Exam 1 Flashcards
Define EBM
- Use of mathematical estimates of risk of benefit or harm, derived from research on samples to inform decision-making in clinical setting of diagnosis, investigation or mgmt. of individual patients.
Steps of EBM
- Ask answerable question (PICO – see flashcard) - Search for best evidence - Critical appraisal for validity and relevance - Integrate evidence, clinical expertise and patient values/preferences & apply - Evaluate results
Elements of an answerable question
- PICO - P: patient/problem/population - I: intervention - C: comparison intervention - O: outcomes
Types of clinical questions
- Background: general knowledge, typically for students, who/what/when/where etc - Foreground: seek specific knowledge for patient management (comprise ¾ PICO elements), for clinicians
What is the best medicine?
- Patient-centered
Qualities of best evidence in medicine?
- Current, valid and clinically relevant
Hierarchy of research studies by type and reliability
- Systematic review of RCTs (or meta-analyses) 2. RCTs 3. Prospective studies (typically cohort studies) 4. Retrospective studies (typically case-control) 5. Cross-sectional surveys 6. Case series 7. Case reports
Initial steps to evaluate a research paper
- Ask: Why study was done? What type of study was it? Was the study design appropriate?
Structure of research papers
- Mnemonic = A(IMRAD) - Abstract: summary - Intro: why research done - Method: how research structured - Result: findings - Analysis - Discussion
When evaluating a research paper, it is important to ask why the study was done and what hypothesis was tested? Where in the paper can this information be found?
- Intro - Hypothesis usually in intro, if not, in methods. Rarely is it found in the discussion (first paragraph).
Primary vs secondary studies
- Primary: experiments, observations, clinical trials, surveys, questionnaires 2. Secondary: reviews (systematic or non), economic analyses, decision analyses
Types of study questions. What study design is appropriate for each type?
- Therapy/intervention: RCT - Diagnosis: diagnostic validation study - Prognosis/prediction: cohort study - Harm/risk/etiology: RCT, cohort study, case-control study - Screening: ?
Define randomized controlled trial
- Subjects randomly assigned to one intervention group or another by random method. Groups should be similar, on average, except for the outcome.
Purpose of randomization
- Decreases selection bias while at the same time creating similar comparison groups.
Define concealed allocation vs blinding
- Concealed allocation: during RCT, randomization of subjects done by someone other than the investigator. - Blinding: prevents investigator or subject (single) or both (double) from knowing the group assignment (tx vs non-tx group).
Purpose of blinding
- Help avoid patients’ behaviors and ideas about treatment affecting results - Help avoid investigators inadvertently altering or changing the study results
Pros/cons of a RCT
- Pro: rigorous eval of a single variable, designed prospectively (less bias), seeks to confirm a null hypothesis, allow for meta-anlayses, minimize bias - Con: expensive, long-term (years sometimes), hidden bias (inadequate randomization, failing to randomize all eligible patients – investigator only offers entry to those who may benefit, failing to blind – see what you want to/expect to see)
Which studies tend to have less bias: retrospective or prospective?
- Prospective. We tend to see what we are looking for through our retrospectors.
Problems with randomization
- Can be unethical. Never randomize in harm study. - Impractical when # of subjects needed for statistical significance is huge
When is randomization inappropriate?
- Study involves prognosis of a disease (unethical) - Validity of a diagnostic / screening test - Investigating quality of care issues when criteria for success are not known yet
Which study designs are observational?
- Cohort studies - Case-control studies
What is a cohort study?
- Two or more groups selected based on exposure or no exposure to something in order to compare outcomes
What is a case-control study? What are case reports?
- Patients with certain conditions are matched with controls usually retrospectively for exposure to a disease-causing agent or circumstance. These studies are mostly concerned with harm or etiology. - Case reports: report of a medical history, sometimes a series of histories are reviewed/analyzed together. Weak statistically usually, but may give insight into rarities or unusual things.
What is a cross-sectional survey?
- Representative sample is interviewed, examined or evaluated about a specific question. Often information is retrospective. Can be used in studies looking to answer questions about etiology.
Studies used for etiology questions
- Case-control and cross-sectional survey
What is a systematic review?
- This is an evaluation/review comparing RCTs, combination of data from RCTs.
T/F. Systematic reviews include all original reports (even those unpublished) available pertaining to the information in the paper.
- True
T/F. Systematic reviews make conclusions based on studies with no pre-set quality criteria.
- False. Conclusions based on studies with pre-set quality criteria
Advantages of systematic reviews
- Large amounts of info assimilated quickly - Explicit limitation of bias based on selection of studies - Studies compared for consistency and generalizability - Inconsistencies between studies easily identified - Conclusions are more reliable - Meta-analyses increase precision of results (don’t have to be present)
What are meta-analyses?
- Statistical synthesis of numerical results of several studies which all addressed the same questions. Incorporates advantages of systematic reviews with powerful statistical analyses. - In other words: every meta-analysis has a systematic review process, but not every systematic review will use meta-analysis statistical synthesis.
Cohort studies are typically retrospective or prospective?
- Prospective (cohort)
Case-control studies are typically retrospective or prospective?
- Retrospective (case-control)
Are diagnostic studies randomized?
- No
How are diagnostic validation studies designed?
