GOOD EVEN
EVERYONE, MY NAME IS TEE YAN CHA
WU, MY EXPERTISE IS THE
STATISTICAL MONITORING. IN THIS
LECTURE, I AM GOING TO PRESENT
STATISTICAL POWER ANALYSIS.
FIRST, I WILL INTRODUCE
DEFINITION OF STATISTICAL POWER
THREE COMMONLY USED STUDY
DESIGNS AND THE CALCULATION.
TODAY WE WILL DISCUSS THE
FACTORS AFFECTING THE POWER
ANALYSIS AND LATER I WILL
PRESENT TWO EXAMPLES OF POWER
ANALYSIS. WITHOUT THIS, IN THIS
LECTURE, THE OUTCOME VARIABLES
ARE STILL TO BE CONTINUES AND
NORMALLY DISTRIBUTED AND THERE'S
A TREATMENT AND CONTROL GROUPS
HAVE -- THE SAME OR SIMILAR
VARIABLES. FIRST I WOULD LIKE
TO INTRODUCE TWO TYPE OF
STUDIES. THAT WE DON'T WANT.
WHY IS UNDER POWER STUDY WHICH
HAS A SAMPLE SIZE TOO SMALL.
BECAUSE OF THE SMALL SAMPLE SIZE
IT USES THE WILD DIFFUSIONS FOR
THE LIMITS FOR EXAMPLE, IF THE
SLIDES OR SAMPLE MEANS MAY HAVE
A LARGE BARRIERS OR ERROR
THEREFORE IT DOES NOT HAVE TO
THE NECESSARY POWER TO DETECT
THE TRUE DIFFERENCE, LEADING TO
A FALSE NEGATIVE CONCLUSION. IT
EXPOSE Z PARTICIPANTS TO RISK
WITHOUT PROVIDING MEANINGFUL
KNOWLEDGE. AND IT ALSO LEAD TO
BIAS CONCLUSION AND LOW
REPRODUCIBILITY OF RESULTS. THE
OTHER ONE IS OVERPOWERED STUDY
WHICH HAS SAMPLE SIZE TOO LARGE
IT MAY RESULT IN STATISTICALLY
SIGNIFICANT DIFFERENCES THAT ARE
NOT CLINICALLY IMPORTANT. FOR
EXAMPLE WITH A LARGE SAMPLE SIZE
THE STUDY MAY FIND A CHANGE IN
THE I 1C OF 0.1% WHICH IS NOT
CLINICALLY IMPORTANT. IT EXPOSE
Z AN UNNECESSARY NUMBER OF
PARTICIPANT TO RISK BOTH
UNDERPOWERED AND OVERPOWERED
STUDIES WASTE RESOURCES. SO DO
WE NEED A POWER ANALYSIS? THE
REASON IS TO AVOID THE STUDY
FROM BEING UNDERPOWERED OR
OVERPOWERED THEREFORE TO ENSURE
THE STUDY HAS SUFFICIENT
STATISTICAL POWER TO DETECT
EFFECTS THAT ARE SCIENTIFICALLY
IMPORTANT AND CLINICALLY UNIFORM
AND TO ALLOCATE SUFFICIENT BUT
NOT EXCESSIVE RESOURCES TO DATA
COLLECTION. POWER ANALYSIS HAS
TWO ROLES. ONE IS TO DETERMINE
THE NECESSARY NUMBER OF SUBJECTS
NEEDED TO DETECT A GIVEN EFFECT
SIZE OR SOME SITE ESTIMATION.
THE OTHER ROLE IS TO DETERMINE
THE POWER GIVEN THE EFFECT SIZE
AND THE NUMBER OF SUBJECTS
AVAILABLE OF POWER ESTIMATION.
SO WE -- HAVE ANALYSIS IS
PERFORMED. IN MOST TIMES, POWER
IS ANALYSIS IS PERFORMED BEFORE
THE DATA IS COLLECTED OR DURING
PROTOCOL DEVELOPMENT. THE
PURPOSE IS TO ESTIMATE A SAMPLE
SIZE OR TO DETERMINE THE POWER
FOR GIVING SAMPLE SIZE. A POWER
ANALYSIS IS REQUIRED FOR THE
PROTOCOLS WITH STATISTICAL
HYPOTHESES. POWER ANALYSIS IS
ALSO PERFORMED IN INTERIM
ANALYSIS. THE PURPOSE IS TO
REESTIMATE THE SAMPLE SIZE BASED
ON REESTIMATED COMPONENTS SUCH
AS STANDARDIZATION AND EFFECT
SIZE ALL TO CALCULATE THE
CONDITIONAL POWER USED FOR
FUTILITY STOPPING. SOMETIMES
POWER ANALYSIS IS EFFECTED AFTER
THE DATA IS COLLECTED. THE
PURPOSE IS TO CALCULATE THE
POWER OR TO USE THE SAMPLE SIZE
FOR THE FUTURE BASED ON THE
COMPONENTS. FOR EXAMPLE, A
STUDY OF THE DIFFERENCE BETWEEN
THE TWO GROUP IS CLINICALLY
IMPORTANT. BUT NOT AS
SPECIFICALLY SIGNIFICANT YOU MAY
CHECK THE POWER. YOU MAY CHECK
THE POWER ANALYSIS COULD CHECK
IN THE STUDY HAS ENOUGH POWER OR
TO ESTIMATE A SAMPLE SIZE FOR
FUTURE STUDY. WE INTRODUCE TWO
TYPES OF HYPOTHESIS AND ERRORS,
ONE IS CALLED NULL HYPOTHESIS
WHICH REPRESENTS WHAT THE
INVESTIGATOR AIMS TO DISPROVE.
THE OTHER ONE IS CALLED
ALTERNATIVE HYPOTHESIS
REPRESENTS WHAT THE INVESTIGATOR
AIMS TO SHOW. FOR EXAMPLE, A
HYPOTHESIS OF THERE IS NO
DIFFERENCE BETWEEN THE TWO
TREATMENTS IS NULL HYPOTHESIS.
