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Sample size and Power |
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Version 0.6 |
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September 29, 2003 |
Copyright (c) 2003 Philippe Glaziou. All rights reserved.
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this manual provided the copyright notice and this permission notice
are preserved on all copies.
This document is free; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
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WITHOUT ANY WARRANTY; without even the implied war ranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU General Public License for more details. You
should have received a copy of the GNU General Public License along
with this program; if not, write to the Free Software Foundation,
Inc., 59 Te mple Place, Suite 330, Boston, MA 02111-1307, USA.
Section: GNU Sampsize (1)
Updated: 2003-05-08
sampsize - Computes sample size and power
sampsize
[-h]
[-v]
[-onesided]
[-onesample]
[-matched]
[-cc continuity]
[-pop pop]
[-e precision]
[-pr prevalence]
[-level level]
[-alpha alpha]
[-power power]
[-c ratio]
[-or odds_ratio]
[-exp exposed]
[-cp comp]
[-means means]
[-rho rho]
[-d delta]
[-nob observed]
[-bi binomial]
[-n sample]
[-obsclus obsclus]
[-numclus numclus]
- -h
- show usage information
- -v
- show program version
- -onesided
- one-sided test for comparisons
- -onesample
- one-sample test
- -matched
- 1:1 matched case-control study
- -cc
- continuity
- -pop
- target population size,
1 value between 0.0 and oo.
Default: `0'
- -e
- precision of estimate (%) -
- prevalence study option,
1 value between 0.0 and 100.
- -pr
- prevalence (%) -- prevalence study option,
1 value between 0.0 and 100.
Default: `50'
- -level
- level of confidence interval (%),
1 value between 50.0 and 100.
Default: `95'
- -alpha
- Risk alpha (%),
1 value between 0.0 and 100.
Default: `5'
- -power
- Power of the test (%),
1 value between 50.0 and 100.
Default: `90'
- -c
- number of controls per case,
1 integer value between 0 and oo with case control options, or
1 value between 0.0 and oo with other relevant options,
Default: `1'
- -or
- Odds Ratio -- case-control study option,
1 value between 0.0 and oo.
- -exp
- Exposed controls (%) -- case-control study option,
1 value between 0.0 and 100.
- -cp
- #p1 (%) #p2 (%) -- two sample comparison of percentages,
2 consecutive values between 0.0 and 100.
- -means
- #m1 #m2 #sd1 #sd2 -- two sample comparison of means,
3 values if onesample is selected or else, 4 consecutive values.
- -rho
- intraclass correlation coefficient -- cluster option
1 value between 0.0 and 1, default 0
- -nob
- minimum number of events observed in the sample,
1 integer value between 1 and 10000.
- -bi
- #obs #succ (binomial events, #obs >= #succ),
2 integer values between 0 and oo.
- -n
- determine power from sample size,
n = size of first group (two-group comparative studies)
n = number of cases (unmatched case-control study)
n = number of pairs (1:1 matched case-control study)
1 integer value between 1 and oo.
- -obsclus
- number of observations per cluster
1 integer value > 0
- -numclus
- minimum number of clusters
1 integer value > 0
- -d
- delta critical value
1 value between 0.0 and oo
Sampsize computes sample size and power for prevalence studies, sample
size and power for one-sample and two-sample comparative studies of percentages
and means, and for unmatched and 1:1 matched case-control studies.
- Prevalence Surveys
-
The following options are relevant to simple prevalence studies:
- -e
- precision (%): we wish to obtain confidence limits equal to prevalence +/- precision
- -pr
- prevalence (%), default 50%
- -pop
- target population size, default 0 (infinite)
- -level
- of confidence interval, default 95%
The population size is the total size of the population from which a
sample will be drawn for a prevalence survey. If the population size
is small, the correction for finite population will result in a
reduced sample size. A prevalence study will need either the -e
option for precision, or the -nob option to specify a finite
number of events (see below).
Entering 50 (50%) for the estimated prevalence (-pr 50), which
is the default value, will result in the highest estimated sample
size. Entering 0 for the population size (-pop 0) will result
in the programme using an infinite population size. If a null
prevalence is entered ( -pr 0), sampsize returns the
estimated sample size needed for a 95% (default) confidence interval
upper limit that is equal to the entered precision (option -e).