- Take a population/sample - Run an experimental test on them, see if positive or negative - Use the reference standard/test on this same population, see if positive or negative - Look at sensitivity vs specificity of experimental test
Questions to ask when appraising diagnosis study?
- Gold standard used to confirm the presence of absence of disorder? - Was comparison between experimental test and gold standard blinded? - Was test evaluated on an appropriate spectrum of patients?
What are important factors to look for when appraising the results section of a diagnosis study?
- Sensitivity vs specificity. An ideal test will produce a high proportion of TPs and TNs - Pre- vs post-test probability - Likelihood ratio
Sensitivity
- How well does a test find people with the condition – TP/(TP+FN) - Mnemonic = SnNout = sensitive, negative, out. So, if test has high sensitivity and a negative result is found, then there is a strong chance to rule out that the person doesn’t have the condition. Why? It does a good job finding those with the condition.
Specificity
- How well does a test find people without the condition – TN/(TN+FP) - Mnemonic = SpPin = specificity, positive, in. So, if test has a high specificity and a positive result is found, then there is a strong chance to rule in that the person has the condition. Why? It does a good job finding those without the condition.
Pre and post-test probability. How can you tell if a diagnostic test is good based on these values?
- Pre-test: estimated probability of disease before the test result is known. This is based on prevalence in population, specific population etc. - Post-test: patient’s probability of having the dz after the test results is known. This tells you if X test really works to delineate the presence of disease. ** Note: a good diagnostic test increases the post-test probability significantly. When these are similar values or equal, then the diagnostic test is not very useful.
What is a likelihood ratio? What does a high LR indicate clinically? Low? Value of 1?
- Predict likelihood of certain result in a patient with the target disorder compared to the likelihood of the same result in one without. - LR >1: increases the probability, ie. the positive test is more likely to occur in people with the dz than in those without. Diagnostic test is helpful. - LR
Most important question to ask when critically evaluating diagnostic test studies
- Will you patients be better off as a result of the test? Does adding the test (and the information obtained from the test) change management that is ultimately beneficial?
What characteristics deem a diagnostic test valuable?
- Target disorder is harmful if undiagnosed - Test has acceptable risks - Effective tx exists
Most common kind of clinical papers
- Therapy studies
Are therapy studies randomized or non-randomized?
- Randomized.
How to assess for validity of therapy studies?
- Were all groups randomized? - Were all subjects accounted for? If too many lost, results can be skewed. Is loss comparable between groups? If less than 80% (lost > 20%) completed follow up, likely invalid study. - Were the participants blinded? - Was tx equal between groups? - Did randomization produce comparable groups at the beginning?
What is the most important thing to look for in RCTs?
- Concealed allocation
What is the ideal blinding?
- No one (researcher, subject) know who receives actual treatment, ie. double-blind.
What is intention to treat?
- All data from subjects in the intervention group is analyzed even if: they withdrew before study complete, they failed to take the assignment treatment, they were reassigned to a different group.
What happens if you fail to analyze subjects within their assigned group in a RCT?
- You can skew results toward intervention
Difference between accuracy and precision?
- Accuracy: did you hit the target? - Precision: did you hit the middle of the target?
What is called when results have been influenced in some way (each and every time) that lead to a false conclusion?
- Systematic error, a type of bias
How to determine the result from a therapy study is d/t chance alone?
- Use: o Use P value: P
What does a p value of
- P
What does a confidence interval that crosses 1.0 mean?
- The result of interest is not statistically significant.
What is EER, CER, ARR, RRR and NNT?
Control Experimental Event A B No Event C D - Control event rate (CER) = A / (A+C) - Experimental event rate (EER) = B / (B+D) - Relative risk (RR) = EER/CER - Absolute risk reduction (ARR) = CER – EER - Relative risk reduction (RRR) = ARR/CER - Number needed to treat (NNT) = 1/ARR
What is NNT (number needed to treat)? What is the clinical relavence of this?
- Number of patients you would have to treat to achieve one good result or to avoid one negative result. NNT = 1/ARR - Lower the NNT, the more useful the intervention to your practice
Hoff made a big deal about not confusing prognosis studies and harm/risk/etiology studies. Tell me about it….stud?
- Harm/Risk/Etiology: what happens of happened as the result of an exposure? - Prognosis: possible outcomes of a disease or condition and/or frequency with which they may occur.
What type of study designs are appropriate for harm/etiology questions?
- Cohort (prospective), case-control (retrospective)
What is the measure/estimate of risk in a harm/risk/etiology study that has a cohort study design?
- Relative risk
What is the measure/estimate of risk in a harm/risk/etiology study that has a case-control study design?
- Odds ratio
What does an OR or RR crossing 1.0 mean?
- Suggestive of no effect
What are prognostic factors?
- Characteristics of patient/population used to more accurately predict that patient’s/population’s outcome. Eg. = demographic, disease-specific, comorbidity
When you see natural history of an ailment in a paper, it is likely a what type of study?
- Prognosis study
What is the best study design for a prognosis study?
- Cohort - Case-control to determine prognostic factors
What is referral bias?
- This is a systematic error that can occurs when people who tend to participate (or are referred to a study) in a study will be different to controls. As a result, this increases the likelihood of adverse or unfavorable outcomes.
How do you evaluate the magnitude of results from a systematic review?
1.) Odds Ratio: describe the odds of a given event in a patient in tx group compared to the odds of that event in a patient in the control group. 2.) Relative Risk: describe the risk of a given event in a patient in tx group vs the risk of an event in a patient in the control group.
