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### Preparation for USMLE Step 1

### Prostate Cancer No Prostate Cancer Total

### Prostate Cancer No Prostate Cancer Total

### Prostate Cancer No Prostate Cancer Total

### Prostate Cancer No Prostate Cancer Total

### Prostate Cancer No Prostate Cancer Total

Ronald J. Markert, PhD ronald.markert@wright.edu

Adrienne Stolfi, MSPH

adrienne.stolfi@wright.edu

Today’s Topics

- Research designs and methods
- Measurement
- Hypothesis testing
- Risk
- Clinical diagnostic testing
- Statistical tests
- Miscellaneous

I. Descriptive studies

Case series

II. Explanatory studies

A. Experimental

Randomized controlled trial (RCT)*

B. Observational

1. Cohort*

2. Case-control (retrospective)

3. Cross-sectional

-------------

*prospective

prospective vs. retrospectiveprospective: characteristic to outcome RCT and cohort studyretrospective: outcome to characteristic case-control study

Internal Validity: can results be believed?

Is confounding avoided?

Is bias avoided?

External Validity (generalizability)

Are results generalizable to your setting or interest?

Systolic hypertension in elderly program (SHEP)

JAMA (265:3255-64, 1991)

60 years of age and older with isolated systolic hypertension

(average follow-up 4.5 years)

antihypertensive

medications placebo

(n = 2365) (2371)

stroke 96 149

but suppose

mean age 61 74

RCT cohort case-control cross-sectional

Questions

1. most time efficient and least financially costly?

2. yields the highest quality of data?

3. not likely to raise ethical issues?

4. medical records can lead to poor data quality?

5. most suitable for studying uncommon diseases?

6. best for avoiding confounding?

RCT cohort case-control cross-sectional

Questions

7. recall bias can be a problem?

8. best for cause-effect relationship?

9. “switching” groups can occur?

Amoxicillin High-dose, short courseStandard course

Randomized Day 0 345 346

Completed regimen/

specimen obtained 335 333

Did not complete regimen/

specimen obtained 10 13

Specimen obtained 345 346

Do you compare 335 to 333? OR Do you compare 345 to 346? Why?

What is the analysis of the 345 and 346 called?

Random Assignment Random Sampling

(Random Allocation) (Random Selection)

in

RCT

Is confounding avoided? Is sample representative

of population?

Internal Validity External Validity

(Generalizability)

Random Assignment Random Sampling

(Random Allocation) (Random Selection)

in

RCT

Is confounding avoided? Is sample representative

of population?

bias: not affected by Is sample representative

random assignment of my practice?

- Independent variable (characteristic)
- Dependent variable (outcome)
- Types of data
- Nominal (categorical, i.e. counts)
- Ordinal
- Numerical: continuous, discrete
- Data distributions
- Mode, Median, Mean
- Standard deviation, Standard Error, Confidence Intervals

Nominal

Sex, Race, Blood Type, ______________

Ordinal

Education Level, Stage of Cancer, ____________

Numerical (continuous, discrete)

age, heart rate, blood pressure, ______________

When data are normally distributed, the mode, median, and mean are identical and are located at the center of the distribution.

Serum cholesterol values for adults (age 40-60)

n = 85

182 229 188

165 218

306 197

mean = sum of values

85

median = point at which 1/2 of values are above and below

(i.e., 43rd highest value)

mode = value that occurred most frequently

standard deviation

Tronvik E et al. Prophylactic treatment of migraine with an angiotensin II receptor blocker. JAMA 2003; 289: 65-69.

Migraine experience during 12-week period

Candesartan (n = 57) Placebo (n = 57)

Migraine hours 59.4±66.6 92.2±76.8

± standard deviation

Is there a small or large amount of variation among subjects regarding migraine hours?

approximately 68% of the observations in a set of data

lie between the mean and 1 standard deviation

~95% lie between the mean and 2 standard deviations

~99.7% lie between the mean and 3 standard deviations

Establishing a normal range (in medicine)

1. locate a disease-free population

(reference population)

2. perform test (e.g., glucose)

3. plot distribution

4. mark off central 95% of reference population

--------------------------------------------------------------------------

serumnormal range

fasting glucose 70-110 mg/dL

sodium 135-146 mEq/L

triglycerides 35-160 mg/dL

standard error of the mean (SEM)

How precisely does the sample statistic (e.g., the mean) estimate the population parameter (e.g., mean)?

SEM = SD

The Standard Error (SE):

The 95% CI for sample means, proportions, and differences between means or proportions are equal to:

Point Estimate +/- 2(SE)

These CIs are symmetric around the point estimate, AND:

For differences between means or proportions:

If the 95% CI includes the value zero, the differences are not statistically significant at alpha = 0.05.

Heart rates: healthy college students

n = 400 = 69.88 SD = 5.90

SD 5.90

SEM = = = .30

95% CI = ± 2 x SEM

69.88 ± 2 x .30

69.88 ± .60

95% CI = 69.28 to 70.48

OSU 95% CI = 72.50 to 73.98

A physician would like to estimate the average heart rate (bpm) in a particular population. In a random sample of 100 individuals from the population, he obtains a mean heart rate of 70 bpm and a standard deviation of 16 bpm.

