Biostats Test 1 (Dlp) Kuma

Front 1

Questions to ask yourself about a study.

Back 1

How generalizabl are the findings?
What degree of clinical severity are being looked at?
How matched are the cases and controls?
how are the scores distributed in the study population?

Front 2

How do you look at the data in a study?

Back 2

Determine what the saa looks like.
What trends are shown?
What are the outliers (mathematicaly unusual scores)?
What statistical tests are most appropriate?
What is the typical value, central tendancy, or average response?
How much spread, or variability, is there in the values? Highly variable = difficult to predict. Less variable = more predictable responses

Front 3

What are the main ways to display one variable, frequency distribution data?

Back 3

Categorical Data:
*Bar chart
*Pie chart
Continuous Data:
*Histogram
*Dot plot
*Box plot
*Stem-and-leaf plot

Front 4

What are the main ways to display two variable, relationship data?

Back 4

Categorical Data - Segmented bar chart

Continuous Data - Scatter plot

Front 5

What are the possible shapes of frequency distribution?

Back 5

Modality - how many peaks does the curve have? unimodal = 1, bimodal = 2, multi-modal = >2

Is the curve semetrical or skewed? The tail end points in the direction of the skew.

Front 6

Arithmetric mean (average)

Back 6

The sum of the values divided by the number of values.

Front 7

Median

Back 7

middle value, 50th percentile

Front 8

Mode

Back 8

the most common value

Front 9

Geometric mean

Back 9

antilog of the mean of the log data (for skewed data)

Front 10

Weighted mean

Back 10

when certain values carry ‘more weight’ or importance than others

Front 11

If the mean = the median

Back 11

the distribution is symmetrical

Front 12

If the mean does not equal the median

Back 12

the distribution is not symmetrical

Front 13

What are the measures of central tendancy?

Back 13

Mean
Median
Mode
Geometric mean
Weighted mean

Front 14

What are the advantages of using the mean as a measure of central tendancy?

Back 14

Uses all data
Algebraically defined

Front 15

What are the advantages of using the median as a measure of central tendancy?

Back 15

Not distorted by outliers
Not distorted if skewed

Front 16

What are the advantages of using the mode as a measure of central tendancy?

Back 16

Easy if categorical data

Front 17

What are the advantages of using the Geometric Mean
as a measure of central tendancy?

Back 17

Transformed, same pros as mean
Good for skewed data

Front 18

What are the advantages of using the Weighted Mean
as a measure of central tendancy?

Back 18

Same pros as mean
Relative importance
Algebraically defined

Front 19

What are the disadvantages of using the mean as a measure of central tendancy?

Back 19

Distorted by outliers
Distorted if skewed

Front 20

What are the disadvantages of using the median as a measure of central tendancy?

Back 20

Ignores most data
Not algebraic

Front 21

What are the disadvantages of using the mode as a measure of central tendancy?

Back 21

Ignores most data
Not algebraic

Front 22

What are the disadvantages of using the geometric mean as a measure of central tendancy?

Back 22

Only good if log transformation yields symmetrical distribution

Front 23

What are the disadvantages of using the weighted mean as a measure of central tendancy?

Back 23

Need good estimates of weights

Front 24

Measures of variability

Back 24

Range (minimum - maximum)

Percentiles – value of x that has n% of the observations below it is the nth percentile
interquartile range = range between the 25th and the 75th percentiles or the central 50%

Variance – average deviation from the mean
s2 = Σ(xi – x)2/n - 1

Standard Deviation – square root of the variance
s = sd = √ Σ(xi – x)2/n - 1

Front 25

What are the advantages of using range to determine variability?

Back 25

Easy to determine

Front 26

What are the disadvantages of using range to determine variability?

Back 26

Uses only 2 data pts.
Distorted by outliers
Increases with sample size

Front 27

What are the advantages of using Inter-Quartile Range
to determine variability?

Back 27

Unaffected by outliers
Independent of sample size
Good for skewed data

Front 28

What are the advantages of using Variance to determine variability?

Back 28

Clumsy to calculate
Uses every data pt.
Algebraic

Front 29

What are the advantages of using Standard Deviation
to determine variability?

Back 29

Same as variance
Units of measure = units of raw data
Easy to interpret

Front 30

What are the disadvantages of using Inter-Quartile Range
to determine variability?