Odds ratio are suited for what studies? What does an odds ratio of 1 mean?
- Odds ratio describes the odds (likelihood) of a given event in a patient in tx group compared to the odds of that event in a patient in the control group. From Geletta: the odds that a person with the dz is exposed to a potential cause for the dz relative to the odds of a person without the disease is exposed to the potential cause. - Case-control - OR = 1 implies that the event is equally likely in both groups
Relative risk (risk ratio) are suited for what studies? What does an odds ratio of 1 mean?
- RR describes the risk of a given event in a patient in tx group vs the risk of an event in a patient in the control group. From Geletta: the ratio of the incidence of a dz in people who are exposed to a risk to the incidence in people without exposure to risk. - RCTs or cohort studies - RR = 1 implies that the event is equally probable in both groups
How to calculate OR and RR?
Adverse Event + Adverse Event - Totals Therapy + A B A+B Therapy – (control) C D C+D Totals A+C B+D N (A+B+C+D) - OR = (a/b)/(c/d) - CER = C/(C+D) - EER = A/(A+B) - RR = EER/CER
Which of these is a feature of the mnemonic PICO? Patient, information, immunization, origin and place?
- Patient. PICO = patient/population, intervention, comparison intervention, outcome
Which of these study designs would be considered lowest in the generally accepted hierarchy of evidence? 1. RCT 2. Cross-sectional survey 3. Prospective cohort study 4. Meta-analysis 5. Retrospective case-controlled study
- Cross-sectional survey
Which of these is the best design for a study of therapy? 1. Case-controlled study 2. Double-blind RCT 3. Single-blind RCT 4. Cohort study 5. Cross-over trial
- Double-blind RCT
Studies of prognosis seek information on which of the following? 1. The reason a particular condition has happened 2. The results of a particular intervention 3. The outcome of a test for a condition 4. The possible outcomes of a disease or condition 5. Which patients survive longest
- Answer = 4
35 yo female to clinic w/ fresh dog bite. It appears clean. The patient does not like to take abx and asks if they’re necessary as you write the rx. Which of these components will help write an answerable question in this situation? 1. Woman with dog bite 2. Oral, prophy abx 3. No antibiotics 4. Wound infection 5. All of these will be useful
- PICO: patient/problem/population, intervention, comparable intervention, outcome - 5. All of these will be useful
Which of these sources would be most likely to provide the best information? 1. Journal of ID 2. PubMed 3. Harrison’s Internal Medicine 4. Current NEJM 5. A current textbook of ID
- PubMed
Best source for systematic reviews
- The Cochrane collaboration
68 yo male to clinic c/o painful left shoulder for several weeks. In past, injection of corticosteroids into shoulders has worked well for your patients. However, you noticed a paper on injecting steroids for tennis elbow has shown short-term improvement but worse long-term outcomes than watchful waiting. You are uncertain how to proceed. 1. What is a useful, answerable question in this situation? a. Do corticosteroids improve shoulder pain? b. In a 68 yo male with shoulder pain, will injection of a corticosteroid into the shoulder result in improvement? c. What is the course of shoulder pain in an elderly man who receives corticosteroids? d. How can shoulder pain best be relieved? e. In patients over 60, does shoulder pain improve with or without corticosteroids?
- E
45 yo healthy male comes to clinic for a routine examination. He has noted no problems during the past year. A part of his PEX includes routine UA. The test shows microscopic quantities of blood. You are worried about the finding but uncertain whether or how to proceed. Give an example of an answerable questions.
- P: male patient with microscopic hematuria - I: renal ultrasound and cystoscopy - C: watchful expectancy - O: no urinary tract disease
Which of the questions can be successfully answered by implementing a statistical technique? A. What results if one repeatedly puts blue litmus paper into acid solutions? B. What results if one repeatedly flips a fair coin? C. What is the acceleration rate of an object that is at constant velocity? D. All of the above questions can be effectively answered using a statistical technique.
- B
Ordinal variables have values A. That differ in name only B. That differ in magnitude C. In which the intervals between values are equal in size D. Both B and C
- B
Which one of the following may be classed as an interval variable? A. IQ B. Height in centimeters C. Hair color D. Percentage correct
- A
Inferential statistical techniques are used to describe data that come from entire populations and so population notation is used. This statement is incorrect because: A. If we have data on the entire population then we do not need inferential statistics. B. When describing entire populations, sample notation should be used. C. None of the statements given here correctly describe why the statement is wrong. D. Entire populations are too large to describe. E. Actually, the statement is correct.
