Estimation of authenticity of results of statistical

research

The necessity estimation of authenticity of results is determined by volume of research.

In full research (general aggregate), when all units of supervision are explored it is possible to get only one value of certain index.

The general aggregate is always reliable because in it included her all units of supervision are included. General aggregate official statistics can exemplify.

The distribution of birthwt is shown.

ObjectiveTo describe the distribution and frequency

of a disease in population.

Four primary types of epidemiology studies

How to describe ?

What is the problem of the disease?

How frequent ?

Who are affected?----person

Where and when does it occur?----place and time

Three distributions

Place Person

Time

Population

Age Behavior

SexRace

1 Age Frequency of disease

Severity of disease

Young people : infectious disease

Old people: noninfectious disease accumulation of environmental factors

Examples Children are more susceptible to some

infectious diseases, measles Prevalence of hypertension increase

with age

Mortality rate ---Age

Figure 6-1

incidence rate---Age

Figure 6-2

Serum HDL-cholesterol in Tromsø 1994/95

1

1,5

2 Men

Women

25-29 35-39 45-49 55-59 65-69 75-79 85-89 30-34 40-44 50-54 60-64 70-74 80-84

ISM, UiT

HDL-cholesterol mmol/L

The Tromsø Study

age

Sex

Frequencies and severity of disease differ between male and female population.

It is helpful to identify the risk factor of disease

e.g. endemic struma female > male

Prevalence of obesity in Han students aged 8-18 years in Urumqi , 2003

0. 0

2. 0

4. 0

6. 0

Age, y

Prev

alen

ce,%

Mal e

Femal e

Race (ethnic) Obesity, hypertension are more

prevalent in blacks than in whites T2D is very prevalent in Pima indians Prevalence of hypertension is quite

different among ethnicities.

Why? Genetic

Environment

Prevalence of obesity among ethnicities (adjusted by age)

4

4, 2

4, 4

4, 6

4, 8

5

5, 2

5, 4

5, 6

Han Hui Uygur KazakEthnicities

Pre

vale

nce o

f ob

esity

%

Prevalence of EH among ethnic adults (1991)

Death rate in the U.S.

Blacks: cause of deaths: hypertensive heart disease, stroke, tuberculosis, syphilis, and accidental death.

Whites: cardio artery disease, suicide, and leukemia.

Behaviors Cigarette smoking, alcohol consumption,

abuse of drugs; high salt intake, fat food, and so on.

Determined by biological and social factors.

Place

Countries

Urban and ruralPlacesin different altitude

Estimated number of people at over 35% risk of a major cardiovascular event in the next decade, by WHO sub-region

CHD mortality. Women and men, age adjusted rates per 100.000.

34

59

75

85

118

156

169

170

173

224

233

241

296

383

432

0 50 100 150 200 250 300 350 400 450 500

Japan

France

Spain

Portugal

Netherlands

Germany

Norway

USA

Sweden

Finland

Denmark

England Wales

Scotland

Russia

Estonia

Source: WHO Health statistics annual 1993/94 ISM, UiT

Time

When does the disease occur and transmit in the population?

Mean Plasma Cholesterol Values in China

0

50

100

150

200

250

mg/

dl

1958 1981 1997 2003

Some terms to describe the “time” of diseases

Long-term or secular trends Periodic fluctuations (cyclical changes)

seasonal trends

cyclical trends Short term fluctuations

Secular trends

Changes in the incidence of disease over a long period of time (several years of decades)

CHD have shown an upward trend in developed countries over decades.

Periodic fluctuations

1. Seasonal trends Diarrhea---summer Respiratory diseases---winter2. Cyclical trends disease occur in cycles spread over

short periods of time (day, weeks, months or years) e.g. influenza 7-10 yrs)

The general aggregate is rarely used in medical-biologic research, mainly part of researches is selective. The law of large numbers is basis for forming of reliable selective aggregate. It sounds so: it is possible to assert with large authenticity, that at achievement of large number of supervisions average of sign, which is studied in a selective aggregate will be a little to differ from an average which is studied at all general aggregate.

