Performance.Threshold.Binomial: Statistical Performance and Alpha Spending For User-defined...
In Sequential: Exact Sequential Analysis for Poisson and Binomial Data
View source: R/Performance.Threshold.Binomial.R
Performance.Threshold.Binomial R Documentation
Statistical Performance and Alpha Spending For User-defined Signaling Threshold With Binomial Data.
Description
The function Performance.Threshold.Binomial calculates power, expected time to signal, expected sample size and alpha spending associated to any user-specified signaling threshold, flat or non-flat, for continuous or group sequential analysis with binomial data.
The user can select the scale for the signaling threshold among MaxSPRT, Pocock, OBrien-Fleming, or Wang-Tsiatis test statistics. Alternatively, the threshold can be informed also in the scale of the binomial data.
Usage
Performance.Threshold.Binomial(N,CV.lower="n",CV.upper="n",z="n",p="n",
GroupSizes="n",Tailed="upper",Statistic=c("MaxSPRT", "Pocock",
"OBrien-Fleming", "Wang-Tsiatis","Cases"),Delta="n",RR)
Arguments
N
The upper limit on the sample size (length of surveillance) expressed in terms of the total number of events (cases plus controls). There is no default value.
CV.lower
Signaling threshold for evidence of "RR<1". It is given in the scale of the selected test statistic infomed in "Statistic". There is no default value.
CV.upper
Signaling threshold for evidence of "RR>1". It is given in the scale of the selected test statistic infomed in "Statistic". There is no default value.
z
For a matched case-control analysis, z is the number of controls matched to each case under the null hypothesis. There is no default value.
p
The probability of having a case under the null hypothesis. If just a single number is given, then it will be used as a constant probability for all groups. Otherwise, the dimension of p must coincide with the dimension of GroupSizes. There is no default value.
GroupSizes
Vector with the total number of events (cases+controls) between two looks at the data with regular and irregular group sizes. Important: Must sums up N. For continuos sequential analysis, specify GroupSizes=1. There is no default value.
Tailed
Tailed="upper" (default) for H0:RR<=1, and Tailed="lower" for H0:RR>=1 or Tailed="two" for H0:RR=1.
Statistic
The test statistic scale used for "CV.lower" and "CV.upper". There is no default.
Delta
Parameter needed when "Statistic=Wang-Tsiatis" is selected. Must be a number in the (0, 0.5] interval. There is no default value.
RR
Vector of relative risks for performance calculation. There is no default value.
Details
For continuous and group sequential analysis with binomial data, alpha spending for
user-specified thresholds are calculated with Performance.Threshold.Binomial.
N must be a positive integer defining the maximum length of surveillance. To avoid very large computation times,
we suggest not using values greater than 1000.
For two-tailed testing (Tailed="two"), both lower and upper signaling thresholds must be informed through
CV.lower and CV.upper. If the user
desires a constant threshold (critical value) in the scale of a test statistic, then a single number can be informed.
For time-variable (non-constant) thresholds, the length of CV.upper and CV.lower must coincide with the length of GroupSizes.
z is a vector of positive numbers representing the matching ratios for each test (group). If a single number is given, then it will be used as a constant
matching ratio for all tests (groups). Otherwise, the dimension of z must coincide with the dimension of GroupSizes.
z represents the number of controls matched to each case. For example, if there are 3 controls matched to each case, z=3.
In a self-control analysis, z is the ratio of the control interval to the risk interval.
For example, if the risk interval is 2 days long and the control interval is 7 days long, z=7/2.
In terms of p, the binomial probability under the null hypothesis, p=1/(1+z), or equivalently, z=1/p-1.
Alternatively, instead of z the user can specify p directly.
Note that only one of these inputs, z or p, has to be specified, but if both are entered the code will only work if z
and p are such that p=1/(1+z). Otherwise, an error message will appear to remind that such condition must be complied.
With GroupSizes the user informs the sample size of each subsequent test. Therefore, only positive integers are accepted in GroupSizes.
The input Statistic specifies the scale selected by the user to inform CV.lower and cvs.upperamong the classic methods:
MaxSPRT (Kulldorf et al., 2011), Pocock (Pocock, 1977), OBrien-Fleming (O'Brien and Fleming, 1979), or Wang-Tsiatis (Jennison and Turnbull, 2000).
For Statistic="Wang-Tsiatis", the user has to choose a number in the (0, 0.5] interval for Delta.
Important: for time-variable matching ratios (i.e. when z or p changes from a test to another), only the "Statistic=Cases" option works.
This is because the test statistic options are non-monotone with the number of cumulative cases under a variable p or z situation.
For RR the user must specify the target relative risks for calculation of the statistical performance measures to be delivered in the output.
It can be a vector of positive number or a single number.
For details about the algorithm used to calculate the critical value, see the paper by Silva (2018).
Value
AlphaSpend
The alpha spending associated to the user-specified threshold.
Performance
A matrix with the following three performance measures for each target RR: statistical power, expected time to signal and expected sample size.
Acknowledgements
Development of the Performance.Threshold.Binomial function was funded by:
- National Institute of General Medical Sciences, NIH, USA, through grant number R01GM108999 (v2.0,2.0 to 3.1).