- A
A researcher discovers that age and income are related in a systematic way. To describe this relationship, we would probably use a: A. clinical technique B. predictive technique C. correlational technique D. collateral technique
- C
Suppose you collect data on your patients and want to find out where most of them live. You have a variable in your data that is named “Place of Residence” with the following values: 1=West DSM, 2=East DSM, 3=North DSM, 4=South DSM. Which of the following graphs should be used to give you the correct answer? A. histogram B. frequency polygon C. ogive D. bar graph
- D
Data: 2, 12, 12, 27, 27, 31. This distribution: A. is unimodal B. is bimodal C. has no mode D. has a mode of 19.5
- B
Which measure of central tendency could be determined by glancing at a bar graph? A. mean B. median C. mode D. all of the above
- C
For a given distribution of scores, you are told that Σ(X - μ) = 2. Which of the following is most likely true? a. a few scores are very far above the mean b. this must be a negatively skewed distribution c. this must be a positively skewed distribution d. an arithmetic error was made
- D
In which of the following would you NEVER calculate the median? a. positively skewed distribution b. a normal distribution c. a distribution with a few very extreme scores at the upper end d. an open-ended distribution e. a distribution of a nominal variable
- E
The mean on a test is 109 and s=0. This show that: a. the distribution is rectangular b. everyone got the same score c. the variable is discrete d. only one person took the test
- B
The standard normal curve a. has relative frequency along the ordinate – which add up to a unity b. can have a mean of 50 c. has a mean = median = mode d. both A and C e. all of the above are correct
- D
Approximately what percentage of the cases in a normal distribution fall between the z-scores 1.96 and – 1.96? a. 30% b. 99% c. 47% d. 95% e. 25%
- D
Which of the following is true of all independent events? a.) P (B|A) > P (A|B) b.) P (B|A) = P (B) c.) P (A)
- B
The probability of occurrence of any one of several events is the sum of the individual probabilities when: a. the events are independent b. the events are mutually exclusive c. sampling is random d. the sum is less than 0.50 e. the events are conditional upon what occurred before
- B
Drawing one random sample from a particular population of scores a. will always produce statistics equal to population parameters b. will always result in a distribution that is exactly the same shape as that of the population c. can never produce statistics that equal the population parameters d. allow us to make inferences about the corresponding population parameters e. A, B and D are all correct
- D
A statistical inference is a.) a true statement about a population made by measuring some sample of that population b.) a guess about a population made by measuring some sample of that population c.) a true statement about a sample d.) a guess about a statistic made on the basis of a parameters
- B
Our goal in testing the null hypothesis is to a) fail to reject the null and the alternative b) reject the null and accept the alternative hypothesis c) reject the alternate and accept the null d) fail to reject the null and accept the alternative
- B
Certain assumptions are made when doing a z-test for a single mean. Which of the following is NOT one of them? a.) participants are randomly selectes b.) the sampling distribution is normal c.) the standard deviation of the population is known d.) actually, all of the above are assumptions made when doing z-test for a single mean
- D
Twenty-two women are sent a “self-confidence” questionnaire and an offer to receive a free beauty and fashion makeover. All 22 women accept and show up with their completed questionnaires. One week after the makeover, the women are again asked to fill out the “self-confidence” questionnaire. What test would you use to see if the makeover significantly changes their confidence rating? a.) z-test for proportion b.) t-test for a single mean c.) t-test for the difference between two independent means d.) z-test for the difference between two independent means e.) t-test for the difference between dependent means
- E
Which of the following statistical analysis procedures is used to measure the accuracy of diagnostic procedures a.) analysis of variance b.) multiple regression analysis c.) sensitivity and specificity analysis d.) none of the above
- C
In diagnostic testing, what is the probability of a positive test result in patients who have the condition under investigation called? a. fortitude of the test b. sensitivity of the test c. specificity of the test d. reliability of the test
- B
What are 2 focuses of statistics? Give examples.
Focus on understanding or dealing with uncertainty. (Ex: random events vs. fixed events; study of variability) Focus on collectives. (Ex: single case vs. distributions; variables)
What are the 3 ways statistics interacts with data?
- Collecting data (ex: survey) 2. Presenting data (ex: charts and tables) 3. Characterizing data (ex: average)
Give the definition of statistics.
Statistics is the science of data. It involves collecting, classifying, summarizing, organizing, analyzing, and interpreting numerical information.
What are the 2 branches of statistical methods and what is the difference?
Descriptive statistics and inferential statistics. Descriptive statistics involves collecting/presenting/characterizing data. The purpose is to describe data. Inferential statistics goes beyond descriptive statistics. It involves estimation, hypothesis testing. The purpose is to make decisions about population characteristics
Define each of the fundamental elements.
Experimental units or elements: we collect data about this object (ex: if studying performance in a hospital, the unit = the hospital) Population: all the items of interest (P: population, parameter) Variable: the characteristic of an individual experimental unit (ex: students have gender/weight/age, etc.) Sample: subset of the units of a population (S: sample, statistic)
Two types of variables? Describe each.
Categorical: some numeric or character codes (ex: qualitative like “male” or “not male”) Quantitative: the numerical result of some measurement, usually taken using some standard unit. (ex: blood pressure)
Define data
- Result of some measurement. Collection of numbers and characteris organized into a file system.
Define process.
A process is a series of actions or operations that transforms inputs to outputs.
Name variable scales that are qualitative
- Nominal and ordinal
Name variable scales that are quantitative
- Interval and ratio
What is a nominal scale?
The simplest level of measurement – categories without order
What is an interval scale?
Measurable difference or interval or distance between observations. Equidistance between the measurements.
What is an ordinal scale?
Nominal variables with an inherent order among the categories. Eg. stages of cancer. Semblance of order with this, but no measurement.
What is a ratio?
Measurable difference or interval or distance between observations with an absolute reference point (such a “0”). Eg. height, weight, age
What’s the difference between an interval scale and a ratio?
The absolute reference point – ratio has the absolute reference point and an interval does not
Give examples of an interval and a ratio.