Back 30

Clumsy to calculate
Not good for small samples
Uses only 2 data pts.
Not algebraic

Front 31

What are the disadvantages of using Variance to determine variability?

Back 31

Units of measure = square of the raw data units
Sensitive to outliers
Not good for skewed data

Front 32

What are the disadvantages of using Standard Deviation
to determine variability?

Back 32

Sensitive to outliers
Not good for skewed data

Front 33

Don't forget to look at your slide for the stem and leaf plot

Back 33

Sept 18th Lecture

Front 34

Don't forget to look at your slide for the Box and whiskers plot

Back 34

Sept 18th Lecture

Front 35

Why do we care about central tendency and variation?

Back 35

* Answers what is the typical value - is it what we expect, how does it compare to other groups?
* Will help us understand how confident we are in our point estimate

* Provides guidance for what statistical test is most appropriate

Front 36

Refer to Mossad article on Zinc Losenges Table 1

How generalizable are the findings for a 70 year old Asian female patient?

Back 36

These findings are not generalizable to a 70 year old Asian woman.

Front 37

Refer to Weaver article on Sleep Apnea Table 2

What is the degree of clinical severity in the patients in this study?

Back 37

Comparing the normal range to the range of scores exhibited by the study participants, there is a large variance in the degree of severity.

Front 38

Refer to Valuck article on B12 deficiency Table

How matched are the case and controls?

Difference in history of acid suppression therapy usage?

Back 38

There is a good match between the percentages of male/female, age, and therapy.

Front 39

Refer to Perez article on Antidepressants Table 1

How is the HAMD, a measure of depression severity, distributed in the study population?

Back 39

The curve is skewed to the left.

Front 40

What are the four main ways to measure risk?

Back 40

* Absolute Risk Reduction (ARR)
* Number Needed to Treat (NNT)
* Relative Risk (RR)
* Odds Ratio (OR)

Front 41

Calculating Absolute Risk Reduction

Back 41

Front 42

Calculate Number Needed to Treat

Back 42

Front 43

Calculate Relative Risk

Back 43

Front 44

Calculate Relative Risk

Back 44

Front 45

Calculate Odds Ratio

Back 45

Front 46

Bias

Back 46

A systematic difference between the results obtained by a study and the true state of affairs

Front 47

Blinding (definition, single, double)

Back 47

When the patients, clinicians, and assessors of response to treatment are unaware of of the treatment allocation (double-blind), or when the patient is aware of the treatment received but the assessor of the response is not (single-blind). Also called masking.

Front 48

Blocking

Back 48

Also called stratification. Grouping experimental units that share similar characteristics into a homogenous block or stratum.

Front 49

Cohort

Back 49

A group of individuals, all without the outcome of interest (e.g. disease), is followed (usually prospectively) to study the effect on future outcomes of exposure to a risk factor.

Front 50

Controls (control group)

Back 50

A term used in comparative studies, e.g. clinical trials, to denote a comparaison group. This group of individuals either does not have the disease or is not receiving the treatment.

Front 51

Experimental study

Back 51

The investigator intervenes in some way to affect the outcome

Front 52

Geometric mean

Back 52

A measure of location for data whose distribution is skewed to the right; it is the antilog of the arithmetic mean of the log data

Front 53

Incidence

Back 53

The number of new cases of a disease in a defined period of time divided by the number of individuals suceptible at the start or mid-period of the period

Front 54

Inclusion/Exclusion criteria

Back 54

A definition of which patients are to be recruited

Front 55

Intention-to-treat

Back 55

All patients in the clinical trial are analysed in the groups to which they were originally assigned

Front 56

Interquartile Range (IQR)

Back 56

The difference between the 25th and the 75th percentiles; it contains the central 50% of the ordered observations

Front 57

Longitudinal study

Back 57

Follows individuals over a period of time

Front 58

Matching

Back 58

A process of creating (usually) pairs of individuals who are similar in respect to variables that may influence the response of interest

Front 59

Mean

Back 59

A measure of location obtained by dividing the sum of the observations

Front 60

Measures of Risk

Back 60

EER, CER, RR, OR, ARR, RRR, and NNT

Front 61

Median

Back 61

A measure of location that is the middle value of the ordered observations

Front 62

Mode

Back 62

The value of a single variable that occurs mist frequently in a data set

Front 63

Nominal

Back 63

A categorical variable whose categories have no natural ordering

Front 64

Numerical – Continuous

Back 64

A numberical variable in which there is no limitation on the values that that variable can take other than that restricted by degree of accuracy of the measuring technique