Any other confidence interval may be selected instead of the 95%
confidence interval, using the option -level. Sampsize
will display the binomial exact confidence interval using the returned
sample size unless a finite population size is specified. It may
happen that this exact interval is larger than the expected interval
(prevalence plus or minus precision), when the number of successful
events is lower than 5, or when sample size minus that number is lower
than 5, due to the lack of precision of the normal approximation
formula with small numbers. In thoses instances, it is advisable to
test different hypotheses of sample size and hypothetical numbers of
successful binomial events using the -bi option (see below).
- Minimum number of events to detect
-
This is a variation over the previous design: prevalence is low and
the capacity to deal with a large sample often necessary to achieve a
reasonable precision of the measured estimate is limited. We will
rather want to detect with probability specified with -level at
least n sampled units with the studied characteristic, given a
probability of occurence = prevalence (-pr). The option -nob instructs sampsize to return the sample size needed to observe
at least -nob successful events, given a -pr probability
of occurence. Relevant options are:
- -nob
- number to observe
- -pr
- prevalence: probability (%) of occurence of one event
- -level
- probability of observing the given number of events
- Binomial confidence intervals
-
The first design options may lead to small samples and the
approximations used to estimate sample size are known to be non valid
if less than 5 sampled units are expected to have the studied
characteristic (equally problemactic: all sampled units minus 5 or
less have that characteristic). One alternative approach is to
calculate the binomial exact confidence intervals that result from
different sets of numbers. Relevant options are:
- -bi
- two parameters: number of observations, number of successes
- -level
- of confidence interval, default 95%
- Comparison of percentages and means: sample size and power
-
Sampsize estimates the required sample size for studies
comparing two groups. Sampsize can be used when comparing
means or proportions for simple studies where only one measurement of
the outcome is planned. Sampsize computes the sample size for
two-sample comparison of means, where the postulated values of the
means and standard deviations are -means m1 m2 sd1 sd2;
one-sample comparison of mean to hypothesized value (option -onesample must be specified and only three parameters to the
option -means are allowed in one-sample tests: m1, m2 and sd1);
two-sample comparison of proportions (option -cp where the
postulated values of the proportions are #1 and #2); and one-sample
comparison of proportion to hypothesized value (option -onesample should be specified), where the hypothesized proportion
(null hypothesis) is #1 and the postulated proportion (alternative
hypothesis) is #2. Default power is 90%. If -n is
specified, sampsize will compute power.
In the case of a cluster sampling design, a sample of natural groups
of individuals is selected, rather than a random sample of the
individuals themselves. Observations are no longer independant as we
would expect had they been drawn randomly from the population.
Nonindependance is measured by the intraclass correlation, which is
specified with option -rho (between 0 and 1). One may then
specify -numclus, the number of clusters (for instance, the
number of physicians who will recruit the patients: typically, the
intraclass orrelation will be fairly small, often between 0 and 0.05),
or alternatively, -obsclus, the minimum number of
observations per cluster. The larger the number of clusters and the
fewer observations per cluster, the less the effect on the standard
error estimates. A sample of 250 consisting of 50 clusters with 5
observations per cluster will have better power than the same sample
size consisting of 25 clusters with 10 observations per cluster. In
fact, with only one observation per cluster, we are back to a simple
random sample. If there is no intraclass correlation, there will be no
increase in the sample size estimate.
By default, no continuity correction is applied when computing sample
size or power for the comparison of two percentages. However, the
correction may be applied with option -cc . The correction
will result in a greater sample size and smaller power. Simulations
showed that the correction is most often too conservative (Alzola C
and Harrell F, An introduction to S and the Hmisc and Design
Libraries: http://hesweb1.med.virginia.edu/biostat/s/splus.html).