THE DIFFERENCE BETWEEN THE TWO
DIFFERENT TREATMENTS IS A NULL
HYPOTHESIS. ONE TYPE IS CALLED
AN ALPHAER ROR. IF WE REJECT
THE NULL HYPOTHESIS, WHETHER IT
IS TRUE, WE COMMIT TYPE ONE
ERROR. FOR EXAMPLE, WHEN
THERE'S NO DIFFERENCE HERE WE
FALSELY CONCLUDE THERE IS A
DIFFERENCE. THE OTHER TYPE OF
ERROR IS CALLED BETA ERROR IF WE
FAIL TO REJECT THE NULL
HYPOTHESIS AND THE NULL
HYPOTHESIS IS NOT TRUE WE COMMIT
ABETA ERROR. FOR EXAMPLE, WE --
THERE'S A DIFFERENCE BETWEEN THE
TWO TREATMENTS.
WE FALSELY CONCLUDE THAT THERE'S
NO DIFFERENCE. THE POWER IS
BASED ON TYPE TWO ERROR. THE
POWER IS DEFINED AS NOT A TWO
ERROR. THIS IS DEFINED AS A
PROBABILITY OF CONCLUDING THAT
THERE IS A DIFFERENCE BETWEEN
THE TWO TREATMENTS. WHEN THE
DIFFERENCE ACTUALLY EXISTS, FOR
EXAMPLE, A STUDY TO COMPARE A
DRUG WITH. THE DRUG IS TRULY
EFFECTIVE. THE NULL HYPOTHESIS
IS A DIFFERENCE BETWEEN NEW ER
WHERE IT IS THE DRUG TREATMENT
AND THE CONTROL POPULATION. IF
WE SPECIFY POWER EQUAL TO 0.8 OR
TYPE TWO ERROR AS 0.2, IMAGINE
THIS STUDY WILL BECOME CONDUCTED
MANY TIMES. THIS MEANS THAT 80%
OF THE TIMES WE WILL REJECT THAT
HYPOTHESIS AND CONCLUDE THAT
THERE IS A STATISTICAL
SIGNIFICANT DIFFERENCE BETWEEN
DRUG A AND THE SPECIFIC GROUPS
HOWEVER THAT 20% OF THE TIMES WE
WILL ACCEPT THE HYPOTHESIS AND
CONCLUDE THAT THERE'S NO
SIGNIFICANT DIFFERENCE BETWEEN
THE TWO GROUPS EVEN THOUGH THE
DRUG IS TRULY EFFECTIVE. SINCE
THE POWER ANALYSIS IS DEPENDING
ON THE TEST METHOD I WILL GIVE
YOU AN OVERVIEW OF THREE
COMMONLY USED DESIGNS. THE
RANDOMIZED CONTROL TRIAL IS THE
MOST IMPORTANT TRIAL IN THE
CLINICAL TRIAL STUDY. IN THE
CLINICAL STUDY. WHICH HAS THREE
FEATURES, INTERVENTION,
RANDOMIZATION AND CONTROL. THIS
IS A GOLD STANDARD FOR
EVALUATING THE EFFECTIVENESS OF
EVALUATION. THE PARALLEL TWO
GROUP DESIGN IS THE SIMPLEST
RANDOMIZED CONTROL TRIAL. IT
INCLUDES ONLY TWO GROUPS,
CONTROL AND TREATMENT. SUBJECTS
ARE RANDOMLY ASSIGNED TO THE
CONTROL GROUP OR TREATMENT
GROUP. T THE NULL HYPOTHESIS IS
A DIFFERENCE BETWEEN QUARTER
ZERO. TO TEST THE HYPOTHESIS,
WE USE TWO SAMPLE T-TEST. WITH
NO SO VARIETY. WITH COVARY YAT
WE USE AN ANALYSIS.
THE SECOND DESIGN IS CROSSOVER
DESIGN. CROSSOVER DESIGN IS A
SPECIFIC TYPE OF RANDOMIZED
CONTROL TRIAL. THE CROSSOVER
DESIGN, THE AB DESIGN IS THE
SIMPLEST ONE. THE AB/BA
INCLUDES TWO SEQUENCE, AB OR BA.
THE SUBJECTS ASSIGNED TO THE AB
SEQUENCE RECEIVE TREATMENT A IN
THE FIRST PERIOD AND TREATMENT B
IN THE SECOND PERIOD AND VICE
VERSA. SUBJECTS ARE RANDOMLY
ASSIGNED TO SEQUENCE AB OR BA.
HERE, THE RANDOMIZATION IS
DIFFERENT FROM THAT USE IN
PARALLEL DESIGN. IN PARALLEL
DESIGN SUBJECTS ARE RANDOMLY
ASSIGNED TO A OR B AND EACH
SUBJECT HAS THEIR OWN TREATMENT.
AND THE SUBJECT RECEIVED TWO
TREATMENT IN THE OTHER DESIGN.
TWO TREATMENT IN DIFFERENT
PERIOD. THEREFORE THEY SERVE AS
HIS OR HER OWN CONTROL. THE KEY
ASSUMPTION FOR CROSSOVER DESIGN
IS NO CARRY OVEREFFECT. THIS
MEANS THE TREATMENT ASSIGNED
DURING THE FIRST PERIOD DOES NOT
INTERFERE WITH THE OUTCOME IN
THE SECOND PERIOD. SO NOW THE
HYPOTHESIS IS 1 AND 0. WE USE
THE PAIRED TEST T-TEST. AND ONE
SAMPLE T-TEST IS BASED ON THE
DIFFERENCE BETWEEN THE PAIRED
OBSERVATIONS. WITH COVARIATES
WE USE REPEATED MEASURES AN KOE
HAVE A.
