1.5 interquartile range) non-outlier limit of Magnesium and upper whisker represnts maximum(Q1+1.5interquartile range) of Magnesium .Any data beyond whiskers of box-plots represents outliers in the sub-groups The big brown point in the box-plots represents mean Magnesium of 2 groups and it has been annotated in the figure itself

Table 13 Summary Table Of Magnesium within Groups

We formally performed a Welch’s independent Sample T test between Two Groups. The mean in Group AECOPD<=2 [ 2.24 ± 0.41 ] was significantly higher than Group AECOPD>=3 [ 1.73 ± 0.44 ] . The mean difference was 0.51 and 95 % confidence interval of the difference was ( 0.33 - 0.69 ) . The p value was <0.001 . The t statistic was 5.76 and degree of freedom of the Welch unpaired two-sample t test was 87.69 .In Formal statistical notation this result is expressed as : t(87.69) = 5.76, p= <0.001.

Table 14 Results Of T test

Figure 7 Boxplot Of Age-Sex Distribution Of Magnesium in our Population

Table 15 Age-Sex Distribution Of Magnesium in our Population

Selected Correlations

Number Of Exacebations and Magnesium

Figure showing Correlation between Number Of Exacebations and Magnesium

The scatter plots above show relationship between Magnesium on X axis and Exacerbations on Y axis. Graphically, we see that as Magnesium increases, Exacerbations decreases . On a formal statistical linear regression analysis, we that line of best fit (blue line signifying line with least square difference) also has a negative slope implying a negative correlation. The gray shaded error around blue line signifies 95% confidence interval of linear regression line of best fit. The correlation between two variables is Significant . The Pearson’s correlation between Magnesium and Exacerbations is -0.55 with 95% Confidence Interval of -0.68 to -0.38. the t statistic is -6.13 The p value is <0.001 .The degree of freedom is 88. In formal statistical notation this expressed as t(88)= -6.13, P= <0.001. r(Pearson) = -0.55 95% C.I. [-0.68–0.38]. n= 90. The correlation is summmarised in table below

Table 16. Table Summarizing correlation between Magnesium and Number Of Exacerbations

Table 17 Table with summary statistics of Magnesium and Number Of Exacerbations

FEV1 and Magnesium

Figure showing Correlation between FEV1 and Magnesium

The scatter plots above show relationship between Magnesium on X axis and FEV1 on Y axis. Graphically, we see that as Magnesium increases, FEV1 also increases . On a formal statistical linear regression analysis, we that line of best fit (blue line signifying line with least square difference) also has a positive slope implying a positive correlation. The gray shaded error around blue line signifies 95% confidence interval of linear regression line of best fit. The correlation between two variables is Significant . The Pearson’s correlation between Magnesium and FEV1 is 0.24 with 95% Confidence Interval of 0.03 to 0.43. the t statistic is 2.31 The p value is 0.02 .The degree of freedom is 88. In formal statistical notation this expressed as t(88)= 2.31, P= 0.02. r(Pearson) = 0.24 95% C.I. [0.03-0.43]. n= 90. The correlation is summmarised in table below

Table 18. Table Summarizing correlation between Magnesium and FEV1

Table 19 Table with summary statistics of Magnesium and FEV1

Correlation Matrix Of selected Variables

Table 20 Correlation table of Selected variables Magnesium,Exacerbations,BMI,FEV1,FVC,Age,Protei with their confidence intervals

Linear regression model

Multiple linear regression was conducted to find best combination of Magnesium,FEV1,BMI,FVC & Age for predicting Exacerbations . Dummy indicator(0/1) were used for categorical variables. The Forest plot above shows standardized regression coefficients of Magnesium,FEV1,BMI,FVC & Age with their confidence intervals as horizontal error bars on X axis. An error bar which crosses vertical line of zero in this plot is non-significant.

The combination of these predictors significantly predicted Exacerbations .There were 90 observations in our model. The number of predictors in model was 5 ,while degree of freedom of residuals(no.of observation-number Of predictors in model) was 84. In statistical notation this is expressed as F(5,84) = 218.16, P = <0.001 .The standard deviation of residual error was 0.32 implying Exacerbations was predicted with average accuracy of +- 0.32 by our model. The adjusted R - Square for our model is 0.92 implying our model predicts 92.42 percentage variation in Exacerbations .

In Our Multivariable linear regression Model,On adjusting for all variables , Magnesium,FEV1,BMI,FVC & Age significantly predicted Exacerbations .

Out of all variables, FEV1 [ Beta = -0.7 +- 0.1 ] had highest standardized regression coefficient and contributed maximum to predicted Exacerbations .

Our Final regression equation was predicted Exacerbations = 15.66+-0.46Magnesium +-0.07FEV1 +-0.07BMI +-0.06FVC +-0.06*Age

Interpretation

1 unit change in Magnesium leads to 0.46 decrease in Exacerbations . 1 unit change in FEV1 leads to 0.07 decrease in Exacerbations . 1 unit change in BMI leads to 0.07 decrease in Exacerbations . 1 unit change in FVC leads to 0.06 decrease in Exacerbations . 1 unit change in Age leads to 0.06 decrease in Exacerbations

Table 21 Univariable and Multivariable Regression coefficients

ROC PLOT

In the ROC and Distribution Curve Magnesium concentration above above predictor above cut off 1.94 had maximum Youden’s index(sum of sensitivity and specificity) to discriminate AECOPD<=2 from AECOPD>=3. A value above 1.94 had sensitivity of 78.57 % and specificity of 70.83 % with area under curve of 0.80 to predict AECOPD<=2. The accuracy of prediction was 74.44 %