Relevant options are (either -cp or -means must be
specified, not both):
- -cp
- percentages (%), two parameters for two proportions to compare
- -means
- two means and two standard deviations (one if one-sample): m1 m2 sd1 [sd2]
- -alpha
- alpha risk (%), default 5%
- -n
- sample size of the first group (total sample size in one-sample comparison)
- -power
- power of the comparison (%), default 90%
- -onesided
- one-sided test
- -onesample
- one-sample comparison against hypothesized value
- -rho
- intraclass correlation (between 0 and 1)
- -obsclus
- number of observations per cluster
- -numclus
- minimum number of cluster
- -cc
- continuity correction
- Case-control studies
-
To specify a case-control design, we need to type the option -exp, which specifies the percentage of exposed controls. If we add
the option -or, the odds-ratio that that we wish to detect,
sampsize will return the sample size for an unmatched design
(option -c specifies the ratio of controls/cases, the default
ratio is 1). The option -matched may be used to specify a 1:1
matched study design (-c may not be used with -matched).
If we specify -exp, -or, and -n, sampsize will return the power of the specified design. If one
specifies -exp and -n, which is the number of cases,
sampsize will return the minimum detectable odds-ratio greater
than one and the maximum detectable odds-ratio lower than one, an
alternative to the power determination. Relevant options are:
- -exp
- percentage exposed among controls
- -n
- number of cases, or number of pairs if 1:1 matched case-control study
- -or
- odds-ratio to detect
- -c
- ratio of controls/cases (truncated to integer), default 1, not used if matched
- -alpha
- alpha risk (%), default 5%
- -power
- power of the comparison (%), default 90%
- -onesided
- one-sided test
- -matched
- 1:1 matched case-control study
- Equivalence trials: sample size
-
The goal of an equivalence trial is to prove that two quantities are
equal. The hypothesis framework for an equivalence trial requires the
specification of no difference in the alternative and a difference in
the null. It contains an additional parameter delta, -d, to
indicate the maximum clinical difference allowed for an experimental
therapy to be considered equivalent with a standard therapy. Binomial
endpoints are defined as the positive difference of the probability of
success for the standard group (ps) and the probability of
success for the experimental group (pt) of patients. These
probabities are entered with -cp #ps #pt (percentages), and
delta is entered as a percentage. In the case of a continuous
endpoint, delta indicates the maximum clinical difference allowed for
the comparison of two means, and is entered using the -d option.
Means and standard deviations are to be entered the usual way with
-means ms me ss se, with ms and me the means in the standard and
experimental group, respectively, and ss and se the standard
deviations.
There is a general misconception that it requires a larger sample to
prove equivalence than difference. The veracity of this assumption is
situation-specific and dependant upon the degree of difference, delta,
one is willing to allow so that the standard and experimental
treatments may still be considered equivalent. Relevant options are:
- -cp
- percentages
(%), two parameters for two proportions to compare
- -means
- two means and two
standard deviations (one if one-sample): m1 m2 sd1 [sd2]
- -alpha
- alpha risk
(%), default 5%
- *
- To calculate the sample size given a 50% prevalence
(default) and infinite population size (also default), with 5%
precision: the upper boundary of the confidence interval will equal
the observed prevalence plus 5%, and the lower boundary will equal
the observed prevalence minus 5%, i.e. [45% - 55%]:
-
- cunegonde:~>sampsize -e 5
Assumptions:
Precision = 5.00 %
Prevalence = 50.00 %
Population size = infinite
95% Confidence Interval specified limits [ 45% -- 55% ]
(these limits equal prevalence plus or minus precision)
Estimated sample size:
n = 385
95% Binomial Exact Confidence Interval with n = 385
and n * prevalence = 193 observed events:
[45.0212% -- 55.2365% ]
- *
- To get the needed sample size after correction for population
size (n = 1500):
-
- cunegonde:~>sampsize -e 5 -pop 1500
Assumptions:
Precision = 5.00 %
Prevalence = 50.00 %
Population size = 1500
95% Confidence Interval specified limits [ 45% -- 55% ]
(these limits equal prevalence plus or minus precision)
Estimated sample size:
n = 306
- *
- Assuming a prevalence of 10%, a precision of 4% estimated
using a 90% confidence interval, and a target population size of
2500:
-
- cunegonde:~>sampsize -pr 10 -e 4 -pop 2500 -level 90
Assumptions:
Precision = 4.00 %
Prevalence = 10.00 %
Population size = 2500
90% Confidence Interval specified limits [ 6% -- 14% ]
(these limits equal prevalence plus or minus precision)
Estimated sample size:
n = 144
- *
- Assuming that the observed prevalence in the sample will be
null, for a 97.5% one-sided confidence interval upper limit that is
equal to the entered precision (2% in this example), type:
-
- cunegonde:~>sampsize -pr 0 -e 2
Assumptions:
Precision = 2.00 %
Prevalence = 0.00 %
Population size = infinite
A null prevalence was entered, we assume here that the observed
prevalence in the sample will be null, and compute the sample
size for an upper limit of the confidence interval equal to the
entered precision. The population size is not taken into account
even if a finite size was entered. Sample sizes are calculated
using the binomial exact method.
