presize
: precision based sample size calculation
It is sometimes desirable to power a study on the precision of an estimate rather than for a particular hypothesis test.
presize
provides a range of functions for performing these calculations.
presize
returns either the confidence interval width that could be expected given a sample size, or the sample size that would be necessary to attain a given confidence interval width.
For instance, it may be that we want to estimate the mean amount of a blood parameter to within 5 units. Based on published literature, we expect the mean value to be 20 units, with a standard deviation of 3. To achieve the 5 unit confidence interval width, participants are required. If we know that we have funding to include 50 participants, we can calculate the confidence interval width that we could expect, and find that it would be units wide.
The different estimators are grouped according to their type (e.g. mean and proportion are under 'Descriptive statistics', while odds and risk ratios are under 'Relative differences'.
Each statistic has a set of fields. Mandatory fields are marked with an asterisk (*). There are also two fields that pertain to the sample size and confidence interval width, indicated by a dagger (†). Only one of these should be entered.
Relevant references are listed on each page.
This site uses the
presize
R package
(version
), which was developed at CTU Bern, the Clinical Trials Unit of the University of Bern and University Hospital Bern, on behalf of the Statistics & Methodology Platform of the
Swiss Clinical Trial Organisation
. The R package version of
presize
can be installed in R using the from CRAN (
install.packages('presize')
). The R code for running the calculations in this site is shown after the results. The
presize
package website can be found
here
.
If you use
presize
, please cite it in your publication as: Haynes et al., (2021). presize: An R-package for precision-based sample size calculation in clinical research. Journal of Open Source Software, 6(60), 3118,
DOI 10.21105/joss.03118
Precision of a mean
Enter the mean and standard deviation you expect. To estimate the confidence interval width from a population of size X, enter the population size in 'Number of observations'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter both of the following
Please enter one of the following
Results
Code to replicate in R:Precision of a proportion
Enter the proportion you expect. To estimate the confidence interval width from a population of size X, enter the population size in 'Number of observations'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Other settings
The Wilson confidence interval is recommended, but others are available.Results
Code to replicate in R:References
Brown LD, Cai TT, DasGupta A (2001) Interval Estimation for a Binomial Proportion, Statistical Science , 16:2, 101-117, doi:10.1214/ss/1009213286Precision of a rate
Enter the rate you expect. To estimate the confidence interval width from a number of events, enter the number of events in 'Number of events'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Other settings
Results
Code to replicate in R:References
Barker, L. (2002) A Comparison of Nine Confidence Intervals for a Poisson Parameter When the Expected Number of Events is ≤ 5, The American Statistician , 56:2, 85-89, DOI: 10.1198/000313002317572736Precision of a mean difference
Enter the mean difference and standard deviations you expect. If you intend to use uneven allocation ratios (e.g. 2 allocated to group 1 for each participant allocated to group 2), adjust the allocation ratio accordingly. To estimate the confidence interval width expected with a particular number of observations, enter the number of observations in 'Number of observations'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'. For the difference between paired observations, use the routine for a simple mean.Please enter the following
Please enter one of the following
Results
Code to replicate in R:Precision of a risk difference
Enter the proportions of events you expect in the groups. If you intend to use uneven allocation ratios (e.g. 2 allocated to group 1 for each participant allocated to group 2), adjust the allocation ratio accordingly. To estimate the confidence interval width from a number of events, enter the number of events in 'Number of events'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Other settings
Results
Code to replicate in R:References
Agresti A (2003) Categorical Data Analysis , Second Edition, Wiley Series in Probability and Statistics DOI: 10.1002/0471249688Agresti A and Caffo B (2000) Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures, The American Statistician 54(4):280-288
Miettinen O and Nurminen M (1985) Comparative analysis of two rates, Statistics in Medicine , 4:213-226
Newcombe RG (1998) Interval estimation for the difference between independent proportions: comparison of eleven methods, Statistics in Medicine , 17:873-890
Fagerland MW, Lydersen S, and Laake P (2015). Recommended confidence intervals for two independent binomial proportions, Statistical methods in medical research 24(2):224-254.
