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Statistics Flashcards

1
Q

Type I Error

A

alpha error = false positive

Statistical test shows that there is a difference when one does not exist

Cause by incorrect stat test or random error

if alpha = 0.05, then 1 in 20 times, a type 1 error will occur even when H0 is rejected
Meaning 5% of the time, a researcher will conclude there is a statistically significant difference when there is not

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2
Q

Type II Error

A

beta error = false negative

Statistical test concludes there is no difference when one exists

Cause by insufficient power

Large sample size helps decrease chance of error

Typical acceptable error rate = 0.10-0.20

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3
Q

Ordinal data

A

Qualitative variable (categorical)

Ranked in a specific oder, but no consistent level of magnitude of different between ranks

Example: Likert Scale (strongly agree, agree, neutral, etc); Wong-Baker Faces Pain Rating Scale; Pain rated 0-10); NYHA I, II, III, IV

NOT real numbers

Do not use mean or standard deviation to report

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4
Q

Interval/Ratio Data

A

Quantitative variables (continuous): can take on any value within a given range

Have a CLEAR numerical value (# hospitalizations, # pregnancies)

Interval has no true 0 but ratio does

Interval: degrees Fahrenheit
Ratio: degrees Kelvin, heart rate, blood pressure, time, distance

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5
Q

Nominal Data

A

Qualitative variable (categorical)

Data with mutually exclusive categories but no rank or order

Ex: presence of event/disease state (yes/no); gender, race; mortality (dead or alive)

Often expressed as a %

Ex: Pain severity using descriptive terms (minimal, moderate, sharp, aching)

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6
Q

Random Error

A

Unavoidable, unidentifiable circumstance randomly introduced into a study that is caused by chance or nonsystematic error

Minimize with statistical testing and increased sample size

May impact reliability of results. Can be controlled but not eliminated

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7
Q

Intention to Treat

A

Once randomized, then analyzed

Maintains integrity of randomization

Conservatively presents results to mimic real world conditions

Preferred type of analysis for superiority trial

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8
Q

Delta Margin

A

Minimum clinically acceptable difference based on previous research

Used in noninferiority trials

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9
Q

Noninferiority trial

A

Alternative design when unethical to use placebo

Aim: demonstrate intervention is no worse than control by delta margin

Large sample needed for adequate power

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10
Q

Practice-based Research

A

Evaluates value of program/service to improve clinical outcomes and/or decrease cost

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11
Q

Confidence Interval

A

Range of values that probably includes the true treatment effect

Large sample size = narrower, more precise confidence interval

Usually expressed as 95% CI (corresponding to alpha of 0.05)

If continuous variables: 95% CI that includes 0 = not statistically significant
If CI for risk ratio (odds, relative risk, hazards), 95% that includes 1 = non statistically significant

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12
Q

Absolute Risk Reduction/Increase

A

Difference in risk between control group and intervention group

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13
Q

Relative Risk Reduction/Increase

A

% reduction in risk in intervention group compared with control group

RRR = (1 - RR) * 100
RRI = (RR - 1) * 100

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14
Q

Relative Risk

A

Incidence of outcome in exposed group compared with unexposed group

Used in cohort studies

RR < 1: risk of disease lower risk in exposed group
RR = 1: Risk is the same
RR > 1: risk of disease is higher in exposed group

The RISK of someone developing a condition when exposed compared to someone who has NOT been exposed (risk of developing developmental neurologic disorders when exposed to thimerosal compared to someone who was not exposed)

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15
Q

Case Report/Case Series

A

Observational study - looks at outcome

Case report = 1 patient
Case series = group of patients or a series of case reports

No measure of association

Pro: identifies potential therapies for rare disease, unusual ADRs
Describes innovative approach
Hypothesis generating
Inexpensive, easy to perform

Con: Weakest form of evidence due to lack of study elements that reduce bias. Does not establish causality OR association

CARE guidelines describe what should be in the report

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16
Q

Surrogate Marker

A

Outcome measure of a lab value, physical biomarker, or other intermediate measure instead of clinical outcome

Convenient

Example: surrogate marker for hypertension is blood pressure

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17
Q

Per protocol (final analysis)