97.5% one-sided Confidence Interval upper limit = 2.00
Estimated sample size:
n = 183
- *
- Assuming that the observed prevalence in the sample will be
null, for 95% one-sided confidence interval upper limit equal to
the entered precision (2% in this example), type:
-
- cunegonde:~>sampsize -pr 0 -e 2 -level 90
Assumptions:
Precision = 2.00 %
Prevalence = 0.00 %
Population size = infinite
A null prevalence was entered, we assume here that the observed
prevalence in the sample will be null, and compute the sample
size for an upper limit of the confidence interval equal to the
entered precision. The population size is not taken into account
even if a finite size was entered. Sample sizes are calculated
using the binomial exact method.
95% one-sided Confidence Interval upper limit = 2.00
Estimated sample size:
n = 149
- *
- A study on the hepatitis C virus aims at describing some
characteristics of the virus strains. It is assumed that the
prevalence of virus positive individuals is 10% in the population.
The investigators wish to calculate the sample size needed to be
95% sure that at least 5 patients will harbour a virus.
-
- cunegonde:~>sampsize -nob 5 -pr 10
Assumptions:
prevalence = 10%
minimum number of successes = 5 in the sample
with probability = 95%
Estimated sample size:
n = 90
- *
- You flip a coin 10 times and it comes up heads only once. You
are shocked and decide to obtain a 99% confidence interval for this
coin:
-
- cunegonde:~>sampsize -bi 10 1
Assumptions:
number of observations = 10
number of successes = 1
Binomial Exact 95% Confidence Interval:
[0.252858% -- 44.5016%]
- *
- Someone claims that US females are more likely than US males to
study French. Our null hypothesis is that the proportion of female French
students is 0.5. We wish to compute the sample size that will give us a 80%
power to reject the null hypothesis if the true proportion of female French
students is 75%.
-
- cunegonde:~>sampsize -cp 50 75 -power 80 -onesample
Estimated sample size for one-sample comparison of percentage to
hypothesized value
Test Ho: p = 50%, where p is the percentage in the population
Assumptions:
alpha = 5% (two-sided)
power = 80%
alternative p = 75%
Estimated sample size:
n = 29
- *
- We want to conduct a survey on people
's opinions of
the President's performance. Specifically, we want to
determine whether members of the President's party have a
different opinion from people with another party affiliation. We
estimate that only 25% of members of the President's party
will say that the President is doing a poor job, whereas 40% of
other parties will rate the President's performance as poor.