THE SECOND DESIGN IS A QUASI
EXPERIMENTAL DESIGN. THE
FIRST -- THE FIRST IS CALLED THE
PARALLEL DESIGN WHICH HAS THE
THREE FEATURES. RANDOMIZATION,
CONTROL AND INDIVIDUAL. FOR THE
QUASI EXPERIMENTAL DESIGN THAT'S
NOT -- QUASI EXPERIMENTAL DESIGN
DOES NOT USE RANDOMIZATION. THE
ADVANTAGE OF THE QUASI
EXPERIMENTAL DESIGN IS LESS
EXPENSIVE. THE WEAKNESS IS THE
RESULTS ARE SUBJECT TO BIAS.
THEREFORE, THESE DESIGNS ARE
USED IN HIGH LEVEL STUDY OR
EARLY PHASE STUDY. ONE GROUP
PRETEST THE POSTTEST DESIGN IS
SIMPLEST. QUASI EXPERIMENTAL
DESIGN. THIS DESIGN EXCEPT THE
RANDOMIZATION HAS NOT CONTROL
GROUP. IT INCLUDE ONLY ONE
GROUP. AND ALL SUBJECTS IN THE
GROUP RECEIVE THE TREATMENT.
BUT THEN THERE'S THE OUTCOME
VARIABLES ARE COLLECTED BEFORE
AND AFTER THE TREATMENT. THE
EFFECT OF TREATMENT IS EVALUATED
BY COMPARING THE POSTTEST WITH
PRETEST. THEREFORE, EACH
SUBJECT SERVES AS THEIR OWN
CONTROL. THIS IS SIMILAR AS
AB/BA CROSSOVER DESIGN. THE
DIFFERENCE IS IN AB/BA CROSSOVER
DESIGN, THERE ARE TWO SEQUENCES
AB AND BA. AND EACH SUBJECT IS
RANDOMIZED TO RECEIVE AB OR BA
SECRETS. BUT IN THE ONE GROUP
DESIGN THERE'S ONLY ONE
SEQUENCE. CALLED AB AND ALL
SUBJECTS RECEIVE SAME SEQUENCE.
BUT NOW HYPOTHESIS IS HERE AND
TO TEST THE HYPOTHESIS WE ALSO
USE PAIRED T-TEST WHICH
EQUIVALENT TO THE T-TEST BASED
ON THE DIFFERENCE BETWEEN THE
PAIRED OBSERVATION. NEXT, I AM
GOING TO PRESENT HOW TO
CALCULATE THE SAMPLE SIZE FOR
TWO SAMPLE T-TEST AND PAIRED
T-TEST. FOR THE PARALLEL
DESIGN -- TWO GROUP PARALLEL
DESIGN THE HYPOTHESIS IS THE
DIFFERENCE BETWEEN THE TWO AND
ZERO. NOTICE THAT THE DATA IS
NOTED AS THE DIFFERENCE THAT HAS
SCIENTIFIC OR CLINICAL
IMPORTANCE. SIGMA IS DENOTED AS
THE POPULAR STANDARD OF
DEVIATION. THE DATA TO SIGMA IS
STANDARDIZED MEAN DIFFERENCE OR
STANDARDIZED EFFECT SIZE AND A
TYPE ONE AND TYPE TWO ERRORS.
THE METHOD FOR THE SAMPLE SIZE
ESTIMATION IS WOE USE THE TWO
SAMPLE TWO SAILED Z TEST. THE
FORMULA TO CALCULATE THE SAMPLE
SIZE IS THIS. AS THIS HERE.
IS AS THIS AND HERE THE Z AT
ALPHA AND Z AT BETA ARE THE
CRITICAL VALUES OF THE
STANDARDIZED NORMAL
DISTRIBUTION. HERE WE USE THE Z
TEST INSTEAD OF THE T-TEST
BECAUSE THEY USE THE POPULATION
TARRED DEVIATION AND NOT USE THE
DEGREE OF FREEDOM. HERE WE CAN
HAVE A SIMPLE FORMULA.
THE T-TEST THAT USES THE SAMPLE
DEVIATION AND THE FREEDOM
INDEED, THE TWO METHODS GIVE
SIMILAR SAMPLE SIZE WHEN SAMPLE
SIZE GREATER THAN 50. THOSE
SLIDES SHOW THE SAMPLE SIZE FOR
PAIRED T-TEST. THE DATA OF THE
DEFINITION SAME AS BEFORE. AND
HERE, THE DIFFERENCE IS SIGMA D.
SIGMA D IS THE POPULAR STANDARD
DEVIATION OF THE PAIRED
DIFFERENCE. IF THE SIGMA NOTED
AS THE POPULATION STANDARD
DEVIATION AND WE CAN USE THIS
FORMULA TO CALCULATE THE P
POPULATION DEVIATION OF THE
PAIRED DIFFERENCE HERE BELOW IS
THE CORRELATION COEFFICIENT
BETWEEN THE PAIRED OBSERVATIONS.
BASED ON THIS FORMULA, WHEN IT
IS 0.5 THE SIGMA D IS EQUAL TO
SIGMA. AND THEN WE HAVE SIGMA D
IS GREATER THAN SIGMA. SO WE
DON'T IN THE POWER ANALYSIS, WE
DON'T KNOW THIS. USUALLY THIS
IS EQUAL TO ZERO OR THE FIVE
WHICH MEANS WE ASSUME THE
POPULA
POPULATION STANDARD DEVIATION IS
EQUAL TO THE POPULATION STANDARD
DEVIATION AND HERE IS THE
EXAMPLE WHERE WE USE THE TWO
TAILED Z TEST AND WE'RE WE GET
THIS FORMULA TO THE FORMULA OF
THE EXAMPLE T-TEST. YOU SEE THE
ONLY DIFFERENCE IN THIS FORMULA
IS TWO. THEREFORE, WHEN SIGMA D
EQUAL TO SIGMA AND THE DATA AND
ALPHA AND THE BETA ARE KEPT THE
SAME, THEN THE SAME SIZE FOR THE
PARALLEL DESIGN WILL HAVE THE
SAMPLE DESIGN IS FOUR TIMES OF
THE SAMPLE SIZE FOR THE
CROSSOVER DESIGN. THIS FORMULA,
WE -- WHEN WE DO PAIRED ANALYSIS
WE NEED ALPHA, BETA, THETA AND
SIGMA. NEXT SLIDE SH, . ALPHA
THE PROBABILITY OF MAKING TYPE
ONE ERROR AND THE BETA IS THE
PROBABILITY OF MAKING TYPE TWO
ERROR. IDEAL THAT WE WANT TO
MINIMIZE THE PROBABILITY OF
COMMITTING ALPHA AND BETA ERROR.
