Organization of statistical research

The role of Biostatisticians

Biostatisticians play essential roles in designing studies, analyzing data and creating methods to attack research problems as diverse as

determination of major risk factors for heart disease, lung disease and cancer

testing of new drugs to combat AIDS evaluation of potential environmental factors

harmful to human health, such as tobacco smoke, asbestos or pollutants

Applications of Biostatistics

Public health, including epidemiology, health services research, nutrition, and environmental health

Design and analysis of clinical trials in medicine Genomics, population genetics, and statistical genetics in

populations in order to link variation in genotype with a variation in phenotype. This has been used in agriculture to improve crops and farm animals. In biomedical research, this work can assist in finding candidates for gene alleles that can cause or influence predisposition to disease in human genetics

Ecology Biological sequence analysis

Applications of Biostatistics

Statistical methods are beginning to be integrated into

medical informatics public health informatics bioinformatics

Types of Data

Categorical data: values belong to categories- Nominal data: there is no natural order to the

categories e.g. blood groups- Ordinal data: there is natural order e.g. Adverse

Events (Mild/Moderate/Severe/Life Threatening)- Binary data: there are only two possible categories

e.g. alive/dead Numerical data: the value is a number

(either measured or counted)- Continuous data: measurement is on a continuum

e.g. height, age, haemoglobin- Discrete data: a “count” of events e.g. number of

pregnancies

Measures of Frequency of Events

Incidence- The number of new events (e.g. death or a particular

disease) that occur during a specified period of time in a population at risk for developing the events.

Incidence Rate- A term related to incidence that reports the number of

new events that occur over the sum of time individuals in the population were at risk for having the event (e.g. events/person-years).

Prevalence- The number of persons in the population affected by a

disease at a specific time divided by the number of persons in the population at the time.

Measures of Association

Relative risk and cohort studies- The relative risk (or risk ratio) is defined as the

ratio of the incidence of disease in the exposed group divided by the corresponding incidence of disease in the unexposed group.

Odds ratio and case-control studies- The odds ratio is defined as the odds of

exposure in the group with disease divided by the odds of exposure in the control group.

Measures of Association

Measures of Association Absolute risk

- The relative risk and odds ratio provide a measure of risk compared with a standard.

Attributable risk or Risk difference is a measure of absolute risk. It represents the excess risk of disease in those exposed taking into account the background rate of disease. The attributable risk is defined as the difference between the incidence rates in the exposed and non-exposed groups.

Population Attributable Risk is used to describe the excess rate of disease in the total study population of exposed and non-exposed individuals that is attributable to the exposure.

Number needed to treat (NNT)- The number of patients who would need to be treated to

prevent one adverse outcome is often used to present the results of randomized trials.

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.

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

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

05

101520253035

South

Northeast

West

Midwest

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

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

Hypertension Trial

DRUG Baseline mean SBP F/u mean SBP

A 150 130

B 150 125

30 Day % Mortality

Study IC STK Control p N

Khaja 5.0 10.0 0.55 40

Anderson 4.2 15.4 0.19 50

Kennedy 3.7 11.2 0.02 250

95% Confidence Intervals

-,40 -,35 -,30 -,25 -,20 -,15 -,10 -,05 ,00 ,05 ,10 ,15 ,20

Khaja(n=40)

Anderson(n=50)

Kennedy(n=250)

Types of Errors

Nodifference

Difference

Nodifference

TYPE IIERROR ()

Difference TYPE IERROR ()

Truth

Conclusion

Power = 1-

Suppose we made three more series of draws, and the results were + 16%, + 0%, and + 12%. The random sampling errors of the four simulations would then average out to:

ERROR ANALYSIS

Note that the cancellation of the positive and negative random errors results in a small average. Actually with more trials, the average of the random sampling errors tends to zero.

ERROR ANALYSIS

So in order to measure a “typical size” of a random sampling error, we have to ignore the signs. We could just take the mean of the absolute values (MA) of the random sampling errors. For the four random sampling errors above, the MA turns out to be

ERROR ANALYSIS

The MA is difficult to deal with theoretically because the absolute value function is not differentiable at 0. So in statistics, and error analysis in general, the root mean square (RMS) of the random sampling errors is generally used. For the four random sampling errors above, the RMS is

ERROR ANALYSIS

The RMS is a more conservative measure of the typical size of the

random sampling errors in the sense that MA ≤ RMS.

ERROR ANALYSIS

For a given experiment the RMS of all possible random sampling errors is called the standard error (SE). For example, whenever we use a random sample of size n and its percentages p to estimate the population percentage π, we have

ERROR ANALYSIS