A

Only patients completing the entire study included in final analysis

Preferred type of analysis for noninferiority

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18
Q

Log Rank Test (Mantel-Cox)

A

Survival analysis

Compare survival distributions between two or more groups (H0 = no difference in survival between the two populations)

Assesses differences between groups in survival rate

Assumes random sampling, consistent criteria for entry or end point, baseline survival does not change as time progresses, censored subjects that same average survival time as uncensored

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19
Q

Cox Proportional-hazards (cox regression)

A

Survival analysis

Most popular method to evaluate impact of covariates

Predict time to experience an event taking into account covariates

Allows for calculation of hazard ratio and CI

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20
Q

Kaplan-Meier Survival

A

Survival analysis

Reflects cumulative proportion of surviving participants and is recalculated every time an event occurs

Estimates proportion of people who would survive a given length of time under the same circumstances

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21
Q

Crossover Clinical Trial

A

Type of RCTs

Subject serve as own control by receiving all interventions under investigation in a sequential order with washout period between different interventions

Do not use in diseases that are not curable

Do not use if patient cannot return to pretreatment status before each treatment

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22
Q

P value

A

Probability that results are due to chance, not the intervention

Calculated chance that a type 1 error has occurred

A lower p-value does NOT mean result is more important or meaningful, just that it is statistically significant and not likely to be attributable to chance

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23
Q

Parallel clinical trial

A

Each subject receives/is assigned to one intervention

Data from all subjects in specific group are pooled together and compared with data from other groups receiving different interventions
+ outcome
intervention – outcome

population
+ outcome
control – outcome

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24
Q

Interventional Study Design

A

Randomized Controlled Trials

Aim: determine cause and effect by investigating whether differences exist and quantify differences between interventional & control groups

Need to employ methods to minimize risk or error, bias, confounding (ex: blinding, randomization, statistical analysis)