FOR CONSIDERATION OF SAMPLE SIZE
WE USUALLY SAID BETA EQUAL TO
0.2. AND ALPHA EQUAL TO 0.05.
YOU MAY WONDER, WHY WE CHOOSING
SMALLER TYPE ONE ERROR THAN TYPE
TWO ERROR. THE MAIN REASON IS
THAT IN MOST SITUATIONS MAKING
THAT TYPE ONE ERROR MIGHT BE
MORE SEVERE OR COSTLY THAN
MAKING TYPE TWO ER ERROR THIS
BALANCE IS CONSIDERED REASONABLE
IN MANY STUDIES. FOR EXAMPLE,
FIRSTLY DECLARING A DRUG TO BE
EFFECTIVE WHEN IT'S NOT.
COULD LEAD TO HARMFUL
CONSEQUENCES FOR PATIENTS.
THEREFORE, RESEARCHERS LIKE TO
SET A HIGHER SIGNIFICANCE LABEL
TO MINIMIZE THIS RISK SUCH AS
0.01 OR 0.001. BASED ON THE
FORMULA TO CORRECT --
CALCULATING SAMPLE SIZE WE NEED
SIGMA, THE POPULATION STANDARD
DEVIATION.
AND THE DATHETA, THE SMALLEST
DIFFERENCE BETWEEN TW TWO GROUPS
THAT HAS SCIENTIFIC OR CLINICAL
IMPORTANCE. TO GET TO THIS
ESTIMATION FOR THIS TWO
COMPONENTS, WE USUALLY GET THIS
FROM LITERATURE REVIEW, PREVIOUS
STUDIES, OR PILOT STUDY. IF
THIS INFORMATION IS NOT
AVAILABLE, WE CAN USE COHEN'S
RECOMMENDATION. COHEN'S
RECOMMENDATION IS BASED ON
COHEN'S D. COHEN'S D IS DEFINED
AS THE DIFFERENCE BETWEEN GROUP
ONE AND GROUP TWO MEANS DIVIDED
BY THE POOLED STANDARD
DEVIATION. COHEN DEFINED D
EQUALS .25 AS TOO SMALL TO
DEFECT AND MEDIUM AND .5
CAREFUL OBSERVATION. COHEN
RECOMMEND THAT 0.5 CAN BE
CLINICAL IMPORTANT EFFECT. YOU
CAN EASILY CALCULATE THE SAMPLE
SIZE BASED ON COHEN'S D EQUAL
0.5. SO IN THE FORMULA, WE CAN
REPLACE THE 0.5 TO THE DATA TO
SIGMA. THE EFFECTIVE SIZE AND
FOR ALPHA EQUAL 0.05 AND FOR 0.8
WE CAN GET Z HALF ALPHA EQUAL TO
1.96. REPLACE THIS THREE NUMBER
TO THE FORMULA. WE GET 63. AND
FOR THE -- IF WE USE A T-TEST.
WE GET 64. LIP SI AND WILSON
DID A META-ANALYSIS OF 302
METAANALYSIS OF OVER 10,000
STUDIES AND FOUND THAT THE
AVERAGE EFFECT SIZE WAS 0.5
WHICH IS PART OF COHEN'S
RECOMMENDATION. KING RECOGNIZED
THAT A STANDARD EFFECT SIZE OF
0.3 CAN BE APPEAR EFFECT -- AN
EFFECTIVE EFFECT.
A PILOT STUDY HAS A SMALL SAMPLE
SIZE SO WHEN USING THE SAMPLE
STANDARD DEVIATION FROM PILOT
STUDY WE SHOULD BE WEARY THE
SAMPLE STANDARD DEVIATION CAN BE
EITHER LARGER OR SMALLER THAN
THAT OF THE MAIN STUDY. THE
DISTRIBUTION OF THE SAMPLE
VARIANCE IS POSITIVELY SKEWED
WITH THE LONG RIGHT TAIL WHICH
MEANS THAT OVER 50% OF THE TIME,
A REALLY LONG VARIANCE -- USING
AN UNDERESTIMATE OF STANDARD OF
DEVIATION WILL YIELD AN
UNDERESTIMATE OF SAMPLE SIZE AND
WILL RESULT IN LESS POWER THAN
ANTICIPATED. BELONG THESE ARE
THE TWO TAILED TWO SAMPLE T-TEST
SHOW THAT HAD. FOR TRIALS WITH
SAMPLE SIZE ESTIMATED FROM
SAMPLE STANDARD DEVIATION UPON
ESTIMATE OF POPULATION STANDARD
DEVIATION. THE PROBABILITY THAT
THE TRIALS ACHIEVE THE POWER
OVER 0.8 IS ONLY ABOUT 50%. FOR
THE TRIALS, WITH THE SAMPLE SIZE
ESTIMATED FROM THE 80% UP ONE
SIDED CONFIDENCE LIMIT ON THE
POPULATION STANDARD OF DEVIATION
THE PROBABILITY THAT THE TRIALS
ACHIEVE THE POWER GREATER THAT
0.8 IS OVER 80%. FOR EXAMPLE,
FROM THE PILOT STUDY WE CAN
ESTIMATE THAT WE CAN SEE THERE'S
60% CONFIDENCE AS THIS. AND
THEN WE WILL GET TO THE 80% UP
ONE SIDED COST LIMITED AS 2.76
THIS MEANS WE ARE 80% SURE THAT
THE TRUE VALUE OF POPULATION
STANDARD OF DEVIATION IS LESS OR
EQUAL TO 2.76. NEXT WE ARE
GOING TO DISCUSS THE FACTORS
EFFECTING THE STATISTICAL POWER.
