Community Medicine

Wednesday, January 2, 2019

Mantel Haenszel

Mantel Haenszel method is one of the method to control for confounders. It gives a single summary measure of association which provides a weighted average of RR or OR across different strata of confounding factors.

To calculates in this method we first have to divide the original two by two table by different strata of confounding variable and then we calculate the weighted average of RR or OR.

formula

                                          outcome (O)
                                             +      -
RISK FACTOR (E)     +      a.    b.       a+b
- c.    d. c+d

                                             a+c. b+d.

RR = (a/(a+b)) ÷ (c/(c+d)) = a(c+d)÷ c(a+b)

OR = a/b. ÷ c/d. = ad/bc

RR (mh) = summation (a(c+d)÷n) ÷ summation (c(a+b) ÷n)

OR (mh) = summation (ad/n) ÷summation (bc/n)

summation is sigma, that is sum of all the values in the different two by two tables

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Skewness and Kurtosis

Skewness: If a histogram/frequency polygon of a distribution is asymmetric, the distribution is said to be skewed.

If the distribution is not symmetric because its graph extends further to the right than to the left, that is, if it has a long tail to the right, we say that the distribution is skewed to the right or it is positively skewed.

A distribution will be skewed to the right, or positively skewed, if its mean is greater than its mode.

If the distribution is not symmetric because its graph extends further to the left than to the right, that is, if it has a long tail to the left, we say that the distribution is skewed to the left or it is negatively skewed.

A distribution will be skewed to the left, or negatively skewed, if its mean is less than its mode.

Skewness >0 indicates positive skewness

<0 indicates negative skewness

Kurtosis: it is a measure of the degree to which the distribution is peaked or flat in comparison to a normal distribution whose graph is characterized by a bell shaped appearance.

Platykurtic: the graph exhibits a flattened appearance

Mesokurtic: normal, bell shaped graph

Leptokurtic: the graph exhibits a more peaked appearance

Platykurtic kurtosis <0

Mesokurtic kurtosis =0

Leptokurtic kurtosis >0

Kurtosis: it is a measure of the degree to which the distribution is peaked or flat in comparison to a normal distribution whose graph is characterized by a bell shaped appearance.

Platykurtic: the graph exhibits a flattened appearance

Mesokurtic: normal, bell shaped graph

Leptokurtic: the graph exhibits a more peaked appearance

Measures of Central tendency

Measures of Central tendency:

Mean: airthmetic average of the overall dataset

Properties:

1. Uniqueness: for a given set of data, there is only one arithmetic mean

2. Simplicity: easy to compute

3. Extreme values have drastic influence on mean

Median: middle value of the dataset when it is arranged in ascending order
its the middle value if the dataset is odd, and average of the two middle values if the dataset is even

it is the value that divides the dataset into two equal parts such that the no. of values equal to or greater than the median is equal to the number of values equal to or less than the median, when the data set is arranged in order of magnitude

In odd data set: it is the (n+1)/2 th value

In even data set: it is the average of n/2 and n/2+1 th value

Properties:

1. Uniqueness: for a given set of data, there is only one median

2. Simplicity: easy to compute

3. Not drastically affected by extreme values as in mean

Mean and median are special cases of a family of parameters known as location parameters, because they can be used to designate certain positions on the horizontal axis when the distribution of a variable is graphed (“locate” the distribution on the horizontal axis)

Mode: most frequent value in the dataset

It may be used also for describing qualitative data.

Suppose the height of the trees (metres) in a garden is represented by following dataset
1,2,3,4,6,7,4,2,3,8,9,1,2

first let us arrange this in ascending order

1,1,2,2,2,3,3,4,4,6,7,8,9

most frequent value in dataset in here is "2" = Mode

now the total no. of values in the datset is 13

Median will be value that is middle value that is 7th one
Median =3

Mean = (1+1+2+2+2+3+3+4+4+6+7+8+9)/13
= 4

Vaccine efficacy and effectiveness

Vaccine efficacy:

Vaccine efficacy- % reduction in disease incidence in a vaccinated group compared to an unvaccinated group under optimal conditions

