Basics of Biostatistics for Health ResearchSession 4 – February 28, 2013

Dr. Scott Patten, Professor of EpidemiologyDepartment of Community Health Sciences

& Department of Psychiatry

patten@ucalgary.ca

Generate Commands Using Logic

generate obese2 = .recode obese2 .=0 if bmi <= 30recode obese2 .=1 if bmi > 30tab obese obese2prtest obese2, by(sex)

Missing as obese, which is strange.

Missing Values and Logical Operators

• http://www.stata.com/support/faqs/data-management/logical-expressions-and-missing-values/

Generate Commands Using Logic

generate obese2 = .recode obese2 .=0 if bmi <= 30recode obese2 .=1 if bmi > 30 & bmi !=.tab obese obese2, missingprtest obese2, by(sex)

This code works.

Statistical Errors

P (non-exposed) 0.1Alt Hypoth. 0.2 (diff. between 2 prop.)P (exposed) 0.3

N (exposed) 30N (non-exposed) 30 (set equal to exposed)

Alpha 0.05

Power 0.5095

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-0.5 -0.4 -0.3 -0.2 -0.14.3715E-160.1 0.2 0.3 0.4 0.5

Null Hypothesis Alternative Hypothesis Reject Indicator

Increase Sample Size

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Power

Reset

Increase Effect Size

Increase Alpha

Sample Size Simulation

Sample Size Calculation in STATA

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Sample Size Dialogue Boxes

Let’s do a calculation!

• You are planning a parallel group RCT – with treatment and control groups.

• Normally, 20% of people die with disease X, but you expect to cut this in half with a new treatment.

• How many do you need in each group to achieve 95% power at alpha = 5%?

Output (sampsi)

n2 = 349 n1 = 349

Estimated required sample sizes:

n2/n1 = 1.00 p2 = 0.1000 p1 = 0.2000 power = 0.9500 alpha = 0.0500 (two-sided)

Assumptions: and p2 is the proportion in population 2Test Ho: p1 = p2, where p1 is the proportion in population 1

Estimated sample size for two-sample comparison of proportions

. sampsi .2 .1, alpha(0.05) power(.95)

Another Calculation

• A QoL scale in a particular disease has a mean score of 20 and a standard deviation of 5.

• You are conducting a placebo controlled trial to evaluate a treatment that is expected to improve the QoL by 2 points on this scale.

• You recruit n=50 into each group – what power will you achieve?

Output (sampsi)

power = 0.5160

Estimated power:

n2/n1 = 1.00 n2 = 50sample size n1 = 50 sd2 = 5 sd1 = 5 m2 = 22 m1 = 20 alpha = 0.0500 (two-sided)

Assumptions: and m2 is the mean in population 2Test Ho: m1 = m2, where m1 is the mean in population 1

Estimated power for two-sample comparison of means

• Go to “www.ucalgary.ca/~patten” www.ucalgary.ca/~patten

• Scroll to the bottom.• Right click to download the files described as

being “for PGME Students”– One is a dataset– One is a data dictionary

• Save them on your desktop

Review: Comparing Proportions

• We’ve looked at several procedures for comparing proportions (e.g. for obesity in men vs. women):

generate obese = .recode obese .=0 if bmi <= 30recode obese .=1 if bmi > 30 & bmi !=.tab obese obese, missingprtest obese, by(sex)

Epitab Commands

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Review: Comparing Proportions

• We’ve looked at several procedures for comparing proportions (e.g. for obesity in men vs. women):

recode sex 2=1 1=0cs obese sex

The output…

chi2(1) = 17.16 Pr>chi2 = 0.0000 Attr. frac. pop .1118099 Attr. frac. ex. .181502 .0997744 .25581 Risk ratio 1.22175 1.110833 1.343743 Risk difference .0265444 .0141393 .0389496 Point estimate [95% Conf. Interval] Risk .1462487 .1197042 .1347732 Total 6571 5004 11575 Noncases 5610 4405 10015 Cases 961 599 1560 Exposed Unexposed Total sex

. cs obese sex

A “non-significant” association

generate highgluc = .recode highgluc .=0 if glucose <= 140 recode highgluc .=1 if glucose > 140 & glucose !=.generate female=sexrecode female (1=0) (2=1)tab highgluc female, exact

How does this look with cs?