LET'S LOOK AT THESE FORMULA
AGAIN. THE LARGEST SAMPLE SIZE
CAN BE CAUSED BY LARGE STANDARD
OF DEVIATION. LARGE Z AT HALF
ALPHA OR LARGE AT BETA. Z BETA.
OR SMALL DATA. THE LARGE SIGMA
MEANS LARGE POPULATION VARIATION
OF OUTCOME. FOR EXAMPLE, THE
SAMPLE SIZE CALCULATED BASED ON
SIGMA TWO WILL BE LARGER THAN Z
FROM SIGMA IF ONE. THE LARGEST
Z AT HALF ALPHA MEANS SMALL TYPE
ONE ERROR. FOR EXAMPLE, THE
SAMPLE SIZE CALCULATED BASED ON
ALPHA WAS 0.01 IS LARGER THAN
THAT FROM 0.05. LARGE Z BETA
MEANS SMALL TYPE TWO ERROR. OR
LARGE POWER. THE SAMPLE SIZE
CALCULATED BASE, FOR EXAMPLE, ON
THE POWER OF 0.9 IS LARGER THAT
THAT BASED ON POWER OF 0.8. THE
SMALL DATA MEANS SMALL TREATMENT
EFFECT. FOR EXAMPLE, THE SAMPLE
SIZE CALCULATED BASED ON DATA
EQUAL TO ONE IS LARGER THAN THAT
BASED ON DATA, BASED ON THAT
FROM DATA EQUAL TO 0. -- EQUAL
TO 2. THIS TABLE SHOWS
RELATIONSHIP BETWEEN SAMPLE SIZE
TYPE ONE ERROR, STANDARDIZED
EFFECT SIZE AND POWER. BY
FIXING THE TYPE ONE ERROR AND
THE STANDARDIZED EFFECT SIZE,
DECREASING THE SAMPLE SIZE,
DECREASING THE POWER. BY FIXING
THE SAMPLE SIZE, AND THE
STANDARDIZED EFFECT SIZE
DECREASING THE TYPE ONE ERROR,
DECREASING THE POWER. BY FIXING
THE SAMPLE SIZE, AND THE TYPE
ONE ERROR, DECREASING EFFECT
SIZE, DECREASING THE POWER.
THEREFORE THE FACTORS LEADING TO
THE UNDERESTIMATED SAMPLE SIZE
OF POWER IS UNDERESTIMATED
STANDARD OF DEVIATION
OVERESTIMATED EFFECTIVE SIZE OF
LARGE TYPE ONE ERROR WHICH MEANS
WE FAIL TO ACCOUNT FOR THE
MULTIPLE COMPARISON. WHICH WILL
BE PRESENT IN THE FOLLOWING
SLIDES. THE PREVIOUS SLIDES ARE
REALLY SHOW THE POWER -- THE
TYPE TWO GO ERROR SLIDE
DEVIATION EFFECT THE SAMPLE
SIZE. THE FOLLOWING SLIDES I
WILL PRESENT HOW STUDY DESIGN
MULTIPLICITY AND THE GROUP
WEIGHTS EFFECT THE ANALYSIS.
THE FACTORS ARE OUTCOME VARIABLE
TYPE, TRIAL TYPE, STATISTICAL
ANALYSIS METHOD, DROPOUT RATE
AND ET CETERA. WHICH I WILL NOT
DISCUSS IN THIS PRESENTATION.
IN THIS SLIDE SHOWS HOW THE
EFFECT OF THE STUDY DESIGN
EFFECTS THE SAMPLE SIZE. IN
THIS TABLE, THE SAMPLE SIZE, THE
TOTAL SAMPLE SIZE IS CALCULATED
USING THE POWER OF ON EIGHT TYPE
ONE ERROR 0.5 AND THE
STANDARDIZED EFFECT SIDES OF 1.5
AND TWO TAILED TEST. FOR
PARALLEL GROUP DESIGN WE USE TWO
SAMPLE T-TEST. BECAUSE EACH
SUBJECT HAS ONLY ONE
OBSERVATION. AND ALL THE
SUBJECTS ARE INDEPENDENT. THE
SAMPLE SIZE WERE 128. FOR THE
CROSSOVER DESIGN AND ONE GROUP
DESIGN WE USE PAIRED T-TEST
BECAUSE EACH SUBJECT HAS TWO
OBSERVATIONS AND TWO OKAY
OBSERVATIONS ARE CORRELATED.
AND IT WAS CORRELATED FROM THE
OBSERVATION FROM THE SAME
SUBJECT OF 0.3 WE CAN SAMPLE
SIZE46 OF 0.5 AND WE HAVE 34.
AND THE -- WE RECALL THE FORMULA
FOR THE -- FROM THE T-TEST UP
HERE THE T-TEST, THE DIFFERENCE
IS THE -- IS A CONSTANT TWO.
AND THE SAMPLE SIZE FOR THE
PARALLEL DESIGN IS FOUR TIMES OF
THE CROSSOVER DESIGN FOR THE
STANDARD DEVIATION. OF THE
DIFFERENCE IS EQUAL TO THE
POPULATION STANDARD DEVIATION.
SO HERE WE HAVE TO STUDY FOR IS
ABOUT ONE QUARTER OF THE 128.
IT IS OBVIOUS THAT IT IS A
CROSSOVER DESIGN IS MUCH SMALLER
SAMPLE SIZE COMPARED TO PAIRED
GROUP DESIGN HOWEVER THE
CROSSOVER DESIGN IS BASED ON
STRONG AND STRICT ASSUMPTION
WHICH IS NO CARRY OVER EFFECT.