Front 65

Numerical – Discrete

Back 65

A numberical variable that can only take integer values

Front 66

Observational study

Back 66

The investigator does nothing to affect the outcome

Front 67

Ordinal

Back 67

A categorical variable whose categories are ordered in some way

Front 68

Prevalence

Back 68

The number or proportion of individuals with a disease at a given point in time (point prevalence) or within a defined interval (period prevalance)

Front 69

Primary endpoint

Back 69

The outcome that most accurately reflects the benefit of a new therapy in a clinical trial

Front 70

Randomization (random allocation)

Back 70

Patients are allocated in a random manner

Front 71

Range

Back 71

The difference between the smallest and largest observations

Front 72

Risk Factor (exposure)

Back 72

A determinant that effects the incidence of a particular outcome e.g. disease

Front 73

Secondary endpoint

Back 73

The outcome(s) in a clinical trial that are not of primary importance

Front 74

Standard deviation

Back 74

A measure of spread equal to the square root of the variance

Front 75

Surrogate endpoint

Back 75

An endpoint measure that is highly correlated with the endpoint of interest but which can be measured more easily, quickly or cheaply than the endpoint

Front 76

Variable

Back 76

Any quantity that varies

Front 77

Weighted mean

Back 77

A modification of the arithmetic mean, obtained by attaching weights to each value of the variable in the data set

Front 78

t-distribution

Back 78

* the parameter that characterizes the t-distribution is the degrees of freedom so we can draw the probablility density function if we know the equation of the t-distribution and its degree of freedom
* its shape is similar to that of the standard normal distribution but it is more spread out with longer tails
* its shape approaches normality as the degrees of freedom increase
*it is particularly useful for calculating confidence intervals for testing hypotheses about one or two means

Front 79

the chi-squared (x2) distribution

Back 79

* it is a right-skewed distribution taking positive values
* it is characterized by its degrees of freedom
* is shape depends on the degrees of freedom.
* it becomes more symetrical and approaches normailty as the degrees of freedom increases
* it is particularly useful for analyzing categorical data

Front 80

the f-distribution

Back 80

* it is skewed to the right
* it is defined by a ratio; the distribution ratio of two estimated variances calculated from normal data approximates the f-distribution
* the two parameters which characterize it are the degrees of freedom of the numerator and denominator
* the f-distribution is particularly useful for comparing two variances, and more than two means using the analysis of the variance

Front 81

the lognormal distribution

Back 81

* it is the probability distribution of a random variable whose log follows normal distribution
* it is highly skewed to the right
*if you take the log of the raw data (which is skewed to the right) and the result is an empirical distribution that is nearly normal, our data is lognormal distribution
* many variables in medicine follow lognormal distribution
* the properties of normal distribution can be used to make inferences about these variables after transforming the data by taking the logs of the raw data
* if the a data set has a lognormal distribution, use the geometrica mean as a summary measure of location

Front 82

binomial distribution

Back 82

* in a given situation there are only two outcomes, sucess and failure
* two parameters describe binominal distribution: n, the number of individuals int eh sample and π, the true probability for success for each individual
* its mean is nπ.
* its variance is nπ(1-π)
* when n is small the distribution is skewed to the right if π < 0.5 and to the left is π > 0.5
* the distribution becomes more symmetrical as the sample size increases and approximates the normal distribution if both nπ and n(1-π) are >5.
* use the properties of the binominal distribution when making inferences about proportions
* the normal approximation to the binominal distribution is often used when analyzing proportions

Front 83

the Piosson distribution

Back 83

* the poisson random variable is the count of the number of events that occur idependently and randomly in time or space at some average rate, μ,
* the parameter that describes the Poisson distribution is the mean or the average rate
* the mean equals the variance in the Poisson distribution
* it is a right skewed distribution if the mean is small, but becomes more symmetrical as the mean increased, when it approcimates normal distribution

Front 84

Why apply transformations to our raw data?

Back 84

When the observations in our ivestigation may not comply with the requirements of the intended statistical analysis
* a variable may not be normally distributed (a distributional requirement for many different analyses)
* the spread of the observations in each of a number of groups may be different (constant variance is an assumption about a parameter in the comparison of means using the unpaired t-test and anaylsis of variance
* two variables may not be linearly related (linearity is an assumption of many regression analyses)

It is helpful to transform our raw data to satisfy the assumptions underlying the proposed statistical techniques.