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chi2(1) = 3.51 Pr>chi2 = 0.0609 Prev. frac. pop .12358 Prev. frac. ex. .2215609 -.0122169 .4013463 Risk ratio .7784391 .5986537 1.012217 Risk difference -.0054099 -.0111474 .0003276 Point estimate [95% Conf. Interval] Risk .0190074 .0244173 .0213998 Total 5682 4505 10187 Noncases 5574 4395 9969 Cases 108 110 218 Exposed Unexposed Total female

. cs highgluc female

Review: Try the cci command to obtain the OR

.

chi2(1) = 3.51 Pr>chi2 = 0.0609 Prev. frac. pop .12358 Prev. frac. ex. .2215609 -.0122169 .4013463 Risk ratio .7784391 .5986537 1.012217 Risk difference -.0054099 -.0111474 .0003276 Point estimate [95% Conf. Interval] Risk .0190074 .0244173 .0213998 Total 5682 4505 10187 Noncases 5574 4395 9969 Cases 108 110 218 Exposed Unexposed Total female

. cs highgluc female

Check your work with the cc command.

Comparing Proportions?

Yes No

Fisher’s Exact Test Parametric Assumptions?

Yes No

Multiple Groups? Multiple Groups?

Yes NoYes No

ANOVA t-test Kruskall-Wallis Wilcoxon’s-Rank Sum

Two situations we haven’t covered…

• Severely skewed distributions• Two continuous variables

Severely Skewed Variables

Solution: Make Some Categories

• For example:– Non-smokers– Light smokers (<20)– Moderate 20-40– Heavy > 40

• Your task: Make a variable with these categories and do a statistical test to compare men to women.

E.g. for the recoding…

generate smoke = .recode smoke .=1 if cigpday==0recode smoke .=2 if cigpday > 0 & cigpday < 20recode smoke .=3 if cigpday >=20 & cigpday <= 40recode smoke .=4 if cigpday > 40 & cigpday !=.tab smoke, missing

Some output…

Fisher's exact = 0.000

Total 4,990 6,558 11,548 4 122 23 145 3 1,754 1,073 2,827 2 686 1,292 1,978 1 2,428 4,170 6,598 smoke 1 2 Total sex

stage 1: enumerations = 0stage 2: enumerations = 142603stage 3: enumerations = 146stage 4: enumerations = 1Enumerating sample-space combinations:

. tab smoke sex, exact

Two continuous variables

• E.g. diastolic blood pressure and BMI• The place to start is always a scatter plot• STATA calls this a “two way” graph

Start with Create

Select the two variables

Submit

The command produced…• Produced by our dialogue box…

twoway (scatter diabp sysbp)• The same dialogue box can fit a line…

twoway (lfit diabp sysbp)

This time select “line”

You can combine the two..

• Try it!twoway (scatter diabp sysbp) (lfit diabp sysbp)

• To assess significance, use the regress command (can you find the menu option?)regress diabp sysbp

Note: the linear output

• Line: y = mx + b

• diabp = 33.42 + 0.364(sysbp) _cons 33.42091 .4606105 72.56 0.000 32.51804 34.32379 sysbp .3639623 .0033325 109.22 0.000 .3574301 .3704946 diabp Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 1580658.92 11626 135.958965 Root MSE = 8.1921 Adj R-squared = 0.5064 Residual 780160.451 11625 67.1105764 R-squared = 0.5064 Model 800498.474 1 800498.474 Prob > F = 0.0000 F( 1, 11625) =11928.05 Source SS df MS Number of obs = 11627

. regress diabp sysbp

(In Class) Assignment for Today

• Assess whether there is an association between systolic blood pressure and death

(you need to decide how)• We’ll define elevated systolic blood

pressure as being > 140 mm of Hg.– What is the risk ratio for death for people with

elevated systolic blood pressure?– Is the risk ratio statistically significant?