- Federal University of Ouro Preto (UFOP), through contract under internal UFOP's resolution CEPE 4600 (v2.0 to 3.1).
See also
Performance.AlphaSpend.Binomial: for calculating signaling threshold for user-specified alpha spending with binomial data.
CV.Binomial: for calculating Wald-type signaling thresholds for continuous sequential analysis with binomial data.
Analyze.Binomial: for performing sequential analysis with group, continuous or unpredictable sequential fashion with binomial data.
Author(s)
Ivair Ramos Silva, Martin Kulldorff.
References
Jennison C, Turnbull B. (2000). Group Sequential Methods with Applications to Clinical Trials, London: Chapman and Hall/CRC.
Kulldorff M, Davis RL, Kolczak M, Lewis E, Lieu T, Platt R. (2011). A Maximized Sequential Probability Ratio Test for Drug and Safety Surveillance. Sequential Analysis, 30: 58–78.
O'Brien PC, Fleming TR. (1979). A multiple testing procedure for clinical trials. Biometrics. 35:549–556.
Pocock SJ. (1977).Group sequential methods in the design and analysis of clinical trials. Biometrika. 64:191–199.
Silva IR. (2018). Type I Error Probability Spending for Post-Market Drug and Vaccine Safety Surveillance with Binomial Data. Statistics in Medicine, 15;37(1), 107-118.
Silva IR, Kulldorff M. (2015). Continuous versus Group Sequential Analysis for Vaccine and Drug Safety Surveillance. Biometrics, 71 (3), 851–858.
Silva IR, Maro J, Kulldorff M. (2021), Exact sequential test for clinical trials and post-market drug and vaccine safety surveillance with Poisson and binary data. Statistics in Medicine, DOI: 10.1002/sim.9094.
Examples
## Performance and Alpha spending of a four-group sequential
# analysis with threshold informed in the scale of the
# binomial data, i.e. Statistic="Cases".
# The analysis is for a maximum sample size of 50 events under
# upper-tailed testing, that is, H0:RR<=1, with irregular group
# sizes of 12, 25, 35, and 45.
# The matching ratio also changes in time with z= 1, 1.5, 2, 1.3.
# The statistical performance is evaluated for RR= 1.2, 1.5, 2:
# res<- Performance.Threshold.Binomial(N=50,CV.upper=c(12,25,35,45),
# z=c(1,1.5,2,1.3),GroupSizes=c(15,15,10,10),Tailed="upper",
# Statistic="Cases", RR=c(1.2,1.5,2))
Sequential documentation built on Oct. 27, 2023, 1:07 a.m.
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View source: R/Performance.Threshold.Binomial.R
| Performance.Threshold.Binomial | R Documentation |
Statistical Performance and Alpha Spending For User-defined Signaling Threshold With Binomial Data.
Description
The function Performance.Threshold.Binomial calculates power, expected time to signal, expected sample size and alpha spending associated to any user-specified signaling threshold, flat or non-flat, for continuous or group sequential analysis with binomial data.
The user can select the scale for the signaling threshold among MaxSPRT, Pocock, OBrien-Fleming, or Wang-Tsiatis test statistics. Alternatively, the threshold can be informed also in the scale of the binomial data.
Usage
Performance.Threshold.Binomial(N,CV.lower="n",CV.upper="n",z="n",p="n",
GroupSizes="n",Tailed="upper",Statistic=c("MaxSPRT", "Pocock",
"OBrien-Fleming", "Wang-Tsiatis","Cases"),Delta="n",RR)
Arguments
N |
The upper limit on the sample size (length of surveillance) expressed in terms of the total number of events (cases plus controls). There is no default value. |
CV.lower |
Signaling threshold for evidence of "RR<1". It is given in the scale of the selected test statistic infomed in "Statistic". There is no default value. |
CV.upper |
Signaling threshold for evidence of "RR>1". It is given in the scale of the selected test statistic infomed in "Statistic". There is no default value. |
z |
For a matched case-control analysis, z is the number of controls matched to each case under the null hypothesis. There is no default value. |
p |
The probability of having a case under the null hypothesis. If just a single number is given, then it will be used as a constant probability for all groups. Otherwise, the dimension of p must coincide with the dimension of GroupSizes. There is no default value. |
GroupSizes |
Vector with the total number of events (cases+controls) between two looks at the data with regular and irregular group sizes. Important: Must sums up N. For continuos sequential analysis, specify GroupSizes=1. There is no default value. |
Tailed |
Tailed="upper" (default) for H0:RR<=1, and Tailed="lower" for H0:RR>=1 or Tailed="two" for H0:RR=1. |
Statistic |
The test statistic scale used for "CV.lower" and "CV.upper". There is no default. |
Delta |
Parameter needed when "Statistic=Wang-Tsiatis" is selected. Must be a number in the (0, 0.5] interval. There is no default value. |
RR |
Vector of relative risks for performance calculation. There is no default value. |
Details
For continuous and group sequential analysis with binomial data, alpha spending for
user-specified thresholds are calculated with Performance.Threshold.Binomial.
