Biostatistics and Informatics: ANCOVA Analysis, Odds Ratio, and Association

This article provides an in-depth analysis of ANCOVA analysis, odds ratio, and association in biostatistics and informatics. It covers topics such as ANCOVA analysis for differences in MAXFWT by GROUP while controlling age and sex, association between OC-use and MI, and odds ratio using the data in the table for drinking status and lung cancer.

Biostatistics and informatics
Biostatistics and informatics
Student’s Name
Institution Affiliation

Biostatistics and informatics
Question One
ANCOVA analysis for differences in MAXFWT by GROUP while controlling age and sex
The following tables show the results of the analysis.
Table 1
Descriptive Statistics
Dependent Variable: MAXFWT
GROUP Mean Std.
Deviation
N
1 54.44 12.057 64
2 44.00 12.654 19
3 51.50 12.946 16
Total 51.96 12.839 99
The table’s information reveals that the groups’ mean MAXFWT are differing while variance
lies within the same range
Table 2
Levene's Test of Equality of Error Variances
Dependent Variable: MAXFWT
F df1 df2 Sig.
.482 2 96 .619
Tests the null hypothesis that the error variance of
the dependent variable is equal across groups.
a. Design: Intercept + GROUP + sex + age
From the table above the P-value (0.619) is greater than 0.05 significant levels. This reveals that
there is no significant difference between the variances of MAXFWT of different groups

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Table 3
Tests of Between-Subjects Effects
Dependent Variable: MAXFWT
Source Type III Sum
of Squares
df Mean Square F Sig.
Corrected Model 7682.804a 4 1920.701 21.313 .000
Intercept 3885.492 1 3885.492 43.116 .000
GROUP 836.852 2 418.426 4.643 .012
sex 79.543 1 79.543 .883 .350
age 6047.920 1 6047.920 67.112 .000
Error 8471.035 94 90.117
Total 283434.000 99
Corrected Total 16153.838 98
a. R Squared = .476 (Adjusted R Squared = .453)
While age and sex control the MAXFWT between groups differ from each other, this has been
revealed by P-value (0.012) groups which is less than 0.05 significant levels.
Estimated Marginal Mean by Groups
Table 4
Dependent Variable: MAXFWT
GROUP Mean Std. Error 95% Confidence Interval
Lower Bound Upper Bound
1 53.701a 1.190 51.337 56.064
2 46.053a 2.198 41.689 50.416
3 52.010a 2.375 47.294 56.726
a. Covariates appearing in the model are evaluated at the
following values: age = 10.073232, sex = 1.40.
The information in the table above reveals that the model estimated statistics of MAXFWT are
different from its observed values statistics. This is evident when table 1 is compared with table
4.

Biostatistics and informatics
Question Two
Table 5: Data of two independent samples of women with different contraceptive-use patterns
MI Status
OC-use group MI yes MI no Total
OC users 13 4987 5000
Non-OC-
users
7 9993 10000
Total 20 14980 15000
a. Association between OC-use and MI
This was determined using the odd ratio.
Below is table to show the result of the computation of odds ratio to explain the level of
association between the OC-use and MI.
Risk Estimate
Value 95% Confidence
Interval
Lower Upper
Odds Ratio for OC-use
Group (Non-OC-user /
OC-user)
3.721 1.484 9.333
For cohort MI Status =
No 1.002 1.000 1.003
For cohort MI Status =
Yes .269 .107 .674
N of Valid Cases 15000
The odd ration is 3.721, which is greater than 1. This indicates that a higher level of
association.

Biostatistics and informatics
b. Use of odds ratio to describe the size of the effect of OC-use on MI
According to when the odds ratio is Tsuang, Tohen &Jones, (2011) odds ratio of 1 or less
than one indicates small effect. In the case above the odds ratio is 3.721, which is greater
than, thus the effect of OC-use on MI is moderately large.
c. Description of the Analysis
From the investigation, it’s clear that that odd ratio is 3.721, which indicate a high level
of association between the use of contraceptive and the MI status. The confidence
interval of odd ration at 95% significance level is (1.48, 9.33), this range is beyond 1,
hence higher of the level of association between the OC-use and IM status. This
revelation, clear shows that MI status in women mainly depends on the use of
contraceptives.
Question Three
a. Odds ratio using he data in the table below
Drinking status Lung cancer
yes
Lung cancer
no
Total
Heavy drinker 33 1667 1700
Non-drinker 27 2273 2300
Total 60 3940 4000

