sample size calculation 2014

8/18/2019 Sample Size Calculation 2014

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Sample size calculation

Assistant Professor: Ahmed S.Ishtiaque

ULAB


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Why calculating samplesize

• Reduce unnecessary expense(time, labor, money, materials)

• Avoid useless research


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Approaches and decisionsa!out sample size

• Depends on research questions andresearch designs

• Some common situations – Estimating prevalence /mean

– omparing t!o groups•

"ean• #roportion


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Sample size for pre"alencestudy

• $or dichotomous data (only %outcomes& sic'/not sic', male/emale,dead/alive)

• he study describe results inpercentage

• $or example, disease prevalencesurvey


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Sample size: pre"alencesur"ey

2

)]1([2

d

p p Z n −=

• p * estimated prevalence(percentage)

• q * +p•

- * critical value or .0 1*+2.3• d * allo!able error• n * sample si4e


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#rror

• Suppose, the survey !ants toestimate the true prevalence o adisease in population

• he estimate !e get rom the survey!ill be !ithin 5/ d0 o the trueprevalence


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#$ample

• A survey is to estimate prevalence oin6uen4a virus inection in school'ids

• Suppose the available evidencesuggests that approximately %70(#*%7) o the children !ill have

antibodies to the virus• Assume the investigator !ants to

estimate the prevalence !ithin 30 othe true value (30 is called allo!able

error& d)


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Sample size for estimationof mean

• A Survey to 8nd an average o aparameter (birth !eight, antibodytitre, blood pressure)

• he study reports average oparameters

• he parameter must be quantitative


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Sample size for estimation ofmean

• SD * Standard Deviation o variableo interest

• d * Allo!able error

• - * value or the desired con8dencelimit

• n * required sample si4e

2

22

d

SD Z n =


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#$ample

• Suppose an investigator has someevidence suggests that the standarddeviation o rat !eight is about 9 g

• :e !ishes to provide an estimate!ithin ;7 g o the true average (;7 gis the allo!able error& d)


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Example• he required sample si4e is

n * (+2.3) % x (9)% & '()*%

+,%-.-

• hus approximately +


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Sample Size to /omparePercentages

• A study to compare percentages ooutcomes rom di=erent groups(incidence, cure rate, mortality rate,survival rate)


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Sample Size to /omparePercentages

• #c * percentage rom control group

• >c * + #c

•

#e * #ercentage rom theexperimental group

• >e * + #e

22

)(

)()(2

+++

=d d

Q P Q P C n eecc


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Sample Size to ComparePercentages

• d = Difference between the twogroups (must be positive)

• C = Constant (See table nextpage)

22

)(

)()(2

+++

=d d

Q P Q P C n eecc


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/ : /onstant

• ?hen po!er is ;70

•#o!er * Ability to 8nd signi8cance!hen the t!o groups are reallydi=erent (the ormula is or t!o sideddi=erence)

alpha 727 727+

@2; ++23;


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#$ample ,

• he research question is !hethersmo'ers have a greater incidence os'in cancer than nonsmo'ers

•

A revie! o previous literaturesuggests that the incidence o s'incancer is about 72% in nonsmo'ers

•

At alpha*727, and po!er*;70, ho!many smo'ers and nonsmo'ers !illneed to be studied to determine!hether s'in cancer incidence is atleast 72< in smo'ers


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#$ample %

• Bull :ypothesis C he incidence os'in cancer does not di=er insmo'ers and nonsmo'ers

• Alternative :ypothesis C heincidence o s'in cancer is di=erentbet!een smo'ers than nonsmo'ers


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#$ample

• #e * 72


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Sample Size to /ompare0eans

• :ypothesisC ompare means odi=erent groups

• he parameters are quantitative(birth !eight, blood pressure)

• Select % groups that you thin' they!ill be most di=erent (such as& a

control and a treatment group)

• $or ttest, ABA


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Sample Size to /ompare0eans

• S * Standard Deviation o thevariable

• d * Di=erence bet!een the % groups• * onstant (rom previous table)

2

21

+=d

sC n


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#$ample

• he research question is to compare theeFcacy o DRGH A and DRGH I in thetreatment o asthma

• he outcome variable is $E+ (orcedexpiratory in + second) + hour ater treatment

• A previous study has reported that the mean$E+ in persons !ith treated asthma !as %27

litres, !ith a standard deviation o +27 litre• he investigator !ould li'e to be able to

detect a di=erence o +70 or more in mean$E+ bet!een the t!o treatment groups


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#$ample

• Bull :ypothesis C "ean $E+ is thesame in asthmatics treated !ithDRGH A as in those treated !ith

DRGH I

• Alternative :ypothesis C "ean$E+ is di=erent bet!een asthmatic

patients treated !ith DRGH A andthose treated !ith DRGH I


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Example

• S * +

• d * +70 o % litre * 72% litre

2

2.0

185.721

×+=n

2

21

+=d

sC n

*

sample size calculation 2014

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