Statistical Methods in Epidemiology Assignment Solution Analysis

This document presents a comprehensive solution to an assignment on statistical methods in epidemiology. It begins by explaining the use of histograms and kernel density plots for representing data distributions and then delves into hypothesis testing using the independent sample t-test to compare the average weight gain of two groups, including calculations for the test statistic and confidence intervals. The assignment further explores confounding and effect modification, detailing the consequences of not adjusting for confounding variables and the methods to address them, such as stratification. It also clarifies the appropriate statistical measures for comparing variables with different scales. The solution then analyzes scenarios involving effect modifiers and confounders in studies of smoking and lung cancer, and social deprivation and coronary events. Finally, it interprets a 95% confidence interval for relative odds ratios. This assignment provides a detailed overview of key statistical concepts and their application in epidemiological studies.

Running Head: STATISTICAL METHODS IN EPIDEMIOLOGY
Statistical Methods in Epidemiology
Name of the Student
Name of the University
Author Note

1STATISTICAL METHODS IN EPIDEMIOLOGY
Answer 1
(i) A histogram usually represents the distribution of numerical data of a continuous
variable graphically. Each bar of the histogram usually represents the frequency of the
category. On the other hand, a kernel density plot is a non-parametric method of plotting
the probability density function of a random variable. Thus, a histogram is a more
appropriate graphical method to describe the frequency distribution of a continuous
variable.
(ii) Here, the target is to compare the average weight gain of the two samples, that is
the average one-month weight gain of the infants taking two types of diets A and B. The
equality of means of two groups can be tested using the technique of independent sample
t-test. Let μ1 and μ2 be the sample means of population 1 and population 2 respectively,
X1 and X2 be the population means of population 1 and population 2 respectively. Let S1
2
and S2
2 be the sample variances and n1 and n2 be the sample sizes of population 1 and
population 2 respectively. The null hypothesis (H0) and alternate hypothesis (HA) for this
test is usually given as
H0: μ1 = μ2 against HA: μ1 ≠ μ2
The test statistic for the test is given by
t= ( X1− X2 )−( μ1−μ2 )
√ S2
n1
+ S2
n2

2STATISTICAL METHODS IN EPIDEMIOLOGY
Where, S2 = pooled variance = ( n1−1 ) S1
2 +( n2−1) S2
2
n1 +n2−1 . In this case both n1 and n2 are equal
to 36. The null hypothesis will be accepted if the observed value of t is less than the
tabulated value of t and rejected otherwise.
The 95% confidence interval for the difference can be given by
(( μ1−μ2 )± t0.05,35
√ S2
n1
+ S2
n2 ).
(iii) To compare the spread or variation for two variables with different measurement
scales, the appropriate statistical measure that has to be used is the F-test.

3STATISTICAL METHODS IN EPIDEMIOLOGY
Answer 2
(i) Confounding is a condition where the association or effect of an exposure with an
outcome is indistinct with the presence of another factor or variable.
Effect modification can be defined as a variable which modifies the risk factor of
effect observed on a disease status positively or negatively.
(ii) The consequences of not adjusting for confounding in its presence while assessing
a disease-exposure relationship are given below:
 This may result in bias in the estimate of assessing the disease-exposure relationship.
 A difference is observed in the study population when in reality, no difference exists.
 A difference is observed in the study population in the absence of true association.
 The effect can be underestimated
 The effect can be overestimated.
It is to be noted that if the data collected on confounders are accurate, then only it
is possible to control the confounding effects or the confounders during the analysis.
Thus, there may arise situations when the confounders cannot be adjusted accurately in
the analysis. In situations like this, residual confounding occurs. For example, The
socioeconomic status of a person or a family affects the multiple health but it is not
possible to measure it accurately.
(iii) Stratification is a more appropriate method for adjusting confounding bias. In case
of matching or regression it is assumed that the residuals are normally distributed
whereas in reality that is not the case. Thus, stratification is more appropriate as there is
no running assumption necessary for this method.

4STATISTICAL METHODS IN EPIDEMIOLOGY
(iv) The limitations for the method of stratification are given as follows:
 Usually only one or two groups or strata can be made and not more than that.
 With the increase in the covariates, there will be more and more empty strata.
 Continuous variables will be classified on the basis of arbitrary criteria.
(v) Relative odds ratio will be equivalent to risk ratio when the events are
independent.
The preferred measure of association in a
a) Case-control study is relative odds ratio
b) Cross-sectional study is relative risk
c) Prospective randomized control study is relative odds ratio
d) Retrospective cohort study is relative risk

5STATISTICAL METHODS IN EPIDEMIOLOGY
Answer 3
In the study of association between smoking and lung cancer, sex is an effect-modifier. In
the study of age adjusted and unadjusted coronary event rates and death subsequent to a coronary
event, for men in north Glasgow, 1991, the exposure of interest is social deprivation. In this case
age is a confounder in the relationship between social deprivation and coronary event rate and
coronary death.
Answer 5
(i) The 95% confidence interval for the relative odds has been obtained as (0.086,
1.875). This means that the odds ratio within this interval will be 95% accurate in
estimating the population.