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25
Observational Study Design
Cross-sectional, Case-control, Cohort Aim: demonstrate association (NOT causation) between exposure and outcome Can be retrospective or prospective Prospective cohort > retrospective cohort > case control > cross-sectional
26
Systematic Error/Bias
Avoidable, identifiable, and non-randomly introduced into a study Most important way to reduce bias = blinding, randomization
27
D4 Approach to Biostats
Design of study (independent/parallel or dependent/crossover) Designated # groups (2 or >2) Data types (Interval/Ratio, Ordinal, Nominal) Distribution
28
Number Needed to Harm
Number of patients needed to treat over a specified period for 1 to experience an adverse event
29
Number Needed to Treat
Number of patients who would need to be treated over a specified period for 1 patient to be spared a harmful event or experience a beneficial event NNT = 100/ARR (%) or 1/ARR (decimal) ARR = Control - intervention (X-Y) Calculate when there are significant results (!!) for primary outcome (nominal data) Extrapolation beyond studied time points should NOT occur.
30
Case-control Study
Observational Study- looks at outcome Examines individuals with an outcome of interest to determine if there are exposures associated with development of the outcome Retrospective. The outcome is known at the beginning of the study. Measure of association: odds ratio Pro: Good for studying rare outcomes with multiple exposures, esp. unknown risk factors Pro: Inexpensive, short duration. Con: Confounding MUST be controlled Con: Observational and recall bias Con: Selection bias (see below) Critical assumptions to minimize bias: 1) cases selected are to be representative of those who have disease. randomly select when possible. 2) controls are representative of general population. identical to cases minus presence of disease. 3) information collected same way for cases & controls
31
Cross-sectional Study
Observational Study --AKA Prevalence study (snapshot) Identify the prevalence of a condition in a group of individuals. Studies done by interview, questionnaire, biomedical info. Measure of association: prevalence Pro: Provides epidemiology information Pro: include larger sample size compared with case report Pro: Include patients regardless of disease severity, access to care Con: Cannot determine incidence of outcomes or study factors in individual over time Con: Not ideal for rare exposure, outcomes, or conditions Ex: prevalence of serious eye disease and visual impairment in north London population Ex: maternal characteristics and migraine pharmacotherapy during pregnancy
32
Cohort Study
Observational Study - looks at exposure Determines ASSOCIATION between exposures/factors and DEVELOPMENT of a disease/condition Can be prospective or retrospective. In both, need to exclude those with outcome already from the study population. Measure of Association: relative risk Retrospective: -better for rare outcomes (can investigate issues that may have ethical/safety issues in RCT). -less expensive. -Con: impacted by confounding variables, recall bias Prospective: -can control confounding variables easier. -can develop temporal relationship. -Con: more expensive and time consuming. -Con: more difficult to study rare outcomes than retrospective. Ex: Framingham Study: prospective cohort of subjects studied over time to evaluate relationship between variety of exposures to development of CV Ex: Thimerosal DTP: retrospective cohort investigated impact of thimerosal on developmental neurologic disorders
33
Selection bias
An error in the selection/sampling of individuals for clinical study, which leads to advantage for one group over the other Impacts case-control studies more than cohort
34
Performance/interviewer bias
Difference in care provided Interviews not conducted in a uniform manner
35
Detection bias
Difference in how the outcome was assessed
36
Attrition bias
Difference in withdrawal rates from the study
37
Observational/information bias
Incorrect determination of outcomes or exposures. Ex: error in recording individual factors for a study (risk factor, timing of blood sample)
38
Compliance/adherence bias
More subjects in one group fail to follow protocol
39
Recall bias
Subject in one group more likely to accurately remember facts of interest "Cases" are more likely to remember exposures than "controls"
40
Odds Ratio
Prevalence of EXPOSURE in group with outcome compared with group without outcome Use in case control study Interpreted as "odds of exposure to a factor in those with a condition or diseases compared to those who do not have the condition or disease" OR <1: odds of exposure is lower in diseased group OR = 1: odds of exposure is same in two groups OR >1: odds of exposure is greater in the diseased group If CI crosses 1, then no statistical difference
41
Intervention = Y Control = X
Positive outcome Intervention (Y) = a Control (X) = c Negative outcome (Y) = b (X) = d Y = a /(a+b) X = c/(c+d) ARR = X - Y RR = Y/X RRR = (1 - RR) * 100 OR = (A/C)/(B/D) or (A*D)/(B*C)
42
Dependent/Normal/Parametric Stats Test for Interval/Ratio data
2 groups: Paired t-test Multiple measures in >=2 groups: repeated measure ANOVA or ANCOVA
43
Dependent Stats Test for Ordinal Data
2 groups: Wilcoxon signed rank Multiple measure in >=2 groups: Friedman
44
Dependent Stats Test for Nominal Data
2 groups: McNemar Multiple measure in >= 2 groups: Cochrane Q
45
Independent Stats Test for Interval/Ratio Data
2 groups: t-test >2 groups: one -way & two-way ANOVA or ANCOVA
46