Precision of an odds ratio
Enter the proportions of events you expect in the groups. If you intend to use uneven allocation ratios (e.g. 2 allocated to group 1 for each participant allocated to group 2), adjust the allocation ratio accordingly. To estimate the confidence interval width from a number of events, enter the number of events in 'Number of events'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Other settings
Results
Code to replicate in R:References
Fagerland MW, Lydersen S, Laake P (2015). Recommended confidence intervals for two independent binomial proportions. Statistical Methods in Medical Research , 24(2):224-254. doi:10.1177/0962280211415469Precision of a risk ratio
Enter the proportions of events you expect in the groups. If you intend to use uneven allocation ratios (e.g. 2 allocated to group 1 for each participant allocated to group 2), adjust the allocation ratio accordingly. To estimate the confidence interval width from a number of events, enter the number of events in 'Number of events'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Other settings
Results
Code to replicate in R:References
Fagerland MW, Lydersen S, and Laake P (2015). Recommended confidence intervals for two independent binomial proportions, Statistical methods in medical research 24(2):224-254.Katz D, Baptista J, Azen SP, and Pike MC (1978) Obtaining Confidence Intervals for the Risk Ratio in Cohort Studies. Biometrics 34:469-474
Koopman PAR (1984) Confidence Intervals for the Ratio of Two Binomial Proportions, Biometrics 40:513-517
Precision of a rate ratio
Enter the proportions of events you expect in the groups. If you intend to use uneven allocation ratios (e.g. 2 allocated to group 1 for each participant allocated to group 2), adjust the allocation ratio accordingly. To estimate the ratio of the upper confidence interval limit to the lower limit from a number of events, enter the number of events in 'Number of events'. To estimate the number of observations required to get a ratio of the upper confidence interval limit to the lower limit of X, enter the ratio in 'Upper-lower ratio'.Please enter the following
Please enter one of the following
Results
Code to replicate in R:References
Rothamn KJ, Greenland S (2018) Planning Study Size Based on Precision Rather Than Power. Epidemiology 29:599-603 doi:10.1097/EDE.0000000000000876Precision of a correlation coefficient
Enter the correlation coefficient you expect. To estimate the confidence interval width from a number of events, enter the number of events in 'Number of events'. To estimate the number of observations required to get a confidence interval width of X, enter the width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Results
Code to replicate in R:References
Bonett DG, and Wright TA (2000) Sample size requirements for estimating Pearson, Kendall and Spearman correlations. Psychometrika 65:23-28 doi:10.1007/BF02294183Precision of an intraclass correlation coefficient
Enter the intraclass correlation coefficient you expect. To estimate the confidence interval width from a number of subjects, enter the number of subjects in 'Number of subjects'. To estimate the number of observations required to get a confidence interval width of X, enter the desired width in 'Confidence interval width'.Please enter the following
Please enter one of the following
Results
Code to replicate in R:References
Bonett DG (2002). Sample size requirements for estimating intraclass correlations with desired precision. Statistics in Medicine 21:1331-1335. doi: 10.1002/sim.1108Precision of limits of agreement
Bland-Altmann (also known as Tukey mean-difference) plots are often used to assess the agreement between two methods of measuring a quantity. A typical plot might look like the following figure. The blue line represents the mean difference between the methods, while the red lines represent the confidence interval of that difference (the limit of agreement). The dotted lines represent the confidence intervals around the limit of agreement. This page calculates the width of the confidence interval around the limit of agreement (as indicated by the black arrows), the width of which is only a function of sample size. To calculate the width of the confidence interval of the difference itself (e.g. the grey line), a paired mean difference can be used.Enter the sample size or confidence interval width to calculate the other.
Please enter one of the following
Result
Code to replicate in R:References
Bland & Altman (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet i(8476):307-310 doi: 10.1016/S0140-6736(86)90837-8Cohen's kappa
Kappa is used to assess the agreement between multiple raters, each classifying items into mutually exclusive categories. This function supports up to 6 raters and 5 categories.Please enter all of the following parameters:
Please enter one of the following:
Result
Code to replicate in R:References
Donner & Rotondi (2010) Sample Size Requirements for Interval Estimation of the Kappa Statistic for Interobserver Agreement Studies with a Binary Outcome and Multiple Raters. International Journal of Biostatistics 6:31 doi: 10.2202/1557-4679.1275Rotondi & Donner (2012) A Confidence Interval Approach to Sample Size Estimation for Interobserver Agreement Studies with Multiple Raters and Outcomes. Journal of Clinical Epidemiology 65:778-784 doi: 10.1016/j.jclinepi.2011.10.019
Cronbach's alpha
Cronbach's alpha is used to assess the internal consistency of tests and measures.Please enter all of the following parameters:
Please enter one of the following:
Result
Code to replicate in R:References
Bonett & Wright (2015) Cronbach's alpha reliability: Interval estimation, hypothesis testing, and sample size planning. Journal of Organizational Behaviour 36(1):3-15 DOI: 10.1002/job.1960Precision of sensitivity
Sensitivity is the proportion of positive test results that are identified as such. It is also known as the true positive rate, recall or probability of detection. It is actually a simple proportion, but as the total sample size, rather than the number of cases, is typically of interect this function requires an estimate of the prevalence of cases.Please enter the following
Please enter one of the following
Optional parameters
Code to replicate in R:
References
Brown LD, Cai TT, DasGupta A (2001) Interval Estimation for a Binomial Proportion, Statistical Science , 16:2, 101-117, doi:10.1214/ss/1009213286Precision of specificity
Specificity is the proportion of negative test results that are identified as such. It is also known as the true negative rate. It is actually a simple proportion, but as the total sample size, rather than the number of non-cases, is typically of interect this function requires an estimate of the prevalence of cases.Please enter the following
Please enter one of the following
Other settings
Results
Code to replicate in R:References
Brown LD, Cai TT, DasGupta A (2001) Interval Estimation for a Binomial Proportion, Statistical Science , 16:2, 101-117, doi:10.1214/ss/1009213286AUC (Area under the curve)
The AUC refers to the areas under the Receiver Operating Characteristic (ROC) curve - the grey area in the figure below. The higher the AUC, the better a predictive model performs.Please enter the following
Please enter one of the following
Code to replicate in R:
References
Hanley, JA and McNeil, BJ (1982) The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve. Radiology 148, 29-36Positive likelihood ratio
Calculate precision or sample size for the positive likelihood ratio based on sensitivity and specificity. Formula 10 from Simel et al is used.Groups here refer to e.g. the disease status.
Please enter the following
Please enter one of the following
Results
Code to replicate in R:References
Simel, DL, Samsa, GP and Matchar, DB (1991) Likelihood ratios with confidence: Sample size estimation for diagnostic test studies. J Clin Epidemiol 44(8), 763-770, DOI 10.1016/0895-4356(91)90128-vNegative likelihood ratio
Calculate precision or sample size for the negative likelihood ratio based on sensitivity and specificity. Formula 10 from Simel et al is used.Groups here refer to e.g. the disease status.