Interval: time of day on a 12-hour clock; political orientation on a standardized scale Ratio: inches or cm on a rule; income; GPA, height, weight
Give examples of a nominal and ordinal scale.
Nominal: Meal preference as breakfast, lunch, dinner; Religious preference as 1=Buddhist, 2=Muslim, 3=Christian, 4=Jewish, etc.; Political orientation as Republican, Democrat, Libertarian, Green, etc. Ordinal: Rank as 1st, 2nd, last place; level of agreement as no, maybe, yes; political orientation as left, center, right.
How is qualitative data presented differently than quantitative data?
Qualitative data: Summary table which can then given as a Bar graph or Pie chart Quantitative data: Dot plot, Stem & Leaf display, or Frequency Distribution (which can then be transformed into a Histogram)
What is a summary table?
It lists categories and number of elements in a category. It may show frequencies (counts), percent or both.
What is a bar graph?
Shows qualitative information. Has a zero point. The vertical bars represent the categories (classes) of qualitative variables and the y-axis is used for frequency or percent with bar height. Bars don’t touch.
What is a pie chart?
Shows qualitative information. Pie chart shows the breakdown of total quantity into categories or slices of pie relative to one another. Angle size is a percent (out of 360) and each slice is proportional to the class relative frequency.
Do the key terms class, class frequency, class percentage or class relative frequency refer to qualitative or quantitative data?
Qualitative
What is a class?
One of the categories into which qualitative data can be classified.
What is class frequency?
The number of observations in the data set falling into a particular class.
What is the class relative frequency?
The class frequency divided by the total numbers of observations in the data set.
What is the class percentage?
Class relative frequency multiplied by 100.
What is a dot plot?
A graphical method for describing quantitative data. Horizontal axis is a scale for the quantitative variable (e.g. percent). Quantitative measurement is represented by a dot; repeating data values are seen as dots stacked on top of each other. No vertical axis. Good at showing density.
What is a stem and leaf display?
It has two columns and divides data into a “stem” (such as 1 for 10 or 5 for 50) and a “leaf” (such as a 6 beside a 2 = 26). Stem values are in the left column with their leaf values in the right adjacent column. Shows density of stems.
What is a histogram?
Similar to a bar graph but bars touch. Horizontal axis has class intervals (not qualitative data) and the bars over each class interval have a height that represents the class frequency or relative frequency.
What is a central tendency?
The tendency of data to cluster or center about certain numerical values.
What is variability?
The spread of data, ie. the wideness or closeness of data in the set. Can compare data sets in terms of overlapping or dispersion.
What’s the difference between a statistic and a parameter?
A statistic comes from a sample; a parameter comes from a population. If a statement is about a very large group of people, it almost always has to be a statistic because there is no way someone asked every single person in a large group of people (ex: 40% of dog owners scoop poop when they walk their dog.) If a statement is about a specific group and EVERYONE in the group/population was asked, then it is a parameter. (ex: 90% of a kindergarten class likes vanilla ice cream or 10% of US senators voted for a cheesecake law.)
What is the standard notation for mean, size, standard deviation, and variance of a sample
Note: English letters Sample mean: x bar Sample size: n Sample standard deviation: s Sample variance: s2
What is the standard notation for mean, size, standard deviation, and variance of a population?
Note: Greek letters Population mean: u (mu) Population size: N or T Population standard deviation: σ (sigma) Population variance: sigma2
Define mean. Is this affected by outliers?
Most common measure of central tendency. Acts as ‘balance point.’ Affected by extreme values (‘outliers’) Denoted x bar in sample, mu in population
Is mean always the center of data distribution?
- No, it follows outliers
What are 3 measures of central tendency? Which is the most common?
Mean (balance point), median (middle value when ordered) and mode (most frequent). Most commonly used = mean.
Define median. Is this affected by outliers?
Measure of central tendency. Middle value in ordered sequence. If n is odd, the median is the middle value of sequence. If n is even, the median is the average of 2 middle values. You find the position of the median in sequence by = (n+1)/2 Not affected by extreme values.
Define mode. Is this affected by outliers?
Measure of central tendency. Value that occurs most often. Not affected by extreme values. May be no mode or several modes. May be used for quantitative or qualitative data.
Define range.
Measure of dispersion. Difference between largest and smallest observations.
T/F. Range can be used to determine distribution of data.
- False. This values simply tells you the difference between the largest and smallest observations in a data set. It ignores distribution of data.
What is the calculation used to determine the distribution of data?
- Variance and standard deviation.
Define variance and standard deviation.
Measures of dispersion. Most common measures. Consider how data are distributed about the mean (x-bar or mu) Standard deviation is the square root of variance.
What’s the important of skew and how does it change based on mean and median? Describe what a left and a right skewed graph looks like?
Skew depends on the mean location compared to the median. Median is stable while mean pulls to the extremes/outliers. Left skew = mean median (largest frequency of data is to the left)
What is the empirical rule?
It approximates the percent of measurements lying a certain distance from the mean. This only applies to mound shaped & symmetric data sets (aka normal distributions).
68% of measurements seen in a data-set that has a normal distribution lie within how many standard deviations from the mean?
- ~1 SD
95% of measurements seen in a data-set that has a normal distribution lie within how many standard deviations from the mean?
- ~2 SD
99.7% of measurements seen in a data-set that has a normal distribution lie within how many standard deviations from the mean?