Independent Stats Test for Ordinal Data
2 groups: Mann-Whitney U (Wilcoxon rank sum) >2 groups: Kruskal-Wallis
47
Independent States Test for Nominal Data
2 groups: Fischer's exact >2 groups: Chi-square
48
Mean
A numerical measure of central tendency used in descriptive statistics Use for continuous & normally distributed data (think interval, ratio) Arithmetic or geometric -geometric involves log-normal distributions
49
Visual methods for descriptive statistics
Frequency distribution Histogram Scatterplot Boxplot
50
Median
Numerical measure of central tendency used for descriptive statistics "50th percentile" Use for ordinal or continuous (interval/ratio) data Not affected by outliers
51
Mode
Numerical measure of central tendency used for descriptive statistics Most common value - sometimes there is more than 1 Can be used for nominal, ordinal, or continuous data
52
Standard deviation
Numerical measure of variability used for descriptive statistics Measure of variability about the mean Only applies to continuous data!! that are normally distributed Empiric rule for normal distribution: 68% of data found within +/- 1 SD 95% of data found within +/- 2 SD 99% of data found within +/- 3 SD
53
Coefficient of variation
SD/mean * 100 Relates mean and the standard deviation
54
Range
Numerical method to describe variability in descriptive statistics Difference in smallest and largest value in data set (easy calculation) but does not provide much info. Very sensitive to outliers. Often reported as actual values (like 0 - 50) instead of range = 50
55
Percentiles
Numerical measure of variability for descriptive statistics Ex: 75th percentile; 75% of all values are smaller Does NOT assume normal distribution
56
Interquartile range
Numerical measure of variability for descriptive statistics defined as 25-75th percentile
57
Frequency distribution
Visual method for descriptive statistics that shows how often a value appears in a set of data
58
Histogram
Visual method for descriptive statistics that plots distribution of numeric values as a series of bars
59
Scatterplot
Visual method for descriptive statistics that has dots represent two different numerical values
60
Box plot
Visual method for descriptive statistics that uses boxes and lines to depict distributions of 1 or more groups of numeric data Box limits = central 50% of data Central line = median
61
Inference
An educated statement about an unknown population
62
Binomial distribution
Population distribution type. Discrete distribution. 2 possible outcomes. Probability of obtaining each outcome is known You want to know the chance of observing a certain # of successes in a certain # of trials (finite) Ex: Flipping a coin. Either heads or tails Probability of getting tails in 10 tries
63
Poisson distribution
Population distribution type Discrete distribution Counting events in a certain period of observation. Avg # of counts is known Aim: likelihood of observing a various number of events (infinite) Probability of 'r' events in a population Ex: How to staff a call center when get x amount of calls in x minutes
64
Normal distribution
Most common model for population distribution How to tell if data is normal: -visually (bell shape) -Mean & median will be about equal (nonvisual, but studies may not report both) -formal test = Kolmogorov-Smirnov
65
Parametric
Term for normally distributed data Parameters, mean, and SD completely define distribution of data
66
Probability
Likelihood that any one event will occur given all the possible outcomes
67
Distribution of means
If you pull separate samples from a single population in normally distributed data, the means will be slightly different However if you take the mean of the 'distribution of the means', it should be equal to unknown population mean
68
Central limit theorem
The distribution of means from random samples is about normal regardless of underlying population distribution
69
Standard Error of the Mean (SEM)
Standard deviation of means in distribution of means SEM = standard deviation / square root of n (sample size) Quantifies uncertainty in the estimate of the mean, which is important for hypothesis testing and 95% CI estimation
70
95% vs 90% confidence interval
95% will always be wider, so it is more likely to encompass the true population mean 95% CI = mean +/- 1.96 * SEM 90% CI = mean +/- 1.64 * SEM
71
Null hypothesis
H0 = states no difference between groups being compared Results of hypothesis testing: Reject H0 = statistically significant difference between groups (unlikely attributable to chance) Accept H0 = no statistically significant difference between groups
72
Alternative hypothesis
HA = states that there is a difference between groups being compared
73
Nondirectional, difference hypothesis test
Asks ''are the means different?'' Use traditional 2 sided t test & CI
74
Nondirectional, equivalence hypothesis test
Asks ''are the means practically equivalent?'' Use two 1-sided t-test (TOST) & CI
75
Directional, superiority hypothesis test
Asks ''is mean 1 > mean 2?" Use traditional 1-sided t-test & CI
76
Directional, noninferiority hypothesis test
Asks ''is mean 1 no more than a certain amount lower than mean 2?'' Use CI
77
Power
power = 1-B (probability of making a type II error) Dependent on: -predetermined alpha -sample size -desired effect size -variability of outcomes you want to measure Decreased by poor study design, small sample size, incorrect statistical tests
78
Effect size
Size of difference between outcomes
79
Necessary components to estimate sample size