Reduction in the chance or odds of developing clinical disease after vaccination relative to the chance or odds when unvaccinated. Vaccine efficacy measures direct protection (i.e. protection induced by vaccination in the vaccinated population sample). WHO

Reduction in the chance of developing the disease after vaccination relative to the chance in unvaccinated as determined in a prospectiverandomised controlled study. EMA

The ability of a vaccine to provide protection against disease under ideal circumstances (e.g. during a clinical trial). CDC

Vaccine effectiveness:

Vaccine effectiveness- ability of vaccine toprevent outcomes of interest in the “real world”

The protection conferred by vaccination in a certain population.
Measures direct and indirectprotection (i.e. protection to non- vaccinated persons). WHO

Direct (vaccine induced) andindirect (population related) protection during routine use, estimated from observationalcohort studies. EMA

The ability of a vaccine to provide protection against disease when used under field conditions(routine practice). CDC

Vaccine impact:
Compares the burden of disease caused by the pathogen included in the vaccine, in a population that has received the vaccine, to the burden of disease in a population that has not received the vaccine.

Vaccine effects
 Direct effect:
Protection in vaccinated persons only
Induced by individual vaccination
 Indirect effect:
Effect of a vaccination programme
At population level, including non-vaccinated

Direct effect
 Depends on vaccine and host characteristics Compares disease in vaccinated to disease in
and unvaccinated in one population Measured in clinical trials or in real life

Efficacy: protection measured in clinical trials Ideal conditions of administration Selected subjects (e.g. underlying diseases often excluded)

Effectiveness: protection if measured in real life situation
 Routine vaccination, including incomplete schedule, delayed administration
 Any person of the target group

Herd effects or indirect:

Effect of widespread vaccination: protection by reduced transmission in the population, when large proportions are vaccinated

Two vaccine exposures
 Individual vaccination
 Vaccination programme Direct effect only Direct + indirect efect

Effect of programme -> sum of effects of vaccination on vaccinated
• If there is an indirect effect

How to measure vaccine effects?

*Halloran et al

Direct effect: Direct effect of vaccination on those vaccinated

 Exposure = individual vaccination
 Vaccinated vs. non vaccinated, same population

Methods: study design must cancel the indirect effect of programme:
cohortstudies (from same population)
 case control studies #
 screening methods #
 Broome method #

# Controls have same exposure/coverage than population giving rise to cases
Indirect, total and overall effect

Comparing two separate but similar populations, one with vaccination, the other without:
 Vaccinated persons: total effect
 Non-vaccinated: indirect effect
 All persons: overall effect
Design:

 Population separated by time or place
 Pre and post-vaccine comparison (time)

 Cluster randomized trials

 Statistical or mathematical modelling

Exposure here is programme

Impact of vaccination programme

WHO: correspond to overall effectVaccination programme
Total population being compared

Major confusion: direct and overall

Direct effect	Overall effect
of individual vaccination	of a vaccination programme
on vaccinated persons	in a population, in which a fraction only is vaccinated
Pre or post-licensure	Post-licensure only
Does not include indirect effect	Direct + indirect effects Potentially replacement disease
Compares groups from same population Need to know vaccine status	Compares 2 populations No need to know vaccine status

The incremental cost-effectiveness ratio (ICER)

•The incremental cost-effectiveness ratio (ICER) is used to summarise the cost-effectiveness of a health care intervention

•It is defined by the difference in cost between two possible interventions, divided by the difference in their effect

•It represents the average incremental cost associated with one additional unit of the measure of effect

•The ICER can be estimated as:

Discounting (Economic evaluation)

•Health benefits and costs related to an intervention occur at different points in time

•Society has a preference for interventions where benefits occur sooner

•Adjusts future health benefits and costs to present value

•What is the present value of ₹ 5,000 received 10 years from now?