- ~3 SD
Define probability.
A measure of the likelihood that something can happen Can only assume a value between 0 and 1. 0=no chance; 1=certainty.
In lecture we spoke about defining probability according to what definition?
- Frequetist
How do you calculate probability?
Divide the frequency of times an outcome occurs by the total number of possible outcomes.
What is probability used for and when is it unnecessary?
Used to predict any random event (outcome can vary). Unnecessary when dealing with a fixed event (outcomes set by design or always the same).
Define relative frequency.
In a long run time period, relative frequency = probability of occurrence.
A researcher randomly selects a sample from a population of 432 people, 212 of whom are women. What is the probability of selecting a woman as the first participant in this study?
P(w) = 212/432 = 0.49
A hypothetical population consists of eight individuals ages 13, 14, 17, 20, 21, 22, 24 and 30. What is the probability that a person in this population is a teenager?
Teenagers = 13, 14, and 17. Probability(teen) = 3/8.
Give 2 definitions for an event.
- An occurrence due to nature. (ex: the event that a 30yo person lives to 70th person) 2. A collection of one or more outcomes of an experiment. (ex: 2 coin tosses – possible outcomes include HH, HT, TH or TT) In probability, events are represented by uppercase letters such as A, B, C.
Define experiment and outcome.
Experiment: the act of observing or taking measurement. Outcome: a particular result of a measurement.
Explain simple vs. compound probabilities.
Simple = single occurrence. Compound events = the probability of more than one event happening together
Characteristics of events in probability
- Independent events. Use special rule of multiplication for this. Special rule of multiplication applies to this. The word “and” is used. - Mutually exclusive events (aka disjoint): events that can not occur simultaneously. Eg. male and female – one can be one but not the other. Additive law applies to this. The word “or” is used. - Complementary events
Explain the difference between the 3 basic operations that can be used to create compound events.
Intersection: where event A and event B overlap = “both A and B.” This is denoted as A ∩ B. Union: all of event A or B or BOTH A and B. This is denoted as A ∪ B. Complement: everything that is not A is considered the complement of A. This is denoted as A^C or A-bar
What is the additive rule of probability (aka special rule of addition)? When do you use it?
Two events A and B that cannot occur simultaneously are said to be mutually exclusive or disjoint (ex: male cannot equal female; pass cannot equal fail). Additive rule of probability: P (A ∪ B) = P(A) + P(B).
What is the general rule of addition? When do you use it?
When the events overlap / are not mutually exclusive. Add the probability of A to the probability of B and then subtract the probability of the overlapping portion. General rule of addition: P (A ∪ B) = P(A) + P(B) – P (A ∩ B)
Given the table, calculate the following 1. P (A) 2. P (D) 3. P (C ∩ B) 4. P (A ∪ D) 5. P (B ∩ D)
see SG 1. 6/10 2. 5/10 3. 1/10 4. = P(A) + P(D) – P(A ∪ D) = 6/10 + 5/10 – 2/10 = 9/10 5. = 3/10
Define independent events. How is their probability calculated?
Independent events = two unrelated events. TO calculate, use the special rule of multiplication.
What is the general rule of multiplication and how do you calculate it?
- If we know event A has occurred, the probability that two events A and B will both occurs is equal to the probability of A multiplied by the probability of B given A. - P(A ∩ B) = P (A) * P (B|A). - Rearrange: P (B|A) = P (A ∩ B)/P (A)
Using the table, calculate? 1. P(A|D) 2. P(C|B)
see SG for table 1. = P (A ∩ D) / P (D) = (2/10)/(5/10) = 2/5 2. = P (C ∩ B) / P (B) = (1/10) / (4/10) = ¼
What is the special rule of multiplication?
In independent events, where P(A|B) = P(A) and P(B|A) = P(B), then you can multiple to get P(A ∩ B) = P(A) * P(B)
Is a coin toss a disjoint or independent event?
Independent because the one event does not affect the other’s probability. Use rule of multiplication.
If two coins are tossed, what is the probability of getting a tail on the first coin and a tail on the second coin?
P (T ∩ T) = P(T) * P(T) = 0.25
Events A, B, C and D occur. What is the probability of A or B or C occurring? If the events are not mutually exclusive, what is the probability of A or D occurring?
- P(A or B or C) = P(A) + P(B) + P(C) - P (A or D) = P (A) + P (D) – P (A and D)
Events A, B and C occur. If these events are independent, what is the probability of events A and B and C occurring? If events and A and B are not independent, then what is the probability of A and B occurring?
- P(A and B and C) = P(A) x P(B) x P(C) - P (A and B) = P (A|B) X P (B)
What is Bayes’ Theorem?
When events are not independent, the multiplicative rule can be used. P(A|B) * P(B) = P(B|A) * P(A)
How is Bayes’ Theorem applied in medicine and why is it important?
It is important because investigators usually only know one of the pertinent probabilities and must determine the other. For example, given a given accuracy level of the PSA test, and a positive PSA test rest, what is the probability that the person tested has the disease? Given that tests give us test probabilities, not real probabilities, Bayes’ theorem finds the actual probability of an event from the results of the tests.
What is prior and posterior probability?
Refer to Bayes’ Theorem P(A) is called prior probability because it is known before the calculation (in the right hand side of Bayes’ Theorem). P(B|A) is called posterior probability because it is known only after the calculation (if on the left hand side of Bayes’ Theorem).