-Acceptable type II error rate (0.10-0.20) -Observed difference in predicted study outcomes that is clinically significant AND its expected variability -Acceptable type I error rate (0.05) -Statistical test used for primary end point
80
Parametric test
Assumes: -Normal or near normal underlying distribution (mean ~ median) -QUANTITATIVE CONTINUOUS DATA (INTERVAL OR RATIO) -Investigated data have homoscedasticity
81
Homoscedasticity
Data being investigated have variances that are homogenous between groups Important for parametric tests
82
Nonparametric tests
Data are NOT normally distributed May be skewed quantitative continuous data, quantitative (discrete) data, or qualitative (ordinal/nominal) data
83
Correlation
Examines strength and direction of association between two variables Correlation does not reflect one variable is useful in predicting the other (correlation does not equal causation) Closer 'r' is to 1, the more highly correlated the variables are Closer 'r' is to 0, the weaker the relationship AKA degree of association Visual inspection of scatterplot is ESSENTIAL before using correlation analysis
84
Regression
Examines ability of one or multiple variables to predict a dependent variable Commonly used to determine whether differences exist btwn groups after controlling for confounding variables Purposes: develop prediction model & estimate accuracy of prediction
85
Pearson correlation
Correlation test that is a measure of strength of relationship between two CONTINUOUS variables that are normally distributed & linearly related Hypothesis test determines whether correlation coefficient is different from 0 -- highly influenced by sample size
86
Spearman rank correlation
Nonparametric correlation test of the strength of a monotonic association (linear or nonlinear) between two CONTINUOUS variables. Can be used for ordinal data as well.
87
Point-biserial correlation
Nonparametric correlation test of strength and direction of association between one dicotomous variable (nominal) and one continuous variable (I/R)
88
Coefficient of determination
r2 or R2 = used to describe how well regression analysis was predicted (extent of variability in dependent variable that can be explained by independent variable) Range from 0 to1 r2 of 0.80 = 80% of variability in Y is explained by variability in X Does not provide info for relationship of X and Y, rather describes how clearly a regression model worked.
89
Multiple linear regression analysis
Regression analysis One continuous dependent variable + two or more continuous or categorical independent variables Aim: find effect of one or more variables on a dependent variable while controlling for the effects of other independent variables
90
ANCOVA
Multiple regression model Continuous & categorical independent variables Aim: determine effect of one or more categorical variables (factors) on a dependent variable while controlling for effects of one or more continuous variables (covariates)
91
Simple logistic regression
Regression model One categorical dependent response variable and one continuous or categorical explanatory variable
92
Multiple logistic regression
Regression model Oen categorical dependent response variable and two or more continuous or categorical explanatory variables Aim: discern the effect of one or more variables on a dependent variable while controlling for effect of covariates
93
Nonlinear regression
Regression model Variables are not linearly related PK equations derived from here
94
Polynomial regression
Regression model Any number of response and continuous variables with a curvilinear relationship (cubed, squared)
95
y=mx + b
linear regression Y = dependent variable m = slope x = independent variable b = y intercept
96
Survival analysis
Studies the time between entry in a study and some event (death, MI)
97
Quasi-experimental study
Evaluate interventions and causality but are NOT randomized
98
Internal validity
Degree to which the outcome can be explained by differences in the assigned groups Related to study methods (proper design, conduction, analysis) Factors that affect internal validity: -poor study design -inadequate randomization -lack of/inappropriate blinding -Using inaccurate measurements -Using inappropriate statistical methods -Incomplete outcome reporting Occurs more in nonrandomized or observational studies
99
External validity
The degree to which findings can be generalized to a population beyond the study Factors that affect external validity (6 S's): -Setting -Selection of patients (inclusion/exclusion, placebo/treatment) -Study patient characteristics (clinical characteristics, race/sex, uniformity of pathology, comorbidities, severity of disease) -Selected trial protocol is not same as routine practice (intervention timing, appropriateness of control, frequency of monitoring) -Study outcome measures & follow up (accepting surrogate markers, reproducibiilty of findings, frequency/adequacy of follow up -Side effects (discontinuation rates, completeness of ADR reporting, intensity of safety procedures
100
Misclassification bias
Subject is categorized into incorrect group
101
Differential bias
Type of misclassification bias when information errors differ between groups Ex: in cohort, difference between those with disease and those without Nonrandom error
102
Non-differential bias
Type of misclassification bias when results collected are incorrect, but affect both groups the same Systematic error
103
Confounding variables