Ans. 3,720.47

Standard Discount Rates

•US Panel on Cost Effectiveness in Medicine

•3% costs and benefits

•5% and 0% in sensitivity analyses

•United Kingdom

•NICE (National Institute of Health and Care Excellence) guidance: 3.5% for cost and benefits

Cost Effectiveness Acceptability Curves (CEAC)

•Represents the uncertainty concerning the cost-effectiveness of a health-care intervention in the context of decisions involving two interventions

•It acts as an alternative to confidence intervals around ICERs

•CEACs have been interpreted as representing the ‘probability that the intervention is cost-effective’ given the data

Cost Analysis

Conditional logistic regression

Logistic regression analysis studies the association between a binary dependent variable and a set of independent (explanatory) variables using a logit model.

Conditional logistic regression (CLR) is a specialized type of logistic regression usually employed when case subjects with a particular condition or attribute are each matched with n control subjects without the condition. In general, there may be 1 to m cases matched with 1 to n controls. However, the most common design is 1:1 matching, followed by 1:n matching in which nvaries from 1 to 5

Ref. https://ncss-wpengine.netdna-ssl.com/wp content/themes/ncss/pdf/Procedures/NCSS/Conditional_Logistic_Regression.pdf

In CLR we must remember that observations are not independent, and participants in different treatment groups have been matched for at least 1 characteristic, and this must be taken into account in the analysis.

The philosophy is the same with logistic regression with the exception that the estimates from conditional logistic regression are conditional on the matched treatment groups or on the cases being linked to the controls in a matched case-control study. This type of analysis is required in individually matched studies.

However, it is different when studies use frequency matching, which deals with selecting individuals for different groups to have the same overall distribution on a matching variable. In this case, it is acceptable to use unconditional (ordinary) logistic regression and include the matching factor in the model.

In conditional logistic regression model, likelihood is formulated in a way that subjects from different treatment groups (or case controls) are only compared within the same matched set; this is called conditional likelihood. The general form of a conditional logistic regression model with a single binary exposure is:

Log odds = a + set + beta1 exposure

- Where (a + set) represents constant term in each set of matched individuals, and beta1 exposure represents estimate of effect
of exposure of interest.
- Constant in each set is eliminated from the model using conditional likelihood, and only the effect of the exposure and other potential predictors are retained. This means that there is no constant term as in the usual logistic regression in the output from a con- ditional logistic regression.

- When modeling our data with conditional logistic regression, we can additionally include other potential

predictor variables or confounders and test for interac- tions in the same way that this is done using ordinary lo- gistic regression

Ref http://dx.doi.org/10.1016/j.ajodo.2017.04.009

Odds ratio, Relative risk, Attributable risk, Population attributable risk

Odds ratio (OR) is a measure of association between an exposure and an outcome. OR represents odds that an outcome will occur given a particular exposure, compared to the odds of outcome occurring in absence of that exposure. Odds ratios are most commonly used in case-control studies, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions).

Odds ratios are used to compare relative odds of the occurrence of the outcome of interest (e.g. disease or disorder), given exposure to the variable of interest (e.g. health characteristic, aspect of medical history). The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome, and to compare the magnitude of various risk factors for that outcome.

1. OR=1 Exposure does not affect odds of outcome

2. OR>1 Exposure associated with higher odds of outcome

3. OR<1 Exposure associated with lower odds of outcome

Relative risk (RR): A synonym for risk ratio. However, the term is also commonly

used to refer to the rate ratio and even to the odds ratio (OR). To minimize confusion,

it may be better to avoid this term in favor of more specific terms.

Rate ratio The ratio of two rates; e.g., the rate in an exposed population divided by the rate

in an unexposed population.

Relative Risk (RR) = (incidence in exposed)/(incidence in non-exposed)

Attributable risk (AR) = (incidence in exposed - incidence in non-exposed)/(incidence in exposed)

Risk difference (RD) = (incidence in exposed - incidence in non-exposed)

Population attributable risk (PAR) = (incidence total- incidence in non-exposed)/(incidence total)

or PAR = P_e (RR_e-1) / [1 + P_e (RR_e-1)]

where, Pe is prevalence of exposure

RRe is relative risk of that exposure

Ie - incidence in exposed

Iu - incidence in unexposed (non-exposed)

Ip - incidence total (exposed + nonexposed)