The selective aggregate always has errors, because not all units of supervision are included in research. Authenticity of selective research depends from the size of this error. That is why greater number of supervisions, teed to less error, the less sizes of casual vibrations of index. That, to decrease an error it is needed to multiply the number of supervisions.

Basic criteria of authenticity (representation):

Error of representation (w) Confiding scopes The coefficient of authenticity (the student

criterion) is authenticity of difference of middle or relative sizes (t)

Basic criteria of authenticity (representation):

The errors of representation of /m/ are the degree of authenticity of average or relative value shows how much the results of selective research differ from results which it is possible to get from continuous study of general aggregate.

Basic criteria of authenticity (representation):

Confiding scopes – properties of selective aggregate are carried on general one, probability oscillation of index is shown in the general aggregate, its extreme values of minimum and maximal possibility, which the size of general aggregate can be within the limits of.

Basic criteria of authenticity (representation):

The coefficient of authenticity (the Student’s criterion) is authenticity of difference of middle or relative sizes (t). The student’s Criterion shows the difference of the proper indexes in two separate selective aggregates.

Measuring the Occurrence of Disease

Counting

Comparisons

Inference

Action

Cases and populations

Measurement

Risk

Methods - descriptive

- analytic

Association and causality

Generalisability

Clinical/health policy

Further research

Epidemiological Measurements

Rates,Ratios,and Proportions Incidence Rates Prevalence Rates Mortality Rates Fatality Rates Infection Rates

RatiosA ratio expresses the relationship

between two numbers in the form x:y or x/y.

Ratios

1. The ratio of male to female births in the United States in 1979 was 1,791,000 : 1,703,000 or 1.052:1.

2. Sex ratio=

number of live born males

number of live born females

Proportions

A proportion is a specific type of ratio in which the numerator is included in the denominator, and the result value is expressed as a percentage.

For example,the proportion of all births that were male is :

Male births 179×104

= Male+female births (179+170)×104

=51.3%

The proportion of male students of the current class is %.

51. 41 51. 33 51. 07 48. 70

48. 39 48. 67 48. 93 51. 30

0

20

40

60

80

100

120

Han Hui Uygur Kazak

Mal e Femal e

n=41640 n=4736 n=6362 n=2770

Proportion of Overweight in children from 7-18 year old, Urumqi, 2003

Gi r l

0. 0

2. 0

4. 0

6. 0

8. 0

Obesi ty Overwei ght

Prev

alen

ce,%

Han Hui Uygur Kazak

A rate measures the occurrence of some particular events in a

population during a given time period.

Particular event: development of disease or the occurrence of death

Rates

Rates are defined as follows:

Number of events in a specified period

×K

Population at risk of these events in a specified period

K=100%, 1000‰ …

Five components of rateDenominator

is the population at risk of

total events

Place specification

at a given time

Time specification

Constant

multiplier K

Numerator is the number of

People,Episodes

Rate is

The rate is the measure that most clearly expresses probability or risk of disease in a defined population over a specified period of time.

In a rate numerator is part of denominator.

What does Rate tell us

Rates tell us how fast the disease is occurring in a population.

Proportion tell us what fraction of the population is affected.

For example, the death rate from cancer in the United States in 1980 was 186.3 per 100,000 population, the formula:

Deaths from cancer among U.S residents in 1980 100,000

×

U.S. population in 1980 100,000

Incidence Rates

Incidence is defined as the number of new cases of a disease that occur during a specified period of time in a population at risk for developing the disease.

1. Time of onset and the numerator

Denominator is population at risk.

Average Population

We can get this number in two ways. (population in 12.31 of last year+this year)/2

midyear population: 7.31 24:00

3.Specification of Denominator

Prevalence Rates

Prevalence measures the number of people in a population who have disease at a given time.

Point prevalence Period prevalence

Formula:

number of existing cases of a disease

at a point in time ×K

total population

5 points

1.NumeratorIt refers to existing cases, currently

affected, including new and old cases.No matter when did he get the disease, if

only he has disease at the study time,he is one of numerator.