What does P(B|A) and P(A|B) mean?
P(B|A) is a conditional probability – the probability of B given that A is true. P(A|B) is also conditional – the probability of A given that B is true.
Apply Bayes’ Theorem to the chance of having cancer according to tests. – Sorry this is long, but helpful.
P(A|X) = (P(X|A)*P(A)) / (P(X|A)*P(A) + P(X|not A)*P(A)) P(A|X) = chance of having cancer (A) given a positive test (X) – how likely is it to have cancer with a positive result? P(X|A) = chance of a positive test (X) given that you had cancer (A) – this is the chance of a true positive. P(A) = chance of having cancer. P(not A) = chance of not having cancer. P(X|not A) = chance of a positive test given that you didn’t have cancer – this is a false positive Simplified – it all comes down to the chance of a true positive result divided by the chance of any positive result: P(A|X) = P(X|A)*P(A) / P(X)
What is a sampling distribution?
It is the probability distribution of a sample statistic calculated from a sample of n measurements.
What’s the difference between an unbiased estimate and a biased estimate of a parameter?
Unbiased estimate: the sampling distribution of a sample statistic has a mean equal to the population parameter that the statistic is intended to estimate. Biased estimate: the mean of the sampling distribution is not equal to the parameter.
What are 2 properties of the sampling distribution of x bar?
- Mean of the sampling distribution equals mean of the sampled population 2. Standard deviation of the sampling distribution equals (standard deviation of sampled population)/(square root of sample size)
What is the standard error of the mean?
The standard deviation (sigma x-bar) is often referred to as the SEM.
How is the sampling distribution of x-bar standardized?
Standardized normal distribution is a normal distribution centered on zero (by converting mean to a z-score).
What is the Central Limit Theorem?
As sample size gets large enough, sample distribution with x-bar mean will be approximately a normal distribution with mean mu.
What is the confidence interval?
- It is a range of possible values containing the population parameter. It includes uncertainty and extends the range over which our population mean might be found with a certain confidence.
With higher confidence, what happens to the interval size/distribution?
- Wider interval. - Example: 95% CI, interval = +/- 1.96 SD above and below mean. - 98% CI, interval = +/- 2.34 SD above and below mean - 99% CI, interval = +/- 2.58 SD above and below mean
What is the meaning of 95% confidence level?
- 95% of our confidence intervals with contain mu (population mean) and 5% will not. The 5% area on either side of the man is referred to as alpha as a total area or alpha/2 for each side.
What conditions are required for a valid confidence interval for µ (mu)?
- A random sample is selected from the target population. 2. The sample size n is large (n>=30). Due to the central limit theorem, this condition guarantees that the sampling distribution of x-bar is approximately normal. Also, for large n, s (sample SD) will be a good estimator of σ (sigma).
What is the difference between a t-statistic and a z-statistic?
- T-statistic: used when we have no idea of the population standard deviation. Sample standard deviation (s) replaces the population standard deviation (sigma). T-statistic has a sampling distribution very much like that of a z-statistic (mound, symmetric, mean = 0). It is more variable than z-statistic.
Define degrees of freedom.
A way to express how much the amount of variability in the sampling distribution of t depends on the sample size n. Df = n-1
How is t-distribution affected by degrees of freedom?
As degree of freedom goes down, the t distribution flattens out. Kind of elastic. Interval around mean widens.
Define sampling error.
An expression of the reliability associated with a confidence interval for the population mean u. The sampling error or margin of error is the interval within which we want to estimate u with 100(1-a)% confidence. Denoted SE. SE = half-width of the confidence interval.
What sample size is needed to be 90% confident the mean is within + or – 5? A pilot study suggested that the SD= 45.
N = ((za/2)2 * a2) / (SE)2 = (1.645)2 * (45)2 / (5)2 = 219.2 = 220
Define hypothesis.
A statistical hypothesis is statement about the numerical value of a population parameter. Ex: I believe the GPA of this class is 3.5!
Define null hypothesis.
Denoted H0 – It represents the hypothesis that will be accepted unless the data provide convincing evidence that it is false.
Define alterative hypothesis.
AKA research hypothesis. Denoted Ha – It represents the hypothesis that will be accepted only if the data provide convincing evidence of its truth.
Characteristics of an alternative hypothesis.
. Opposite of null hypothesis 2. Hypothesis that will be accepted only if the data provide convincing evidence of its truth 3. Designated Ha 4. Stated in one of the following forms: Ha is either , or does not equal (some value)
When do we use hypothesis testing?
In observational studies to find the “true” population parameter. Eg. What is the prevalence of AIDS in some community?
What is a test statistic?
A sample statistic, computed from information provided in the sample, that the researcher uses to decide between the null and alternative hypotheses.
Define type 1 error (aka alpha error).
A type 1 error occurs if the researcher rejects the null hypothesis in favor of the alternative hypothesis when, in fact, the null (H0) is true.
Define rejection region.
The rejection region of a statistical test is the set of possible values of the test statistic for which the researcher will reject H0 in favor of Ha.
Define type II error (aka beta erro).
A type II error occurs if the researcher accepts the null hypothesis when, in fact, it (H0) is false.
List the 7 elements of a test of hypothesis.