Front 85

typical transformations

Back 85

* Logarithmic transformation, z=log y
* Square root transformation, z= √y
* recipricol transformation, z= 1/y
* square transformation, z = y2
* the logit (logistic) transformation, z = ln (p/1-p)

Front 86

Logarithmic transformation, z=log y

Back 86

The effects of Logarithmic transformation are normalizing, linearizing, and variance stabilizing

Front 87

Primary study

Back 87

collect de novo (new) data to answer a specific question in a population (Example: single clinical trial)

Front 88

Secondary study

Back 88

attempt to combine or “synthesize” results (ie, existing data) from 2 or more primary studies, to generate a global/overall answer to a question (Example: meta-analysis of several clinical trials)

Front 89

Probablility

Back 89

Measures the chance of a given event occuring. It is a measure of uncertainty. It is a value from 0-1. 0 means that there is no chance that the event can occur. 1 means that the event must occur.

Front 90

The Probability of the complementary event (the event not occuring) is …

Back 90

1- the probability of the event occuring

Front 91

Approaches to calculating probability

Back 91

Subjective, frequentist, and a priori

Front 92

Subjective approach to calculating probability

Back 92

our personal degree of belief that the event will occur

Front 93

Frequentist

Back 93

the proportion of times the event would occur if we were to repeat the experiment a large number of times (tossing a coin)

Front 94

A priori

Back 94

based on a theoretical model called the probability distribution, which describes the probabilities of all possible outcomes of the experiment.

Front 95

The rules of probability

Back 95

The addition rule and the multiplication rule

Front 96

The addition rule

Back 96

If two events A and B are mutually exclusive then the probability that either one or the other will occur is equal to the sum of their probabilities. Prob (A or B) = Prob (A) + Prob (B)

Front 97

The multiplication rule

Back 97

if two events A and B are independent then the probability that both events occur is equal to the product of the probability of each. Prob (A and B) = Prob (A) x Prob (B)

Front 98

Random variable

Back 98

a quantity that can take nay one of a set of mutually exclusive values with a given probability

Front 99

Probability distribution

Back 99

shows the probabilities of all possible values of the random variable. It is a theoretical distribution that is expressed mathematically, and has a mean and a variance that is analogous to those of an empirical distribution.

Front 100

Normal (Gaussian) distribution

Back 100

One of the most important distributions in statistics. Its probability density function is: *completely described by two parameters, the mean and the variance *bell-shaped (unimodal) *symmetrical about its mean *shifted to the right if the mean is increased and to the left if decreased (assuming constant variance) *flattened as the variance is increased and more peaked as the variance is decreased (for a fixed mean) *the mean and the median of a Normal distribution are equal *the probability that a Normally distributed random variable, x, with mean u, and standard deviation SD, lies between (u-SD) and (u+SD) is 0.68 (u- 1.96SD) and (u+ 1.96SD) is 0.95 (u- 2.58SD) and (u+ 2.58SD) is 0.99. These intervals may be used to define reference intervals.

Front 101

The standard normal distribution

Back 101

The standard normal distribution has a mean of 0 and a variance of 1. If the random variable, x, has a normal distribution with mean u and variance v, then the standardized normal deviate (SND), z= (x-μ)/δ, is a random variable that has a standard normal distribution

Front 102

Z Scores

Back 102

A "Z-score" is a standardized score showing many standard deviations a subject's score is from the mean.

z= (x-μ)/δ

where x = raw score
μ = the mean
δ = the standard deviation

Front 103

Perez article objective

Back 103

Depression is a serious health problem that affects over 5% of the population. Antidepressants, SSRIs in particular, are not effective in over a third of the patients with this condition. In addition, traditional antidepressants have a slow onset of action. This study analyzed the effect of adding pindolol, a serotonin receptor and beta-adrenoceptor antagonist, to a fluoxetine antidepressant treatment.

Front 104

Perez article study type

Back 104

Experimental study

Randomized, double-blind, clinical trial

Front 105

Perez article outcome/findings

Back 105

More patients responded favorably to treatment with pindolol and fluoxetine than to treatment with placebo and fluoxetine . However, there was no reduction in the onset of action.