Transcript Statistics - Stony Brook University School of Medicine

Research Tools
Robert Woroniecki, MD, MS
Why do we need research tools?
• To answer research questions, i.e.
• Choice of tools will depend on asked question
• Question choice will depend on
– Motivation
– Available tools
– People’s around
Telemachus and Mentor
Antonie van Leeuwenhoek
& microscope
Darwin
& Beagle
Wilhelm Röntgen
& X-ray
Jonas Salk
& Henrietta Lacks
Ronald Fisher
& statistical tests
Mario Capecchi
& knockout mice
A tool is any item that can be used to
achieve a goal, especially if the item is
not consumed in the process.
IRB
• A federally mandated committee charged with
responsibility:
– To review proposed research
– To ensure that the rights of research participants are
protected
– To ensure that risk of harm to participants is
minimized
– To ensure selection of subject is equitable
– To ensure additional safeguards for any vulnerable
subjects
Formulating Question and Choosing the Tool
• Formulating a study question is the first step in a designing
research project and choosing the tools that might work.
• Knowing you want to do a research in an area is not enough eg.
- I want to do research on kidney or kidney transplantation - too
general, and not a question
Examples of possible research questions
- What proportion of ESRD patients receive kidney transplant
- Does blood type determine length of waiting time on tx list
How to select research question
• Interest/motivation
• What will be the impact of your findings?
• Novelty , if already done is there room for
improvement?
Feasibility: do you have tools?
• Time – residency lasts only 3 years, time goes by
fast!!
• Sufficient study population – can enroll enough
subjects to report a meaningful result
The 4-question schema
Causation
(mechanism)
Ontogeny
(development)
Adaptation
(function)
Phylogeny
(evolution)
Molecule
Cell
Organ
Individual
Family
Group
Society
Alcock, 2001
Study Question Quality
• Descriptive – are descriptive !
eg. Prevalence of CKD in a specified population
Graft survival after kidney transplantation
Proportion of patients with Alport’s syndrome who go on to develop ESRD.
Proportion of patients who develop CMV viremia in the first year of Tx
• Analytic - comparative
eg. Is graft survival better with LRD when compared to DDRT ?
Do ACE/ARB reduce the risk of progression to ESRD in patients with alport’s?
Are patients who receive prophylaxis less likely to develop CMV viremia?
Has your question been answered?
Look up literature and keep references organized!
• PubMed: http://www.ncbi.nlm.nih.gov/pubmed
• EndNote: http://it.stonybrook.edu/software/title/endnote
Hypothesis
Primary research question should be driven by the hypothesis rather
than the data, i.e. a statement of expectation or prediction that will
be tested by research
• Null Hypothesis (H0) - no difference
- no association
• Alternative Hypothesis (HA) - difference exists
- association exists
Eg.
H0 : there is no difference in graft survival between deceased and
living donor kidney transplants
H0: There is no association between dialysate sodium concentration
and post dialysis serum sodium concentration in adult patients
receiving hemodialysis
Study Question
• Analytic are more interesting than descriptive
• Answering analytic questions enables
development of intervention
• For Both types
- Need to specify study population eg. Men,
Adults, elderly, kidney transplant recipients,
ESRD patients etc..
Data and tools to manage it
Variables
• Continuous (interval) age, BP, temp, cholesterol, mRNA,
immunofluorescence optic density
• Categorical
– Dichotomous eg Yes or No, Male or female, Alive or dead
– Ordinal eg. Scale - NYHA classification for CHF, Likert scale
– Nominal : can’t be ordered eg. Ethnicity
DEFINE OUTCOME
For conducting a study you need to decide
- what is the outcome of interest?
eg. graft survival
- what variable best describes/measures your outcome of interest.
eg. serum creatinine (interval variable)
return to dialysis (categorical variable yes/no)
- What independent variables should you also measure
eg. age, gender, ethnicity, DM, HTN
• Outcome variable = dependent variable
• Independent variable= explanatory variable, grouping
variable
Data collection
• Source - National databases eg. UNOS, USRDS, DHS
-
DCI
Institutional database (EMR)
Questionnaire
Patient Chart
Interview
• Entry/Storage - EpiData or Epi-info
http://www.epidata.dk
http://wwwn.cdc.gov/epiinfo/7/
- Excel
- Access
• Data analysis software – SPSS, STATA, SAS
Software
Software
http://biostat.mc.vanderbilt.edu/wiki/Main/PowerSampleSize
Univariate Statistics
Analysis of a single variable.