FOR THIS, FOR THIS ASSUMPTION,
VERY FEW TREATMENTS CAN MEET
THIS -- CAN MEET THIS ASSUM
ASSUMPTION. THE OTHER
ADVANTAGE -- DISADVANTAGE FOR
THE CROSSOVER DESIGN IS A
DROPOUT HAS A MORE NEGATIVE
EFFECT THAN ON THE PAIRED
DESIGN. FOR THE PARALLEL
DESIGN, THE DESIGN CAN BE
BALANCED OR UNBALANCED DEPENDS
ON THE GROUP WEIGHTS. THE GROUP
WEIGHTS ARE THE SAMPLE SIZE
ALLOCATION WEIGHTS FOR THE TWO
GROUPS. IF THE DESIGN HAS EQUAL
WEIGHTS WE CAN BALANCE DESIGN IF
THE DESIGN HAS UNEQUAL WEIGHTS
WE CAN UNBALANCE THE DESIGN. IN
THIS TABLE, THE SAMPLE SIZE IS
CALCULATED BASED ON POWER OF
0.8, ALPHA TYPE TWO AS 0.05.
STANDARD DEVIATION OF ONE WHICH
MEANS THE MEAN DIFFERENCE IS
EQUIVALENT TO COHEN'S D AND WE
USE THE TWO-TAILED T-TEST. FOR
THE BALANCED DESIGN FOR THE
EFFECT SIZE OF 0.5, THE SAMPLE
SIZE IS 64 FOR EACH GROUP. IF
WE WANT TO REDUCE THE SUBJECTS
IN THE PLACEBO GROUP WE CAN USE
THE RATIO OF 2:3 AND HERE WE GET
1 84 AND -- 81.
IT IS OBVIOUSLY HERE, THE4 AND
IT IS OBVIOUSLY HERE, THE54 AND
IT IS OBVIOUSLY HERE, THE TOTAL
NUMBER OF SUBJECTS THE TOTAL
SAMPLE SIZE IS ALWAYS LESS THAN
FOR THE UNBALANCED DESIGN. IT
IS CRITICAL TO NOTE THAT THE
TYPE ONE ERROR IS SET FOR SINGLE
COMPARISON. YET WE DO MULTIPLE
COMPARISONS. THE OVERALL TYPE
ONE ERROR IS NOT 0.05 AIM. WITH
INDEPENDENT COMPARISONS WITH THE
TYPE ONE ERROR OF THE FAMILY
ERROR RATE. CAN BE CALCULATE
USING THIS FORMULA. FOR
EXAMPLE, IF WE DO K -- IF WE DO
5 INDEPENDENT COMPARISONS, AT
SIGNIFICANT LEVEL OF 0.5 OF ALL
TYPE ONE ERROR WILL BE 0.226 AND
THE WEIGHT -- IF K GO TO 20 AT
ALPHA EQUAL TO 0.05 THE TYPE ONE
ERROR WILL BE 0.64 AND FOR
THE -- IF WE DO 5 INDEPENDENT
COMPARISON AND WE SAID ALPHA
EQUAL TO 0.01 AND THEN THE
FAMILY TYPE WE STILL HAVE 0.05
FOR EXAMPLE THE STUDY INCLUDE
ONE PRIMARY OUTCOME AND FIVE
EXPLANATORY VARIABLES FOR THE
ASSOCIATION TEST. TO KEEP FWER
AT 0.05 WE SHOULD SET ALPHA AT
0.01 IN POWER ANALYSIS. HOWEVER
IT IS ESTIMATE 0 ON POWER OF 0.8
AND 0.05 THE STUDY WOULD HAVE
POWER OF 0.8 AFTER ADJUSTING THE
P-VALUES FOR THE MULTIPLE TESTS.
MULTIPLICITY CAN ARISE IN THE
FOLLOWING SITUATIONS. IF THE
PROTOCOL INCLUDES MULTIPLE
PRIMARY HIYPOTHESES OR MULTIPLE
PRIMARY OUTCOMES OR MULTIPLE
EXPLANATORY VARIABLES OR
SUBGROUP ANALYSES OR INTERIM
ANALYSIS IF ANY OF THE ABOVE
SITUATION WE NEED TO SET THE
LEVEL TO 0.05 TO ACCOUNT FOR THE
COMPARISON IN ORDER TO KEEP THE
PLANNED POWER. OUR ANALYSIS IS
BASED ON ASSUMPTIONS AND GUESSES
AND MAYBE THE TWO UNDER --
OVERESTIMATE SAMPLE SIZE. SO IT
IS RECOMMENDED THAT TO PLAN --
IF WE ARE NOT SURE -- ESPECIALLY
WE ARE NOT SURE ABOUT THE
COMPONENTS WE SHOULD -- WE NEED
TO PLAN AN INTERIM ANALYSIS. TO
ESTIMATE THE SAMPLE SIZE USING
THE ESTIMATED DATA OF SIGMA.
ALL TO RUN THE POWER ANALYSIS
USING SEVERAL VALUES OF THE
COMPONENTS. SUCH A AS THETA AN
SIGMA AND TO GET MULTIPLE SAMPLE
SIZE. THE SAMPLE SIZE BY
CONSIDERING SOME OTHER FACTORS
SUCH AS RESOURCES AND THE
MINIMAL CLINICAL IMPORTANT
EFFECT SIZE. SAY THERE'S A
SAMPLE SIZE IS BASED ON
ASSUMPTIONS AND GUESSES, WE
CANNOT ESTIMATE PROCESSES
PRECISELY. WE MAKE IT WITH THE
OVER OR UNDERESTIMATED SAMPLE
SIZE. HOWEVER, OVERESTIMATED
SAMPLE SIZE IS TYPICALLY SAFE
NEVER TERMS OF -- SAFE NEVER
TERMS OF ACHIEVING RELIABLE
SEARCH RESULTS.