The 95% confidence interval is?

Steps of statistical hypothesis testing:

1. Formulate null and research hypotheses

2. Set alpha error (Type I error) and

beta error (Type II error)

3. Compute statistical test and

determine statistical significance

4. Draw conclusion

1. Formulate null and research hypotheses

Null Hypothesis (H0):There is no difference between groups;

there is no relationship between the independent and

dependent variable(s).

Research Hypothesis (HR): There is a difference between

groups; there is a relationship between the independent

and dependent variable(s).

2. Set alpha error (Type I error) and beta error (Type II error)

Acceptable error in hypothesis testing:

Alpha (): 0.05 conventional

Beta (): 0.10 to 0.20

Thus, power (1 - ) = 0.80 - 0.90

Consequences of error:

A drug or treatment is judged effective when it

may not be

Consequences of error:

A possibly effective drug or treatment is judged

ineffective

The possible outcomes in statistical hypothesis testing

Patients with in-hospital procedures and events

Stanford (n = 233), %McGill (n = 285),%p

Invasive procedures

angiography 55 34 <.0001

angioplasty 30 13 <.0001

bypass surgery 10 4 <.0001

Noninvasive procedures

exercise test 20 56 <.0001

left ventricular

function test 59 86 <.0001

Events

reinfarction 1 1 >.05

mortality 12 11 >.05

Power of an inferential statistical test is determined by:

- alpha
- sample size
- effect size (clinically meaningful difference)
- Examples of effect size:
- 1. New therapy should reduce CHD mortality 10% compared to usual care.
- 2. Drug A should reduce SBP more than Drug B by 7 mmHg.

Mr. Statistician: How many subjects (patients) do I need?

- In planning a study, the researcher specifies
- effect size (i.e., clinicaly meaningful difference)
- alpha
- beta or power (1 - beta); power = prob that a specified
- effect size will be statistically significant
- Plug alpha, beta, and ES into appropriate formula to determine sample size needed.

Relative Risk and Odds Ratio

- RCT or cohort study incidence relative risk
- case-control study prevalence odds ratio

RCT or cohort study incidence relative risk

JAMA Sept 25, 2002: losartan vs. atenolol for patients with isolated systolic HTN and LV hypertrophy

pts randomly assigned to losartan (n = 660) or atenolol (n = 666)

mean = 4.7 years

Outcome: cardiovascular death, stroke, or MI

Outcome

yes no total % w/outcome

losartan 75 585 660 11.4%

atenolol 104 562 666 15.6%

RCT incidence relative risk

RR = 75/660 ÷ 104/666 = 0.71

(95% CI = 0.53 to 0.92)

RR = % of the losartan group with outcome ÷ % of atenolol group with outcome = 11.4% ÷ 15.6% = 0.71 (95% CI = 0.53 to 0.92)

Relative Risk

10-year stroke follow-up

stroke no stroke

diabetes 20 80

no diabetes 10 90

cohort study incidence relative risk

RR = 20/100 ÷ 10/100 = 2.00

(95% CI = 1.20 to 2.70)

case-control study prevalence odds ratioJAMA June 19, 2002: vasectomy and risk of prostate cancer

923 cases vs. 1224 controls

- matched in 5-year age groups
- all were white New Zealanders

Outcome

Cases (Prostate Ca) Controls (No Ca)

Vas 216 333

No Vas 707 891

case-control prevalence odds ratio

OR = 216/333 ÷ 707/891= 0.82

(95% CI = 0.67 to 0.99)

cases (prostate ca) with risk factor (vasectomy) / controls (no prostate ca) with risk factor÷ cases without the risk factor / controls without the risk factorOR = 216/333 ÷ 707/891= 0.82 (95% CI = 0.67 to 0.99)

e.g.: sign

symptom

lab test

safer/less invasive

less costly

simpler

less painful

exercise angiography

EKG

CAD

The first step toward wisdom is knowing what the words mean. Aristotle

EBM Concepts

EBM CategoryResearch DesignConcepts to Know

diagnosis cross-sectional true positive (TP)

false positive (FP)

true negative (TN)

false negative (FN)

sensitivity (sens)

specificity (spec)

positive predictive value (PPV)

negative predictive value (NPV)

rule-in/-out diagnosis

ROC curve

status (gold standard)