Continuous
Categorical
Variable may be independent or outcome variable
Continuous :- Age of the study population, eGFR, blood pressure
- mean
- median
- mode
- variance & standard deviation
Categorical variables/discrete variables
eg. Gender, ethnicity , death, ESRD, Likert scale
- Proportion/percentage
- Frequency tables
- Events that occur over time - survival curves and incidence rate
Graphic Display of Univariate statistics
Graphic Display of Univariate statistics
Graphic Display of Univariate statistics
Graphic Display of Univariate statistics
Graphic Display of Univariate statistics
You have to know what you are doing
What is the problem with this picture?
Bivariate statistics
Measure of association between 2 variables.
Association of discrete outcomes (categorical variables) (eg.
yes/no)
• Chi square test
• Fisher’s exact
Continuous outcomes:
• t-test
• ANOVA
• Correlation
Measuring association between 2 dichotomous variables
Condition
(disease)
No Condition
(no disease)
Incidence
Incidence in exposed = a/a+b
Exposed
a
b
Unexposed
Incidence in unexposed = c/c+d
C
d
Odds
Odds (probability of disease) in
exposed= a/b
Odds of disease in unexposed = c/d
• Relative risk : - the risk of developing disease
Ratio of incidence in exposed to that in
a
b
unexposed.
C
d
(a/a+b)/ (c/c+d)
• Odds Raito :- odds of developing disease in
exposed divided by that in unexposed.
(a/b)/(c/d) = a*d/b*c
• For rare diseases odds ratio approximates
relative risk !
Chi Square test
• Compares observed outcome to expected outcome.
• Independent and outcome variable are both categorical
OR=ad/bc
CMV
NO CMV
Valcyte
a
b
No Valcyte
C
d
If expected cell size <5 then use Fisher’s exact test
t-test
• Association of a dichotomous variable and a continuous
variable
• Independent variable is dichotomous and outcome variable
is continuous.
• Used to compare the mean between two groups. eg. eGFR
between men and women
•
t=mean of eGFR in men – mean of eGFR in women
Standard error of the difference between the two
Assumptions – eGFR is normally distributed in both men and women
The variances are equal
Non parametric test if assumptions not met – Mann-Whitney test which is based on ranking instead of mean (mean is
not an accurate reflection of distribution in a non-normally distributed population)
ANOVA
• Association of a nominal variable with a continuous variable
• Compare means in more than 2 groups
eg. Difference in mean blood pressure readings between
blacks, whites and Hispanics.
Assumption – normal distribution, equal variance
If assumptions not met – Kruskal-wallis test
Correlation ≠ causation
• Measure of the strength and direction of a relationship
between two continuous variables
• Typically represented by Pearson r
• Eg. Age and eGFR
Pearson’s correlation coefficient (r) ranges from -1 to +1
0 means there is no relationship
Correlation ≠ causation
• Possible causes of correlation: reverse causation, common
causes
If non normally distributed continuous variables use spearman’s rank correlation.
Confounding
• Apparent association between a risk factor
and an outcome is affected by the relationship
of a third variable to the risk factor.
Risk Factor
Outcome
Confounder
Confounding Example
How do you prevent confounding ?
OBESITY
CKD
DM II
Eg. If you want to investigate whether obesity is a risk factor for CKD, type II
DM (which is also associated with obesity) may be a confounder.
If you observe that obesity is a risk factor for CKD must make sure the effect
you are seeing is not the effect of DM II on CKD .
Question
How can you minimize confounding?
• If confounder is unknown – randomization
• If confounder is known – adjust for it
Multivariate analysis
• A statistical tool for determining the unique (independent)
contribution of various factors to a single outcome.
• Essential b/c most clinical events have more than one cause and a
number of confounders.
We live in a multivariable world – most outcomes have multiple causes.
Eg. A bivariate analysis may tell us that smoking, obesity, sedentary life
style, hypertension and diabetes are associated with an increased
risk for coronary artery disease but … are these factors independent
of one another? i.e does a risk factor remain significant after
adjusting for the other risk factors ?