We compute the sample size for alpha = 5% (two-sided) and power =
90%:
-
- cunegonde:~>sampsize -cp 25 40
Estimated sample size for two-sample comparison of percentages
Test H: p1 = p2, where p1 is the percentage in population 1
and p2 is the percentage in population 2
Assumptions:
alpha = 5% (two-sided)
power = 90%
p1 = 25%
p2 = 40%
Estimated sample size:
n1 = 216
n2 = 216
- *
- Following the calculation for the survey on the
President
's performance, we realize that we can sample only
n1 = 300 members of the President's party and a sample of n2
= 150 members of other parties, due to time constraints. We wish to
compute the power of our survey:
-
- cunegonde:~>sampsize -n 300 -cp 25 40 -c 0.5
Estimated power for two-sample comparison of percentages
Test Ho: p1 = p2, where p1 is the percentage in the population 1
and p2 is the percentage in the population 2
Assumptions:
alpha = 5 (two-sided)
p1 = 25%
p2 = 40%
sample size n1 = 300
sample size n2 = 150
n2/n1 = 0.5
Estimated power:
power = 87.8976%
- *
- We wish to study the proportion of patients who have not
recovered from a back pain by 4 weeks, and compare the outcome
between patients in whom sciatica was diagnosed and patients without
sciatica. We know that typically, about 20% of acute low back pain
patients have not recovered by 4 weeks and think that the percentage
may be 30% for patients who also have sciatica. The sample size we
would need to detect this difference between the two groups, with a
two-sided alpha of 5% and a power or 80% is 313:
-
- cunegonde:~>sampsize -cp 20 30 -power 80
Estimated sample size for two-sample comparison of percentages
Test H: p1 = p2, where p1 is the percentage in population 1
and p2 is the percentage in population 2
Assumptions:
alpha = 5% (two-sided)
power = 80%
p1 = 20%
p2 = 30%
Estimated sample size:
n1 = 313
n2 = 313
- *
- Now we look at the same example using 10 observations per
cluster and an intraclass correlation of 0.1:
-
- cunegonde:~>sampsize -cp 20 30 -power 80 -obsclus 10 -rho 0.1
Estimated sample size for two-sample comparison of percentages
Test H: p1 = p2, where p1 is the percentage in population 1
and p2 is the percentage in population 2
Assumptions:
alpha = 5% (two-sided)
power = 80%
p1 = 20%
p2 = 30%
Estimated sample size:
n1 = 313
n2 = 313
Sample size adjusted for cluster design:
Intraclass correlation = 0.1
Average obs. per cluster = 10
Minimum number of clusters = 119
Estimated sample size per group:
n1 (corrected) = 595
n2 (corrected) = 595
- *
- Taking into account the cluster design of the study, our
samples have increased to 595 per group and a total of 119
physicians (clusters). Finally, we try the calculation assuming only
40 physicians:
-
- cunegonde:~>sampsize -cp 20 30 -power 80 -numclus 40 -rho 0.1
Sample size adjusted for cluster design:
Error: for rho = 0.1, the minimum number of clusters possible is:
numclus = 63
- *
- We got an error message telling us that, given these sets of
sample size parameters, it is not possible to estimate a sample size
with fewer than 63 clusters. We need to rerun sampsize with
different parameters in order to get a manageable number of
patients.
-
- cunegonde:~>sampsize -cp 20 30 -power 80 -numclus 40 -rho 0.05
Sample size adjusted for cluster design:
Intraclass correlation = 0.05
Average obs. per cluster = 69
Minimum number of clusters = 40
Estimated sample size per group:
n1 (corrected) = 1378
n2 (corrected) = 1378
- *
- We wish to test the effects of a low-fat diet on serum
cholesterol levels. We will measure the difference in cholesterol
level for each subject before and after being on the diet. Since
there is only one group of subjects, all on diet, this is a
one-sample test. Our null hypothesis is that the mean of individual
differences in cholesterol level will be zero; i.e., mdiff =
0mg/100ml. If the effect of the diet is as large as a mean
difference of -10mg/100ml, then we wish to have power of 95% for
rejecting the null hypothesis. Since we expect a reduction in
levels, we want to use a one-sided test with alpha = 2.5%. Based on
past studies, we estimate that the standard deviation of the
difference in cholesterol levels will be about 20mg/100ml:
-
- cunegonde:~>sampsize -means 0 -10 20 -onesample -alpha 2.5 -onesided -power 95
Estimated sample size for one-sample comparison of mean to
hypothesized value
Test Ho: m = 0, where m is the mean in the population
Assumptions:
alpha = 2.5 (one-sided)
power = 95
alternative m = -10
sd = 20