sick healthy

diagnostic test positive TP FP

results negative FN TN

test characteristics

sensitivity = TP

TP + FN

specificity = TN

TN + FP

test performance

positive predictive value = TP

TP + FP

negative predictive value = TN

TN + FN

Pos: PSA > 4.0 ng/ml Neg: PSA < 4.0 ng/ml

Prevalence = No. Prostate Ca = 200 = 2%

Positive 160 (TP) 6,860 (FP) 7,020

Negative 40 (FN) 2,940 (TN) 2,980

200 9,800 10,000

Total

10,000

Pos: PSA > 4.0 ng/ml Neg: PSA < 4.0 ng/ml

Sensitivity = TP = 160 = 80%

Positive 160 (TP) 6,860 (FP) 7,020

Negative 40 (FN) 2,940 (TN) 2,980

200 9,800 10,000

TP + FN

200

Pos: PSA > 4.0 ng/ml Neg: PSA < 4.0 ng/ml

Specificity = TN = 2,940 = 30%

Positive 160 (TP) 6,860 (FP) 7,020

Negative 40 (FN) 2,940 (TN) 2,980

200 9,800 10,000

TN + FP

9,800

Pos: PSA > 4.0 ng/ml Neg: PSA < 4.0 ng/ml

Positive Predictive Value = TP = 160 = 2.3%

Positive 160 (TP) 6,860 (FP) 7,020

Negative 40 (FN) 2,940 (TN) 2,980

200 9,800 10,000

TP + FP

7,020

Pos: PSA > 4.0 ng/ml Neg: PSA < 4.0 ng/ml

Negative Predictive Value = TN = 2,940 = 98.7%

Positive 160 (TP) 6,860 (FP) 7,020

Negative 40 (FN) 2,940 (TN) 2,980

200 9,800 10,000

TN + FN

2,980

Sensitivity and specificity are altered by adjusting the cut-off for a

positive/negative test.

diabetic nondiabetic

>100450500

positive TP FP

>110 430 400

blood glucose

>100 50 2000

negative FN TN

>110 70 2100

Sens 450/500 = 90% Sens 430/500 = 86%

Spec 2000/2500 = 80% Spec 2100/2500 = 84%

When you have a positive test, high values for _____________ and ___________ help rule-in a disease.

When you have a negative test, high values for _____________ and _____________ help rule-out a disease.

gold standard

diseased not diseased

pos TP FP

test

neg FN TN

Frederickson et al. (1990) captopril test and renovascular hypertension

Purpose: Is captopril test an accurate, inexpensive,

non-invasive screening test for renovascular

hypertension?

RVH EH

Pos

TEST

Neg

29 71

prevalence: cases at the present time

What is prevalence of RVH?

prevalence = 29% (29 of 100 have RVH)

RVH EH

pos test 29 14 sens = 100% PPV = 67%

neg test 0 57 spec = 80% NPV = 100%

29 71

Is the captopril test

sensitive? RVH has serious consequences

specific? further studies invasive and expensive

Frederickson et al: “ideal for outpatient use”

prevalence = 29% (29 of 100 have RVH)

RVH EH

pos test 29 14 sens = 100% PPV = 67%

neg test 0 57 spec = 80% NPV = 100%

29 71

prevalence = 5% (5 of 100 have RVH)

RVH EH

pos test 5 19 sens = 100% PPV = 21%

neg test 0 76 spec = 80% NPV = 100%

5 95

prevalence = 1% (1 of 100 have RVH)

RVH EH

pos test 1 20 sens = 100% PPV = 5%

neg test 0 79 spec = 80% NPV = 100%

1 99

principle: as prev PPV NPV

Laya MB et al. Effect of estrogen replacement therapy (ERT) on the specificity and sensitivity of screening mammography.

J Natl Cancer Inst 1996; 88:643-9.

Current users

Postmenopausal

age 50 mean age = 63.1

Breast cancer (1 yr after mamm)

Yes No

Pos 9 367

Mammography

Neg 41720

13 2087

prevalence = 13 = 0.62%

2100

characteristic/performance result (%) 95% CI (%)

sensitivity 69 38 to 91

specificity 82 81 to 84

PPV 2 1.5 to 3.5

NPV 99.8 99.6 to 100

principle: Screening in a low prevalence population yields many FPs.

What five statistical tests (procedures) should you know?

- t test: two groups with continuous outcome
- analysis of variance (ANOVA): ≥ 2 groups with continuous outcome
- chisquare test: both variables are categorical
- correlation: ranges between -1.00 to +1.00
- regression (prediction): e.g., what are the risk factors for an MI?

r, the correlation coefficient: a measure of the linear association between two continuous variables; ranges from -1.00 to +1.00

The closer to -1.00 or +1.00, the stronger the association

Epidemiological Terms

For example:

Case fatality rate =

Deaths from a specific disease Cases of that disease

No. of spinal cord injuries No. of fatal spinal cord injuries

Highway traffic 101 54

Falls 20 4

Recreational 12 1

Occupational 11 6

Based on these data, what is the case-fatality rate for recreational spinal cord injuries?

Group A is given Treatment X for Disease Y; 1 in 1000 die of Disease Y

Group B is given a Placebo for Disease Y; 5 in 1000 die of Disease Y

How many patients need to be treated with Treatment X to prevent one death from Disease Y?

5 in 1000 die if no treatment (placebo)

1 in 1000 die if Treatment X

THUS: 4 in 1000 saved if treated

Number Needed to Treat

NNT = 1 / Absolute Risk Reduction

NNT = 1 / .004 = 250 must be treated to avoid ONE death

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