Useful to eliminate confounding during the analytic phase of a study!
Multivariable analysis
• Multiple Linear regression
• Multiple Logistic regression
• Survival analysis & Proportional hazards
analysis
Linear Regression
•
•
•
•
Outcome variable is continuous eg. Creatinine, age, blood pressure
Independent variables may be continuous or categorical
Also determines the strength of association between outcome and independent variables
Specifically allows one to predict and quantify what happens to an outcome variable for
different values of independent variables.
•
Simple (bivariate) regression:
What value of Y would we predict given a value of X?
For multiple regression –adjust for additional regressors (independent variables) that may also
affect outcome
•
Increase in risk associated with a unit change in the independent variable
–
–
How much does income rise with one more year of education.
How much more (or less) income do males earn (as compared to females)?
Each additional year of education is associated with x amount increase in income.
Eg. For each additional year of education, annual income increases by an average of 1000 dollars.
Compared to women, on average men earn x amount more income
Logistic regression
• Dichotomous outcome
• Independent variable may be categorical or continuous
• Gives odds ratios
Eg. Effect of weight on development of diabetes
Effect of race on development of hypertension
As weight increases the odds of developing diabetes also increases by x fold.
Blacks are more likely to be diagnosed with hypertension that Caucasians (
OR= x)
Interpretations
Eg. OR= 2 => 2 fold increased risk of …
OR=1.3 => 30% increased risk of …
Multiple Logistic regression
• Outcome variable dichotomous
• Reports odds ratio
• Adjusts for other variables in the model - > reveals risk
independent of the other variables in the model
Interpretation of OR
• Odds ratio of 1 means no difference in risk between 2
groups
• OR <1 means less risk
• OR >1 means higher risk
What does a regression do?
• Predict a dependent variable (or response variable or
outcome) using an independent variable (or explanatory
variable or treatment)
• Show the “effect” of the independent variable on the
dependent variable
– Independent variables also called:
• explanatory variable
• treatment variable
– Dependent variable also called:
• response variable
• outcome variable
Choosing regressors
• Select potentially relevant variables on basis
of theoretical arguments rather than
statistical ones
• From statistical arguments, there is always
small probability of drawing the wrong
conclusions (prob of rejecting null when null is
true-Type I error)
How to choose regressors?
• Include potential confounders
• Factors identified in previous studies
• Factors hypothesized to matter on substantive grounds
• DON’T include alternative measures of the outcome,
predictors eg. GFR and creatinine
• DON’T include intervening variables eg. If studying the
effect of education on income do not include
occupation
Adjusted Risk factors for death and graft failure
Death
Graft Failure
OR (95% CI)
OR (95% CI)
CMV Disease
3.44(1.29-9.17)*
2.9(1.26-6.65)*
Age
1.03(1.01-1.06)*
0.99(0.98-1.02)
Gender
1.35(0.66-2.81)
0.96(0.55-1.70)
Black †
0.4(0.15-1.04)
1.76(0.93-3.34)
Hispanic†
0.61(0.22-1.39)
0.91(0.40-2.10)
Live Donors
0.56(0.27-1.15)
0.40(0.21-0.77)*
CAD
1.35(0.66-2.77)
1.29(0.69-2.43)
HTN
0.45(0.09-2.2)
0.48(0.14-1.66)
Diabetes
0.97(0.47-1.9)
1.23(0.66-2.28)
Events that occur over time
• Compare outcomes that occur over time
• outcome variable is the time until the occurrence of an
event of interest.
• Kaplan Meier analysis – use log rang test to assess survival
difference between two groups
• Proportional hazard analysis – comparison of event rate in
two or more groups. Assumes a given risk factor is constant
over the entire study period (proportionality assumption)
A risk factor is independently associated with
an outcome when the effect persists after
taking into account the other risk factors and
confounders.