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The table below show that the results of the computation of Odds ratio in SPSS.
Risk Estimate
Value 95% Confidence
Interval
Lower Upper
Odds Ratio for
Drinking status (Heavy
drinker / Non-drinker)
.600 .359 1.002
For cohort Lung Cancer
Condition = No .992 .984 1.000
For cohort Lung Cancer
Condition = Yes 1.654 .998 2.739
N of Valid Cases 4000
From the table,the Odd ratio is 0.6, which is less than 1. On the other hands, the confidence of
the odd ration is (0.359, 1.002), this suggests that at 95% significance level the odd ration
between heavy drinkers and non-drinkers rangers between 0.36 and 1. According to
Rosenthal(1996), an odds ratio below one describes a negative and small association and an odds
ratio of 1 indicates no association between the variables. This reveals that drinking status and
Lung cancer condition in the above case are negatively related and the level of association
between them is also small or no association at all as the odd ratio ranges between 0.36 and 1.

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b. Odd ratio of Smoker and non-smokers
I. Smokers
The following table shows the results of the computation of odd ration between the heavy
drinker and non-drinker for smokers’ category.
From the table, the odds ratio between heavy drinkers and non-driver is 1. This indicates that
there no association between the Drinking status and Lung cancer condition in patients.
II. Non-smokers
Risk Estimate of Smokers
Value 95% Confidence
Interval
Lower Upper
Odds Ratio for
Drinking status (Heavy
drinker / Non-drinker)
1.000 .403 2.480
For cohort Lung Cancer
Condition = No 1.000 .973 1.028
For cohort Lung Cancer
Condition = Yes 1.000 .414 2.413
N of Valid Cases 1000

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Risk Estimate of Non-Smokers
Value 95% Confidence Interval
Lower Upper
Odds Ratio for Drinking
status (Heavy drinker /
Non-drinker)
1.000 .456 2.192
For cohort Lung Cancer
Condition = No 1.000 .992 1.008
For cohort Lung Cancer
Condition = Yes 1.000 .460 2.175
N of Valid Cases 3000
From the table, the odds ratio between heavy drinkers and non-driver in non-smokers’ category
is 1. This indicates that there no association between the Drinking status and Lung cancer
condition in patients.
The following table shows the result of Cochran-Mantel-Haenszel analysis
Mantel-Haenszel Common Odds Ratio Estimate
Estimate .600
ln(Estimate) -.511
Std. Error of ln(Estimate) .261
Asymp. Sig. (2-sided) .051
Asymp. 95%
Confidence Interval
Common Odds
Ratio
Lower
Bound
.359
Upper
Bound
1.002
ln(Common Odds
Ratio)
Lower
Bound
-1.023
Upper
Bound
.002
The Mantel-Haenszel common odds ratio estimate is asymptotically
normally distributed under the common odds ratio of 1.000
assumptions. So is the natural log of the estimate.

Biostatistics and informatics
From the table, the P-value of the test is 0.051, which greater than the significance level (0.05).
This reveals that the odds ratio is less than 1 and therefore, no significant association between
drinking status and Lung cancer conditions in patients
c. Description of the Analysis
The three tests reveal that there’s no significant association between drinking status of a patient
and the lungs cancer condition. This has been supported the odds ratios of the three test, 0.6, 1
and 1, which are either 1 or slightly less than 1. Moreover, the Cochran-Mantel-Haenszel test,
which leads to a P-value (0.051) greater than 0.05 revealed that the odds ratio between heavy
drinkers and non-drinkers is not significantly different from 1 thus insignificant level association
or no association.
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References

Biostatistics and informatics
Rosenthal, J. A. (1996). Qualitative descriptors of strength of association and effect size. Journal
of social service Research, 21(4), 37-59.
Tsuang, M. T., Tohen, M., & Jones, P. (Eds.). (2011). Textbook of psychiatric epidemiology.
John Wiley & Sons.