HOWEVER, THIS IS SEEN AS LESS
RISKY THAN UNDERESTIMATING
SAMPLE SIZE. NEXT I'M GOING TO
PRESENT TWO EXAMPLES OF POWER
ANNUAL SIS -- ANALYSIS.
POWER ANALYSIS HAS TWO LOTS, ONE
IS -- ONE IS SAMPLE SIZE
ESTIMA
ESTIMATION. THE OTHER ONE IS
POWER ESTIMATION. THE FIRST
EXAMPLE DRAWS UP SAMPLE SIZE
ESTIMATION. THE SECOND EXAMPLE
SHOW -- WILL SHOW THE POWER
ESTIMATION. THIS EXAMPLE SHOW
HOW TO USE -- THE PILOT STUDY OF
THE SAMPLE SIZE. THE FIRST IS A
PARALLEL GRIPE DESIGN. THE NULL
IS BETWEEN THE TREATMENT OF
ZERO. TO TEST THOSE HYPOTHESIS
WE USE TWO SAMPLE T-TEST WHICH
MEANS WE DON'T USE ANY
COVARIANTS. THE CLINICAL SIZE
IS 1.1 UNITE. THE PILOT STUDY
IS CONDUCTED TO ASSESS
FEASIBILITY AND ESTIMATE
STANDARD DEVIATION. THIS IS
ALSO THE PARALLEL GROUP DESIGN
WITH SAMPLE SIZE 12 N GROUP. AT
FIRST WE DID A TWO SAMPLE T-TEST
USING THE PILOT STUDY. FROM THE
TREATMENT GROUP, WE CALCULATED A
SAMPLE AS THIS AND A SAMPLE
STANDARD DEVIATION AT 2.6. WITH
THE CALCULATED GROUP WE HAVE THE
SAMPLE AS 4.2 AND THE STANDARD
DEVIATION AT 2.15. THEY
WEIGHTED EQUITY OF VARIANCE TEST
AND GET P EQUAL 0.536 THIS
INDICATES THAT THE VARIANCE FROM
THE TWO GROUPS ARE SIMILAR.
THEN WE CAN CALCULATE THE POOLED
STANDARD DEVIATION. FOR THE
TREATMENT EFFECT, WITH THE
SAMPLE TREATMENT FACTOR IS 1.64.
CALCULATED FROM THE DIFFERENCE
FROM THE TREATMENT AND THE
CONTROL GROUP. AND THE 95
INTERVAL IS THIS. SINCE THE 95%
INTERVAL INCLUDE ZERO THEREFORE
THE DIFFERENCE IS NOT
SIGNIFICANT FROM ZERO AT
SIGNIFICANCE LABEL OF 0.05. SO
THIS MEANS THAT WE ARE 95% SURE
THAT THE TRUE VALUE OF DATA IS
EXIST IN THE INTERVAL. TO
CALCULATE THE SAMPLE SIZE WE
NEED TO CALCULATE THE 80% UP AND
GIVE IT OF THE DATA, OF THE
SIGMA AND FIRST WE CALCULATE THE
60% INTERVAL AS THIS AND THEN WE
GET THE 80% UP ONE SIDED
CONFIDENCE LIMIT AS THIS. WHICH
MEANS WE ARE 80% SURE OF THE
TRUE VALUE OF SIGMA. AND THEN
WE DO POWER ANALYSIS USING THE
TWO TAILED TWO SAMPLE T-TEST.
AND POWER OF 0.8 AND ALPHA AT
0.05 FOR THE SAMPLE SIDE 1.1 WE
CALCULATE IT AS ONE HUNDRED
GROUP. YET WE DO NOT KNOW THE
EFFECT SIZE. WE CAN DO THE SAME
THING AS WE ESTIMATE THE
POPULATION STANDARD DEVIATION IS
UP OF ONE SIDE INTEGRAL HERE WE
USE LOWER ONE SIDED INTERVAL
BECAUSE WE DON'T WANT TO
UNDERESTIMATE THE OVER -- SORRY,
WE DON'T WANT TO OVERESTIMATE
THE EFFECT SIZE. AND THEN WE
GET A 60% INTERVAL AND THEN WE
GET 80% LOWER. THEREFORE WE ARE
80% SURE THAT THE TRUE VALUE OF
THE DATA IS GREAT THAN 0.81.
BASED ON THIS WE GET THE SAMPLE
SIZE AS 184. YOU SEE THE BIG
DIFFERENCE BETWEEN THESE TWO
SAMPLE SIZE. AND THIS PLOT WAS
CREATED USING THE EFFECT SIZE
FROM LOWER ONE SIDED LIMIT OF
0.8 AND THE TWO ESTIMATE OF 164
YOU WILL SEE THE SAMPLE SIZE
DECREASE AS THE EFFECT SIZE
INCREASES. THE SECOND EXAMPLE
SHOW TO DETERMINE THE POWER WITH
GIVING THE SAMPLE SIZE AND
EFFECT SIZE. THE OBJECTIVE OF
THIS STUDY IS TO ASSESS THE
EFFECTIVENESS OF GROUP PSYCHO
CHAIRPERSON FOR PATIENTS WITH
CONVERSION DISORDER. THE
DESIGN, FIRST WE WANT THE DESIGN
AS PARALLEL GROUP DESIGN. SO
AFTER THE INITIAL ASSESSMENT THE
CD PATIENT WILL BE RANDOMIZED TO
THE PSYCHOTHERAPY TREATMENT
GROUP OR CONTROL GROUP. THE
EFFICACY OF THE THERAPY WILL BE
EVALUATED BY THE DIFFERENCE IN
THE SCORE BETWEEN THE TREATED
GROUP AND THE CONTROL GROUP. SO
THE HYPOTHESIS IS 0. THE
PRIMARY OUTCOME MEASURE IS THE
SCORE OF ABILITY OF PARTICIPATE
IN SOCIAL ROLES AND ACTIVITIES.