Software
Outline
• Study Design
–
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–
–
–
–
Study question
Choosing the study design
Hypothesis
Type I and Type II error
Power and Sample size
Confounding and Bias
Statistical significance
• Data collection and management
• Statistical Analysis
- Univariate statistics
- Bivariate statistics
- Multivariate statistics
- Predictive studies
Predictive studies
•
•
•
•
•
Sensitivity
Specificity
Positive predictive value
Negative predictive value
Likelihood ratio
Sensitivity
Proportion of people with the disease who are
positive on the test
Subjects with positive results/total number of
subjects with disease
= TP/TP+FN
Specificity
Proportion of subjects without the disease who
are negative on the test
Subjects with true negative results/total number
of subjects without the disease
= TN/TN+FP
• No mater how sensitive the test it does not
help to rule in the diagnosis
• b/c sensitivity does not tell you the possibility
of a positive test is a false positive
• Conversely no matter how specific a test it
does not help to rule out the diagnosis b/c it
does not tell you the possibility that your
negative results is a false negative
Predictive values
• PPV = subjects with true positive test/total
number of subjects with positive results
= TP/TP+FP
• NPP= subjects with true negative test/total
number of subjects with negative results
= TN/TN+FN
Accuracy
= TP+TN/Total sample size
Likelihood Raito
Likelihood ratio of a positive test =
probability of a positive test in someone with disease
probability of positive test in someone without the disease
= Sensitivity/(1-specificity)
Likelihood ratio of a negative test =
Probability of a negative test in someone with the disease
Probability of a negative test in someone without the disease
= (1-Sensitivity)/specificity
Study Design
• Observational
- Investigator assesses a study population without
altering the condition or group assignment
eg. - Cross sectional
- Cohort - prospective or retrospective
- Case control
• Experimental
- Investigator manipulates the condition or group
assignment. Typically one group receives a treatment
and the other group receives a different treatment or a
placebo.
Cross-sectional
•
•
•
•
Easy to conduct
Fast
Takes a snap-shot of the study population
Used to answer descriptive questions eg.
Prevalence of a disease
• Not good at answering analytic questions – cause
and effect can not be established
 Helpful to determine prevalence which is used in estimating
sample size for analytic studies.
Cohort Studies
Prospective cohort
Study population is assembled prior to development of an
outcome and followed overtime.
At entry subjects are assessed for exposures of interest and
evaluated to make sure they do not already have the
outcome being studied.
eg. If you want to follow individuals prospectively to see if
they would develop CKD and assess risk factors for CKD it
doesn’t make sense to include CKD patients in the cohort.
Provide stronger evidence for a causal relationship and help
to exclude reverse causality
Eliminate recall bias
Determine incidence
Cohort studies cont..
Famous prospective cohort
Framingham Heart Study
Disadvantage – take tooo long esp if disease
develops slowly , costly , inefficient for
studying rare diseases.
Retrospective Cohort – outcome has already
occurred – you go back (recall bias)
Case-control studies
• Subjects are assembled based on whether they have
experienced the outcome (cases) or not (controls).
• Once cases and controls identified the frequency or
risk factors are compared b/n the groups.
• Advantage: Efficient esp for studying rare diseases
• Recall bias is a problem
• Selection bias – if disease is deadly most of the cases
are dead and “cases” may not be fully representative
Type I error (aka alpha error)
• Rejecting the null hypothesis when it is true.
Null Hypothesis (H0) – no difference/no association - TRUE
Alternative Hypothesis (HA) – difference/ association exists - False
• The probability of a type I error is the level of
significance of the test of hypothesis
• Denoted by alpha (α)
• Mostly set at 0.05
Statistical significance
• .05 (i.e., a 95% probability of not detecting an impact,
when if fact there is no impact)
• Or “The statistical analysis shows that there is <5% chance
of the findings being due to chance alone”
• When alpha <0.05 we reject the null hypothesis
• Rejecting the null=>implicit evidence for the alternative
hypothesis
• There is a statistically significant difference!
Type II error
• occurs when one fails to reject the null hypothesis when
it is actually false (i.e the alternative hypothesis is true)
Null Hypothesis (H0) – no difference/no association - False
Alternative Hypothesis (HA) – difference/ association exists - TRUE
Conclude there is no difference when one exists
• The probability of a type II error is denoted by beta (β)
Power
• Probability of rejecting the null when Ha is true (the
alternative hypothesis)
Null Hypothesis (H0) – no difference/no association - False
Alternative Hypothesis (HA) – difference/ association exists - TRUE
• Alternative phrasing: “detecting an impact, when in fact
there is an impact”
• Power = 1-Prob(Type II error)
• Power = 1- β
• Power of .80 is desirable (i.e., an 80% probability of
detecting an impact, when in fact there is an impact)
Type I error
Type II error
Power
α
β
1-β
H0
True
False
False
HA
False
True
True
Action
Reject
Fail to reject
Reject
Probability
0.05
0.2
0.8
Sampling
Why sample ?
