Direct method of standardization of indices

The most important part The most important part is concerned with reasoning in an environment where one doesn’t know, or can’t know, all of the facts needed to reach conclusions with complete certainty. One deals with judgments and decisions in situations of incomplete information. In this introduction we will give an overview of statistics along with an outline of the various topics in this course.

Ternopil State Medical University Case control study Ternopil State Medical University

In the early 1940s, Alton Ochsner, a surgeon in New Orleans, observed that virtually all of the patients on whom he was operating for lung cancer gave a history of cigarette smoking. He hypothesized that cigarette smoking was linked to lung cancer.

Again in the 1940s, Sir Norman Gregg, an Australian ophthalmologist, observed a number of infants and young children in his ophthalmology practice who presented with an unusual form of cataract. Gregg noted that these children had been in utero during the time of a rubella (German measles) outbreak. He suggested that there was an association between prenatal rubella exposure and the development of the unusual cataracts.

Case-Control Study Design of case-control study Conduction of case-control study Analysis of case-control study

Design of a case-control study Were not exposed Were not exposed Were exposed Were exposed HAVE THE DISEASE DO NOT HAVE THE DISEASE

Design of Case-Control Studies First Select Controls (Without Disease) Cases (With Disease) Then Measure Post Exposure Were exposed Were not exposed a b C d a + c b + d Total a /a+c Proportions exposed b / b+c

If the exposure is associated with disease, we expect that a/a+c > b/b+c

A case-control study of Coronary Heart Disease and Cigarette Smoking CHD Cases Controls Smoke cigarettes 112 176 Do not smoke cigarettes 88 224 Total 200 400 % Smoking cigarettes 56.0 44.0

Question Can we get prevalence of disease in our study? Is it 200/(200+400) ?

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.

Population Selected cases Selected controls All cases in this population All normal people in this population

The Case-Control Study

Definition Last J. A Dictionary of Epidemiology, 2001 The observational epidemiologic study of persons with the disease (or other outcome variable) of interest (cases) and a suitable control (comparison, reference) group of persons without the disease.

Source of cases: Hospital patients; Patients in physicians’ practices; Clinic patients.

Selection of cases 1. Generalizability: incident /prevalent alive/dead hospital /population based 2. Case criteria: specific definitions inclusion and exclusion criteria

Select cases from a single hospital or multiple hospitals From single hospital From multiple hospitals in the community Identified risk factors may be unique to the hospital Risk factors are generalizable to all patients with the disease

Select incident or prevalent cases Select Incident cases Select prevalent cases Risk factors identified are more likely related to development of the disease Risk factors identified are more likely related to survival of the disease

Sources of controls • Sampling Frames: Population of an administrative area 2. Hospital patients (often same service, variety of conditions) 3. Relatives of the cases (spouses and siblings) 4. Associates of the cases (neighbors, co-workers, etc) • The controls should be drawn from the population of which the cases represent the affected individuals.

Advantages of hospital controls

Advantages of hospital controls Easily accessible Participants have time Participants motivated to cooperate Cases and controls drawn from similar social or geographic environments Differential recall likely to be minimised

Disadvantages of hospital controls

Disadvantages of hospital controls Differential hospitalisation patterns may produce bias Difficult to blind disease status of cases and controls May underestimate exposure in controls

Advantages of community controls May reduce selection biases Study results more generalizable May provide convenient control of extraneous variables

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

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.

Correlation coefficient

Correlation coefficient

Correlation coefficient

Types of correlation There are the following types of correlation (relation) between the phenomena and signs in nature: а) the reason-result connection is the connection between factors and phenomena, between factor and result signs. б) the dependence of parallel changes of a few signs on some third size.

Quantitative types of connection functional one is the connection, at which the strictly defined value of the second sign answers to any value of one of the signs (for example, the certain area of the circle answers to the radius of the circle)

Quantitative types of connection correlation - connection at which a few values of one sign answer to the value of every average size of another sign associated with the first one (for example, it is known that the height and mass of man’s body are linked between each other; in the group of persons with identical height there are different valuations of mass of body, however, these valuations of body mass varies in certain sizes – round their average size).

Correlative connection Correlative connection foresees the dependence between the phenomena, which do not have clear functional character. Correlative connection is showed up only in the mass of supervisions that is in totality. The establishment of correlative connection foresees the exposure of the causal connection, which will confirm the dependence of one phenomenon on the other one.

Correlative connection Correlative connection by the direction (the character) of connection can be direct and reverse. The coefficient of correlation, that characterizes the direct communication, is marked by the sign plus (+), and the coefficient of correlation, that characterizes the reverse one, is marked by the sign minus (-). By the force the correlative connection can be strong, middle, weak, it can be full and it can be absent.

Estimation of correlation by coefficient of correlation Force of connection Line (+) Reverse (-) Complete +1 Strong From +1 to +0,7 From -1 to -0,7 Average from +0,7 to +0,3 from –0,7 to –0,3 Weak from +0,3 to 0 from –0,3 to 0 No connection

Types of correlative connection By direction direct (+) – with the increasing of one sign increases the middle value of another one; reverse (-) – with the increasing of one sign decreases the middle value of another one;

Types of correlative connection By character rectilinear - relatively even changes of middle values of one sign are accompanied by the equal changes of the other (arterial pressure minimal and maximal) curvilinear – at the even change of one sing there can be the increasing or decreasing middle values of the other sign.

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

Standard Normal Distribution Mean +/- 1 SD  encompasses 68% of observations Mean +/- 2 SD  encompasses 95% of observations Mean +/- 3SD  encompasses 99.7% of observations

n=130 w=4cm n=1000, w =1cm

Distribution curve In general, as the number of observations, n, approaches infinity, and the width of class interval approaches zero, we will find a smooth curve such as is show in Figure 3. Such smooth curves are used to represent graphically the distribution of continuous random variables. We also call distribution curves. (or probability distribution curves)

Histogram (Frequency distribution graph) Frequency distribution curve Relative frequency distribution curve Probability distribution curve n is large

The probability distribution curve has some important consequences: The total area under the curve is equal to one; The relative frequency of occurrence of value between any two points on the X-axis is equal to area under curve between these two points; The probability of any specific value of the random variable is zero, because a specific value is represented by a point on the X-axis and the area above a point is zero.

a b

The Normal Distribution What is the normal distribution? The normal density is given by : It is the most important distribution in all of statistics.

μ σ The normal distributions are symmetric, single-peaked, bell-shaped density curves.

Characteristics of the normal distribution: It is symmetrical about its mean ,μ; The mean, the median, and mode are all equal; The total area under the normal curve above the X-axis is one square unit;

Characteristics of the normal distribution: The normal distribution is completely determined by the parameters μ and σ. In other words, a different normal distribution is specified for each different value of μ and σ. This implies that the normal distribution is really a family of distributions in which one member is distinguished from another on the basis of the value of μ and σ.