Null hypothesis, Alternative (research) hypothesis, Test statistic, Rejection region, Assumptions, Experiment and calculation of test statistic, and lastly Conclusion (if test statistic falls in rejection region, we reject null and conclude Ha to be true).
Define assumptions.
Clear statement(s) of any assumptions made about the population(s) being sampled. It is an element of a test of hypothesis.
How do you apply p-value?
The p-value is a function of the observed sample results that is used for testing a statistical hypothesis. Before the test is performed, a threshold value is chosen, called the significance level of the test, traditionally 5% or 1% and denoted as α. If p-value > or = to α, do not reject H0 (fail to reject) If p-value
What conditions are required for a valid hypothesis test for µ (mu)?
- A random sample is selected from the largest population. 2. The same size n is large (n >/= 30). Due to the central limit theorem, this condition guarantees that the test statistic will be approximately normal regardless of the shape of the underlying probability distribution of the population.
Describe the 2 possible conclusions for a test of hypothesis.
- If the calculated test statistic falls in the rejection region, reject H0 and conclude that the alternative hypothesis Ha is true. State that you are rejecting H0 at the α level of significance. Remember that the confidence is in the testing process, not the particular result of a single test. 2. IF the test statistic does not fall in the rejection region, conclude that the sampling experiment does not provide sufficient evidence to reject H0 at the α level of significance. [Generally, we will not “accept” the null hypothesis unless the probability B of a type II error has been calculated.
If working with 2 qualitative variables, what are the different approaches to determine the relationship between the 2 variables?
Tabular approach: table of data compares the 2 Graphic approach: bar graphs compares side by side the placebo (control) vs. experiment Numerical approach: table can be summarized into a single number in the form of an odds ratio
If working with 1 qualitative and 1 quantitative variable, what are the different approaches to determine the relationship between the 2 variables?
Tabular or graphic (bar graph) descriptions. (For example, of stages of cancer with average age) Box-Whisker plot (better): median = line within box, lower and upper limits of box = lower and upper quartile boundaries, whiskers point upper quartile to max and lower quartile to min. Stars indicate outlier. Numerical summery of the relationships using Spearman rank-order correlation coefficient (If there are no repeated data values, a perfect Spearman correlation of +1 (strong +ve relationship) or −1 (strong –ve relationship) or 0 = no relationship.
When working with two quantitative variables, what are the different approaches to determine the relationship between the variables?
Histogram Scatter plot: valid to see relationship between variables if no outliers
What is the strength of a correlation and how is it determined?
The strength of a correlation reflects how consistently scores for each factor change. When plotted in a graph, scores are more consistent the closer they fall to a regression line. Zero correlation = no linear pattern; perfect correlation = data point falls exactly on a straight line.
What is a regression line?
The best fitting straight line to a set of data points. A best fitting line is the line that minimizes the distance of all data points that fall from it. Positive regression = low left, high right. Negative regression = high left, low right.
What is the Pearson correlation coefficient?
(r) is used to measure the direction and strength of the linear relationship of two factors in which the data for both factors are measured on an interval or ratio scale of measurement. -1 or +1 = strong relationship
What is a regression analysis?
A statistical procedure used to determine the equation of a regression line to a set of data points to determine the extent to which the regression equation can be used to predict values of one variable, given known values of one variable, given known values of a second factor in a population.
What type of correlation analysis is used for quantitative dependent variable?
- Regression analysis
What type of correlation analysis is used for qualitative dependent variable?
- Logistic regression analysis
How are rates similar to proportions?
- Proportions are a number of observations divided by the whole. - Rates: similar to proportions except a multiplier is used (eg. 100). These have a time reference.
What are vital statistic rates?
- Aka demographic measures, these describe the health status of a population. - Examples: mortality rates (crude and specific) and morbidity rates
What is mortality rate? Two types of mortality rates?
- Rate of deaths in population 1. Crude: # of all deaths in a given geography over a given year divided by total population in same geography during the same year. 2. Specific: as above but specific to certain populations based on gender, race, age, cause etc.
What is morbidity rate? What is this aka?
- # of individuals who develop a dz in a given period of time in a certain geography divided by the total population of geography over the same given period of time. - Aka: prevalence rate of dz
What is incidence vs prevalence?
- Incidence: # of new cases that have occurred during a given interval of time divided by the total population at risk - Prevalence: proportion of individuals who have the disease
Why is it necessary to adjust mortality and morbidity rates sometimes?
- Mortality and morbidity rates can be influenced by different characteristics of a population. - To make a fair comparison between different populations, adjustment techniques are used to remove confounding factors (age, gender, race, ethnicity etc.) - Eg. If we have an aging population, mortality rate is likely going to be high because high age = high probability of death.
Define ARR (absolute risk reduction) and RRR (relative risk reduction)
- The reduction in risk (with the experiment/intervention) compared with the baseline risk. - The amount of risk reduction relative to the baseline risk
What does a RR (relative risk) or OR (odds ratio) of
- Experiment or exposure was protective
What does a RR (relative risk) or OR (odds ratio) of > 1 mean?
- Experiment or exposures was risky/not protective
What does a RR (relative risk) or OR (odds ratio) of 1 mean?
- Experiment or exposures had no relationship or effect on the outcome
T/F. The distribution of RR (relative risk) or OR (odds ratio) do follow the theoretical probability distribution.
- False, The natural log of RR and OR do follow the normal distribution. In other words, you need to transform with log to general inferential statistics.