Estimated sample size:
n = 52
- *
- We decide to conduct the cholesterol study with n = 60
subjects, an we wonder what the power will be at a one-sided
significance level of alpha = 1%:
-
- cunegonde:~>sampsize -n 60 -means 0 -10 20 -onesample -onesided -alpha 1
Estimated power for one-sample comparison of mean
to hypothesized value
Test Ho: m = 0%, where m is the mean in the population
Assumptions:
alpha = 1% (one-sided)
alternative m = -10
sd = 20
sample size = 60
Estimated power:
power = 93.9024%
- *
- We are doing a study of the relationship of oral
contraceptives (OC) and blood pressure (BP) level for women ages
35-39. From a pilot study, it was determined that the mean and
standard deviation BP of OC users were 132.86 and 15.34,
respectively. The mean and standard deviation BP of OC users were
127.44 and 18.23. Since it is easier to find OC nonusers than users
in the country were the study is conducted, we decide that n2, the
size of the sample of OC users, should be twice n1, the size of the
sample of OC users; that is, c = n2/n1 = 2. To compute the sample
sizes for alpha = 5% (two-sided) and the power of 80%:
-
- cunegonde:~>sampsize -means 132.86 127.44 15.34 18.23 -power 80 -c 2
Estimated sample size for two-sample comparison of means
Test Ho: m1 = m2, where m1 is the mean in population 1
and m2 is the mean in population 2
Assumptions:
alpha = 5 (two-sided)
power = 80
m1 = 132.86
m2 = 127.44
sd1 = 15.34
sd2 = 18.23
n2/n1 = 2
Estimated sample size:
n1 = 108
n2 = 216
- *
- We now find that we only have enough money to study 100
subjects from each group for the above oral contraceptives study. We
can compute the power for n1 = n2 = 100
-
- cunegonde:~>sampsize -n 100 -means 132.86 127.44 15.34 18.23
Estimated power for two-sample comparison of means
Test Ho: m1 = m2, where m1 is the mean in the population 1
and m2 is the mean in the population 2
Assumptions:
alpha = 5% (two-sided)
m1 = 132.86
m2 = 127.44
sd1 = 15.34
sd2 = 18.23
sample size n1 = 100
sample size n2 = 100
n2/n1 = 1
Estimated power:
power = 62.3601%
- *
- Patients for the study on oral contraceptives and blood
pressure will be recruited in 12 clinics, and we suspect some
intraclass correlation (patients recruited in the same clinic are
more alike than patients recruited from different clinics). Due to
the cluster sampling design, patients are not independant
observations, and we wish to correct the above sample size (sampsize
returned a sample size of 108 in the first group, and 216 in the
second group). We think that the intraclass correlation is fairly
small (0.02), and compute:
-
- cunegonde:~>sampsize -means 132.86 127.44 15.34 18.23 -power 80 -c 2
-numclus 12 -rho 0.02
Estimated sample size for two-sample comparison of means
Test Ho: m1 = m2, where m1 is the mean in population 1
and m2 is the mean in population 2
Assumptions:
alpha = 5 (two-sided)
power = 80
m1 = 132.86
m2 = 127.44
sd1 = 15.34
sd2 = 18.23
n2/n1 = 2
Estimated sample size:
n1 = 108
n2 = 216
Sample size adjusted for cluster design:
Intraclass correlation = 0.02
Average obs. per cluster = 58
Minimum number of clusters = 12
Estimated sample size per group:
n1 (corrected) = 232
n2 (corrected) = 464
The design effect is rather important despite a small intraclass
correlation, due to the small number of clusters. Sampsize returned n1
= 232 and n2 = 464, more than twice the initial sample size.
- *
- We wish to conduct a case control study to assess whether
bladder cancer is associated with past exposure to cigarette
smoking. Cases will be patients with bladder cancer and controls
will be patients hospitalized for injury. It is assumed that 20% of
controls will be smokers or past smokers, and we wish to detect an
odds-ratio of 2 with power 90%. Three controls will be recruited
for one case:
-
- cunegonde:~>sampsize -or 2 -exp 20 -c 3
Assumptions:
Odds ratio = 2
Exposed controls = 20%
Alpha risk = 5%
Power = 90%
Controls / Case ratio = 3
Total exposed = 23.3333%
Estimated sample size:
Number of cases = 150
Number of controls = 450
Total = 600
- *
- The above study on bladder cancer needed a total sample size
of 600. An alternative is to conduct a matched case-control study of
bladder cancer and cigarette smoking rather than the above unmatched
study design. One case will be matched to one control. Again, the
percentage of exposed controls is 20%, and we wish to detect a
two-fold increased risk (OR = 2). With these specifications, we need
226 pairs (total sample size 452).