Nonrandomized variable Affects independent or dependent variable - unable to determine true effect on measured outcome (may hide OR exaggerate true association) Minimize: -randomize -match subjects in analysis by stratification, propensity score matching, or multivariable analysis techniques
104
Point prevalence vs period prevalance
Point prevalence: prevalence on a given date Period prevalence: prevalence in a period (year, month)
105
Hazards ratio
Estimates risk at any given point in time within a certain time period HR <1: lower risk of the event in experimental group than in control (experimental treatment better than control treatment) HR = 1: event rates are the same in both groups HR >1: greater risk of event in experimental group than in control group (experimental treatment is worse than control treatment)
106
RR/OR = 0.75? RR/OR = 3.0?
0.75: RR = 25% reduction in risk (1-0.75) OR = odds are 0.75/1 3.0: RR = 200% (3x increase in risk) OR = odds are 3/1 higher So for RR, take the RR value - 1 to get the reduction or increase in risk OR will be the OR value/1
107
Types of blinding (single, double, triple, double dummy, open)
Single: either subject or investigator blinded Double: both subject and investigator blinded Triple: subject, investigator, and analysis group blinded Double dummy: match active & control groups when difference in delivery (IV or PO, will get placebo of the opposite) Open label: everyone aware
108
Types of randomization (block, stratification, cluster)
Block: divide groups into blocks, then randomize Stratification: group based on similar characteristics Cluster: randomly assign groups, not individuals
109
Types of treatment controls (active, historical)
Active: compare experimental with established treatment Historical: compare new treatment to a group of patients treated in the past
110
Factorial design
Answers two separate research questions in a single group of subjects Used in RCTs
111
Composite end point
Used in RCTs - combines several events into 1 event category (CV events) - even combining morbidity and mortality Results for each individual end point within composite should also be reported Several limitations -difficult to interpret -dilute effect -average overall effect (if component end points move in opposite directions, the overall composite would be averaged) Benefits -increase # of events, so can reduce sample size & cost (good for investigator) -do not need multiple tests
112
As-treated analysis
Type of analysis where subjects are analyzed by actual intervention received If assigned to active treatment, but did not take active treatment, then analyzed as if in placebo group Destroys randomization process. Use with caution.
113
Narrative review
Summarizes several studies, but no systematic methods. Subjective. Ex: standard literature review
114
Qualitative Systematic Review
Comprehensive literature search using explicit methods (inclusion/exclusion criteria), critically appraise it, and synthesize Objective Includes systematic review.
115
Quantitative Systematic Review
AKA Meta analysis Systematic review using statistical techniques to summarize the results of all studies evaluated Details of each study are essential -- relies on criteria for inclusion of previous studies & statistical methods to ensure validity Use FOREST PLOT to summarize
116
Heterogeneity
use in Meta Analysis states the degree of variation or difference in results across several studies included in analysis. Do not want a lot of heterogeneity. Common tests: Chi2, Cochran Q, I2 i2 < 25% = low heterogeneity = studies similar i2 25-50% = moderate heterogeneity = caution needed i2 50% = substantial heterogeneity = difficult to draw conclusions from meta analysis Chi2 = p value for null hypothesis that there is no heterogeneity in the studies If p <0.01, then reject null and assume there is heterogeneity
117
funnel plot
assesses publication bias in meta analysis studies Y axis = study precision (standard error) X axis = estimate of effect of each study Graph should look like an inverted funnel, because higher sample size studies will have higher effect size Asymmetrical plot = publication bias **look at examples
118
Absolute risk
Chance of an outcome occurring Absolute risks are more important than relative risks
119
Absolute risk difference (reduction/increase)
Difference in the absolute risk (chance of outcome occurring) in exposed vs unexposed group
120
Guidelines for clinical trials
CONSORT = clinical trials STROBE = observational studies PRISMA = meta-analysis and systematic reviews EQUATOR = international guidelines
121
Cost minimization
Pharmacoeconomic study that shows the difference in cost among comparable therapies are evaluated therapies must have similar outcomes
122
Cost effectiveness
Pharmacoeconomic study to measure the cost impact when health outcomes are improved ex: years of life saved, number of symptom free days, blood glucose, blood pressure
123
Cost utility
Pharmacoeconomic study that compares outcomes related to mortality when mortality may not be the most important outcome Ex: quality adjusted life years (QALY)
124
Cost benefit
Pharmacoeconomic study that analyzes cost of treatment and cost saved with beneficial outcomes
125
Sensitivity vs specificity
Sensitivity: proportion of TRUE POSITIVES that are CORRECTLY identified by test. high sensitivity = negative test can rule out disorder Calculated as true positive/(true positive + false positive) Specificity: proportion of TRUE NEGATIVES that are CORRECTLY identified in a test. High specificity = positive test can rule IN the disorder Calculated as true negative/(true negative + false negative)

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