2.Denominator

Total population.

Not population at risk.

3.A point in time

In survey of prevalence rate, time should be very short.

Generally, time should be no more than 1 month, such as 1 week or 2 weeks. (point prevalence)

Coefficient of variation is the relative measure of variety; it is a percent correlation of standard deviation and arithmetic average.

Terms Used To Describe The Quality Of Measurements

Reliability is variability between subjects divided by inter-subject variability plus measurement error.

Validity refers to the extent to which a test or surrogate is measuring what we think it is measuring.

Measures Of Diagnostic Test Accuracy

Sensitivity is defined as the ability of the test to identify correctly those who have the disease.

Specificity is defined as the ability of the test to identify correctly those who do not have the disease.

Predictive values are important for assessing how useful a test will be in the clinical setting at the individual patient level. The positive predictive value is the probability of disease in a patient with a positive test. Conversely, the negative predictive value is the probability that the patient does not have disease if he has a negative test result.

Likelihood ratio indicates how much a given diagnostic test result will raise or lower the odds of having a disease relative to the prior probability of disease.

Measures Of Diagnostic Test Accuracy

Expressions Used When Making Inferences About Data

Confidence Intervals- The results of any study sample are an estimate of the true value

in the entire population. The true value may actually be greater or less than what is observed.

Type I error (alpha) is the probability of incorrectly concluding there is a statistically significant difference in the population when none exists.

Type II error (beta) is the probability of incorrectly concluding that there is no statistically significant difference in a population when one exists.

Power is a measure of the ability of a study to detect a true difference.

Multivariable Regression Methods

Multiple linear regression is used when the outcome data is a continuous variable such as weight. For example, one could estimate the effect of a diet on weight after adjusting for the effect of confounders such as smoking status.

Logistic regression is used when the outcome data is binary such as cure or no cure. Logistic regression can be used to estimate the effect of an exposure on a binary outcome after adjusting for confounders.

Survival Analysis

Kaplan-Meier analysis measures the ratio of surviving subjects (or those without an event) divided by the total number of subjects at risk for the event. Every time a subject has an event, the ratio is recalculated. These ratios are then used to generate a curve to graphically depict the probability of survival.

Cox proportional hazards analysis is similar to the logistic regression method described above with the added advantage that it accounts for time to a binary event in the outcome variable. Thus, one can account for variation in follow-up time among subjects.

Kaplan-Meier Survival Curves

Why Use Statistics?

Cardiovascular Mortality in Males

0

0.2

0.4

0.6

0.8

1

1.2

'35-'44 '45-'54 '55-'64 '65-'74 '75-'84

SMR Bangor

Roseto

Descriptive Statistics

Identifies patterns in the data Identifies outliers Guides choice of statistical test

Percentage of Specimens Testing Positive for RSV (respiratory syncytial virus)

Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun

South 2 2 5 7 20 30 15 20 15 8 4 3

North-east

2 3 5 3 12 28 22 28 22 20 10 9

West 2 2 3 3 5 8 25 27 25 22 15 12

Mid-west

2 2 3 2 4 12 12 12 10 19 15 8

Descriptive Statistics

Percentage of Specimens Testing Postive for RSV 1998-99

0

5

10

15

20

25

30

35

Jul Sep Nov Jan Mar May Jul

SouthNortheastWestMidwest

Distribution of Course Grades

0

2

4

6

8

10

12

14

Number of Students

A A- B+ B B- C+ C C- D+ D D- F

Grade

Describing the Data with Numbers

Measures of Dispersion• RANGE • STANDARD DEVIATION• SKEWNESS

Measures of Dispersion

• RANGE • highest to lowest values

• STANDARD DEVIATION• how closely do values cluster around the

mean value• SKEWNESS

• refers to symmetry of curve

The Normal Distribution

Mean = median = mode

Skew is zero 68% of values fall

between 1 SD 95% of values fall

between 2 SDs

.

Me

an

, Med

ian

, Mo

de

1

2