-
- cunegonde:~>sampsize -or 2 -exp 20 -matched
Assumptions:
Odds ratio = 2
Exposed controls = 20%
Alpha risk = 5%
Power = 90%
Probability of an
exposure-discordant pair = 40%
Estimated sample size (number of pairs):
Number of exposure discordant-pairs = 91
Number of pairs = 226
Total sample size = 452
- *
- The following table (Kline et al., 1978) shows previous
induced abortions among multigravid cases and controls.
(Primiigravidae were excluded since these women did not have prior
pregnancies.):
| |
Spontaneous |
Controls |
| |
abortions |
|
| PIA: |
|
|
| yes |
171 |
90 |
| no |
303 |
165 |
| Total: |
474 |
255 |
The power of the study for detecting a relative risk of R = 1.5 is
calculated as follows:
, percentage exposed in
controls =
:
-
- cunegonde:~>sampsize -or 1.5 -exp 35.29 -c 0.538 -n 474
Assumptions:
Odds ratio = 1.5
Exposed controls = 35.29%
Alpha risk = 5%
Controls / Case ratio = 0.538
Total exposed = 41.6005%
Number of cases = 474
Number of controls = 255
Total = 729
Estimated power:
power = 72.0774%
- *
- Kessler and Clark (1978) studied 365 males with bladder
cancer and an equal number of controls, 35 percent of whom reported
past use of nonnutritive sweeteners. Using a one-sided test at the
alpha = 5% level, the smallest relative risk greater than one that
can be detected with 90% power is RR = 1.55:
-
- cunegonde:~>sampsize -n 365 -exp 35 -onesided
Assumptions:
Exposed controls = 35%
One-sided alpha risk = 5%
Power = 90
Number of cases = 365
Number of controls = 365
Total = 730
Estimated smallest and highest detectable odds-ratio:
Highest odds-ratio < 1 = 0.623181
Smallest odds-ratio > 1 = 1.55439
- *
- Researchers want to show that a new treatment is "as good as"
the standard one. The success rates of both treatments are expected
to be approximately 90%. The researchers want to be sure that the
new treatment is no worse than the standard treatment by an amount
of 10%. Then, the sample size for each treatment group is 155
patients:
-
- cunegonde:~>sampsize -cp 90 90 -d 10
Estimated sample size for two-sample non-inferiority comparison of percentages
Test H0: p2 < p1 - delta, where p1 is the percentage in population 1,
p2 is the percentage in population 2, and delta is the critical value
Assumptions:
alpha = 5% (two-sided)
power = 90%
p1 = 90%
p2 = 90%
delta = 10%
Estimated sample size per group:
n = 155
The most recent distributions of sampsize can be found at:
- http://prdownloads.sourceforge.net/sampsize/
sampsize project home page:
- http://sampsize.sourceforge.net/
Some parts of sampsize are translated and adapted from
publicly available code written in the stata language (Statacorp
Inc.).
- Cephes mathematical library. Release 2.8: June 2000.
http://www.moshier.net/cephes-math-28.tar.gz, accessed and
downloaded May 2002.
- Garrett JM. Sample size estimation for cluster designed samples.
STB Reprints 2002: 10; 387-393.
- Levy PS, Lemeshow S. Sampling of populations. Methods and
Applications. Wiley Series in Probability and Statistics, John Wiley
and Sons, Inc. 1999.
- Pagano P., Gauvreau K. Principles of biostatistics. 2d ed.
Pacific Grove, CA: Brooks/Cole 2000.
- Rosner B. Fundamentals of Biostatistics. 5th ed. Pacific Grove,
CA: Duxbury Press.
- Schlesselman JJ. Case-Control Studies. Design, Conduct,
Analysis. Oxford Univ. Press 1982.
- Blackwelder WC. "Proving the null hypothesis" in clinical
trials. C ontrolled Clinical Trials 1982; 3: 345-353.
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Sample size and Power |
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Version 0.6 |
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September 29, 2003 |
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