N must be a positive integer defining the maximum length of surveillance. To avoid very large computation times,
we suggest not using values greater than 1000.
For two-tailed testing (Tailed="two"), both lower and upper signaling thresholds must be informed through
CV.lower and CV.upper. If the user
desires a constant threshold (critical value) in the scale of a test statistic, then a single number can be informed.
For time-variable (non-constant) thresholds, the length of CV.upper and CV.lower must coincide with the length of GroupSizes.
z is a vector of positive numbers representing the matching ratios for each test (group). If a single number is given, then it will be used as a constant
matching ratio for all tests (groups). Otherwise, the dimension of z must coincide with the dimension of GroupSizes.
z represents the number of controls matched to each case. For example, if there are 3 controls matched to each case, z=3.
In a self-control analysis, z is the ratio of the control interval to the risk interval.
For example, if the risk interval is 2 days long and the control interval is 7 days long, z=7/2.
In terms of p, the binomial probability under the null hypothesis, p=1/(1+z), or equivalently, z=1/p-1.
Alternatively, instead of z the user can specify p directly.
Note that only one of these inputs, z or p, has to be specified, but if both are entered the code will only work if z
and p are such that p=1/(1+z). Otherwise, an error message will appear to remind that such condition must be complied.
With GroupSizes the user informs the sample size of each subsequent test. Therefore, only positive integers are accepted in GroupSizes.
The input Statistic specifies the scale selected by the user to inform CV.lower and cvs.upperamong the classic methods:
MaxSPRT (Kulldorf et al., 2011), Pocock (Pocock, 1977), OBrien-Fleming (O'Brien and Fleming, 1979), or Wang-Tsiatis (Jennison and Turnbull, 2000).
For Statistic="Wang-Tsiatis", the user has to choose a number in the (0, 0.5] interval for Delta.
Important: for time-variable matching ratios (i.e. when z or p changes from a test to another), only the "Statistic=Cases" option works.
This is because the test statistic options are non-monotone with the number of cumulative cases under a variable p or z situation.
For RR the user must specify the target relative risks for calculation of the statistical performance measures to be delivered in the output.
It can be a vector of positive number or a single number.
For details about the algorithm used to calculate the critical value, see the paper by Silva (2018).
Value
AlphaSpend |
The alpha spending associated to the user-specified threshold. |
Performance |
A matrix with the following three performance measures for each target RR: statistical power, expected time to signal and expected sample size. |
Acknowledgements
Development of the Performance.Threshold.Binomial function was funded by:
- National Institute of General Medical Sciences, NIH, USA, through grant number R01GM108999 (v2.0,2.0 to 3.1).
- Federal University of Ouro Preto (UFOP), through contract under internal UFOP's resolution CEPE 4600 (v2.0 to 3.1).
See also
Performance.AlphaSpend.Binomial: for calculating signaling threshold for user-specified alpha spending with binomial data.
CV.Binomial: for calculating Wald-type signaling thresholds for continuous sequential analysis with binomial data.
Analyze.Binomial: for performing sequential analysis with group, continuous or unpredictable sequential fashion with binomial data.
Author(s)
Ivair Ramos Silva, Martin Kulldorff.
References
Jennison C, Turnbull B. (2000). Group Sequential Methods with Applications to Clinical Trials, London: Chapman and Hall/CRC.
Kulldorff M, Davis RL, Kolczak M, Lewis E, Lieu T, Platt R. (2011). A Maximized Sequential Probability Ratio Test for Drug and Safety Surveillance. Sequential Analysis, 30: 58–78.
O'Brien PC, Fleming TR. (1979). A multiple testing procedure for clinical trials. Biometrics. 35:549–556.
Pocock SJ. (1977).Group sequential methods in the design and analysis of clinical trials. Biometrika. 64:191–199.
Silva IR. (2018). Type I Error Probability Spending for Post-Market Drug and Vaccine Safety Surveillance with Binomial Data. Statistics in Medicine, 15;37(1), 107-118.
Silva IR, Kulldorff M. (2015). Continuous versus Group Sequential Analysis for Vaccine and Drug Safety Surveillance. Biometrics, 71 (3), 851–858.
Silva IR, Maro J, Kulldorff M. (2021), Exact sequential test for clinical trials and post-market drug and vaccine safety surveillance with Poisson and binary data. Statistics in Medicine, DOI: 10.1002/sim.9094.
Examples
## Performance and Alpha spending of a four-group sequential
# analysis with threshold informed in the scale of the
# binomial data, i.e. Statistic="Cases".
# The analysis is for a maximum sample size of 50 events under
# upper-tailed testing, that is, H0:RR<=1, with irregular group
# sizes of 12, 25, 35, and 45.
# The matching ratio also changes in time with z= 1, 1.5, 2, 1.3.
# The statistical performance is evaluated for RR= 1.2, 1.5, 2:
# res<- Performance.Threshold.Binomial(N=50,CV.upper=c(12,25,35,45),
# z=c(1,1.5,2,1.3),GroupSizes=c(15,15,10,10),Tailed="upper",
# Statistic="Cases", RR=c(1.2,1.5,2))
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