THE HIGHER SCORES REPRESENT
BETTER ABILITIES. BASED ON THE
POPULATION AND THE STANDARD
DEVIATIONS CAN HAVE THE MEAN OF
50. THE INVESTIGATOR CONSIDERS
A 15% CHANGE AS A CLINICAL
IMPORTANT. THUS EFFECT SIZE IS
7.5. THE INVESTIGATOR HAS
RESOURCES ONLY 20 SUBJECTS SO
THE POWER ANALYSIS IS TO
DETERMINE THE POWER FOR GIVING
SAMPLE SIZE OF 20 AND EFFECT
SIZE OF 7.5. WE DID -- I DID
THE TWO-SAMPLE T-TEST AT AN
ALPHA 0.05 AND THE SIGMA 10.
AND FOR THE SAMPLE SIZE 28. AND
WE ESTIMATE THE POWER AS 0.355
THIS MEANS FOR SAMPLE SIZE OF 10
WE ONLY HAVE 0.355 THE
DIFFERENCE OF 7.5 AT THE
TREATMENT GROUP. FOR THE POWER
0.8 THE SAMPLE SIZE IS 58 OR 29
PER GROUP. THEN WE CHANGE THE
DESIGN AS QUASI EXPERIMENTAL
DESIGN. OF ONE GROUP PRETEST OR
POSTTEST DESIGN. THIS DESIGN
COMPARE WITH THE PRETEST DESIGN.
SO UNDER THE INITIAL ASSESSMENT,
ALL 20 PATIENTS WILL GET THE 6
MONTHS OF PSYCHOTHERAPY. THEN
WE WILL BE ASSESSED AGAIN
POSTTEST. EACH SUBJECT SERVES
AS HIS/HER OWN CONTROL. THE
EFFICACY OF THE THERAPY IS
EVALUATED BY THE DIFFERENCE IN
THE SCORE BETWEEN THE PRETEST
AND THE POSTTEST THE POWER
ANALYSIS DETERMINE THE POWER FOR
GIVING SOME AT 20 AND THE
EFFECTS AS 7.5. BASED ON THE
PAIRED T-TEST FOR THIS DESIGN
AND ALPHA AT 0.05 STANDARD
DEVIATION WE USE THE 10. HERE
WE SEE THE CORRELATION IN THE
SCORE BETWEEN PRE AND POSTTEST
IS AT 0.5. AND FOR SAMPLE SIZE
OF 20, WE GET THE POWER OF
0.889. WHAT THIS MEANS THE
STUDY WITH ONE GROUP DESIGN AND
THE SAMPLE SIZE OF 20 WOULD HAVE
POWER OF 0.89 TO DETECT THE
SAMPLETIZE OF 7.5 AT A LABEL OF
0.05. FOR POWER OF 0.8 THE
SAMPLE SIZE IS 16. PLEASE
NOTICE THE CONCLUSION FROM THIS
STUDY IS SUBJECT TO BIAS.
BECAUSE LACK OF RANDOMIZATION
AND CONTROL GROUP. THEREFORE,
THE CONCLUSION FROM THE QUASI
EXPERIMENTAL -- THIS QUASI
EXPERIMENTAL DESIGN IS MUCH,
MUCH WEAKER THAN FROM THE
PARALLEL DESIGN. AS WE COME TO
THE END OF THE LEK CHUCTURE. ID
LIKE TO EMPHASIZE THE IMPORTANCE
OF POWER ANNUALYSIS NOT ONLY TO
AVOID THE STUDY FROM BEING
UNDERPOWERED OR OVERPOWERED BUT
ALSO TO IMPROVE THE STUDY DESIGN
SUBSTANTIALLY. BECAUSE
PERFORMING POWER ANALYSIS
REQUIRE INVESTIGATORS TO THINK
THROUGH THE FOLLOWING ISSUES.
HOW TO GENERATE THE HYPOTHESIS.
WHAT ARE -- WHAT IS THE OUTCOMES
WE SHOULD USE? WHICH ONE SHOULD
BE PRIMARY? WHICH ONE SHOULD BE
SECONDARY? AND WHAT TYPE OF
VARIABLE SHOULD WE USE?
CONTINUOUS, CATEGORICAL, AND
ALSO THINK ABOUT DO WE NEED
INTERIM ANALYSIS TO ESTIMATE THE
COMPONENTS FOR POWER ANALYSIS?
AND WHAT EXPERIMENTAL DESIGN
SHOULD WE USE? OBSERVATIONAL
STUDY? LONGITUDINAL,
CROSS-SECTIONAL AND WHAT METHOD
SHOULD WE USE? REGRESSION, AND
DO WE INCLUDE THE COVARIATE OR
NOT. AND WHAT RANDOMIZATION DO
WE USE? DO WE USE THE COVARIATE
RANDOMIZATION. AND FINALLY, FOR
THE SIGNIFICANCE OF LEVEL. WHAT
KIND OF SIGNIFICANCE SHOULD WE
USE. IS BASED ON NUMBER OF
COMPARISONS. THE NUMBER OF
PRIMARY HYPOTHESES OR WE NEED --
OR WE JUST INCLIUDE SUBGROUP
ANALYSIS AND FINALLY THE DROPOUT
RATE DEFINITELY SHOULD BE
CONSIDERED. AND IF YOU WANT TO
GET TO THE POWER ANALYSIS HERE'S
THE REFERENCES I USED FOR THIS
LECTURE. AND THANK YOU VERY
MUCH, ANY QUESTIONS?
>> SLIDES WILL BE AVAILABLE AT
SOME POINT AFTER THE
PRESENTATION.
>> I DON'T THINK I SEE ANY
FURTHER QUESTIONS COMING
THROUGH, YEAH. ALL RIGHT, THANK
YOU, ALL, FOR JOINING.
>> TIANXIA: THANK YOU VERY MUCH.
ANY QUESTIONS, YOU CAN ALSO
E-MAIL ME. 911 00:55:25,188 >> THANKS, TIANXIA.