Not feasible to study the entire population
Uses of sampling
• Make generalizations about the population of interest
• A large population of interest can be studied efficiently
and accurately through examination of a carefully
selected subset or sample
• Obtain information at an acceptable cost
Sample ideally is representative of the population under
study.
Confidence Interval
• Confidence Interval
= Best Guess (Point Estimate) plus or
±
minus about 2 standard errors
• Provides a range or boundary around a sample estimate
• This range of values will contain the truth 95% of the
time.
Sample Size calculation
Depends on the type of the study design and type of variable and analysis
planned
Eg. For a bivariate analysis comparing 2 means you will need
-
Alpha level (Type 1 error ) mostly 0.05
Power (Type II error) mostly 80%
Effect size (anticipated difference b/n the two means)
Standard deviation of the interval variable (estimated sd of the variable)
*If you have a sample power can be calculated
Softwares!
Things to consider when planning a study
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Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
•
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Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
•
•
•
•
•
•
Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
Bias
• Systematic Error
• Can occur with both randomized and observational studies
• Can occur at all stages of the study
Selection of subjects
eg. Investigator steering subjects into one group.
Measurement
eg. Investigator and subjects forming an expectation based on the subjects’
assigned group that alters their assessment of improvement
Follow up
eg. Subjects assigned to placebo group may drop out of the study.
In a study investigating if angioplasty is better
than medical management for renal artery
stenosis – if patients with poor baseline renal
function are preferentially assigned to the
angioplasty group – the results of the study
may be biased against angioplasty.
How do you eliminate bias?
Strategy to eliminate bias
• Group assignment should be done at the time of enrollment
by someone who has not contact with the participant using a
random table generator.
• Blinding & Double Blinding
But not always possible + sometimes ethical problem eg. Sham
procedure – giving IV contrast without angioplasty to compare
PTA vs medical management for RAS .
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Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
Generalizability
• Ability to apply the results of a study to a population other than
the study sample.
• More of a problem with randomized studies.
– Conditions of randomized subjects are different from the
conditions of clinical practice – given more attention and
monitoring
– Randomized subjects by definition different from the
general population – volunteer, willing to take frequent
exams and blood draws etc….
 Here lies the difference between efficacy and effectiveness
of a treatment!!!
•
Observational studies more closely approximate treatment
effectiveness but still – Participants in observational studies
may receive more attention than standard clinical care.
Merely observing participants changes their behavior –
Hawthorne effect!
Increasing Generalizabillty requires
Appropriate sampling to ensure sample is representative of
the population under study.
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Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
Length of time to conduct
• Observational studies may be faster to
conduct if you have an existing database or
can use a case control design.
• But cohort studies (even observational) take
long – more than one’s lifetime
•
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Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
Expense
• Randomized – expensive!!
• Even more expensive than observational cohort b/c in
observational trial the cost of interventions is not paid by the
study b/c investigators are merely observing whereas in trials
the cost of all interventions – drugs, surgery, procedure, test is
covered by the study.
•
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Confounding
Bias
Generalizability
Length of time to conduct
Minimize expense
Addressing a broader range of questions
Addressing a broader range of questions
• Observational studies are able to answer a broader
range of questions than randomized
• Eg. It will be unethical to randomize people to smoke
– but can observe outcome in smokers
Propensity score adjustment can be done to see if there are differences
in covariates (independent variables) among smokers vs non smokers.
• Randomized studies are not helpful in identifying
causes of disease outbreaks, food borne illnesses.
Specific advantage of randomized and observational studies
Randomized
Eliminating Confounding
X
Minimizing Bias
X
Observational
Increasing Generalizability
X
Speed in conducting study
X
Minimizing Expense
X
Addressing a broader range of questions
X
Reserve the use of observational studies to instances where it is unethical or
infeasible to perform randomized controlled trials, or when time is of an
essence in obtaining a result.