Performance.Threshold.CondPoisson: Performance and alpha spending for user-defined signaling...

Description Usage Arguments Details Value Acknowledgements See also Author(s) References Examples

View source: R/Performance.Threshold.CondPoisson.R

Description

The function Performance.Threshold.CondPoisson calculates the statistical 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 conditional Poisson data, all for a pre-specified upper limit on the sample size.

Usage

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Performance.Threshold.CondPoisson(K,cc,CV.upper="n",
Person_timeRatioH0="n",GroupSizes="n",Tailed="upper",RR)
      

Arguments

K

The upper limit on the sample size (length of surveillance) expressed in terms of the number of events arriving in the surveillance period. There is no default value.

cc

Number of events observed in the historical period. There is no default value.

CV.upper

User-specified signaling threshold given in the scale of the CMaxSPRT test statistic. There is no default value.

Person_timeRatioH0

Test-specific amount of information of each test given in terms of the ratio between the person-time in the surveillance period and the overall person-time of the historical period. See Details. There is no default value.

GroupSizes

Test-specific number of events between two looks at the data for group or continuous sequential analysis. There is no default value. See Details.

Tailed

Tailed="upper" (default) for H0:RR<=1, and Tailed="lower" for H0:RR>=1 or Tailed="two" for H0:RR=1.

RR

Vector of relative risks for performance calculation. There is no default value.

Details

For continuous and group sequential analysis based on monitoring Poisson data conditioned on matched historical Poisson data, the power, expected time to signal, expected sample size and alpha spending impplied by user-specified thresholds are calculated with Performance.Threshold.CondPoisson. The user can select one between two scales to enter with the threshold, the the Conditional Maximized Sequential Probability Ratio Test statistic (CMaxSPRT) scale (Li and Kulldorff, 2010), or the surveillance versus historical person-time ratio (Silva et al., 2019a). For the CMaxSRT scale, the input is CV.upper. This can be entered as a vector for group sequential analysis. For example, for a three-group sequential test, the i-th entry represents the critical value for the i-th test, with i=1, 2, 3. If a single number is informed in CV.upper, then a flat critical value for all tests is used for both continuous or group sequential fashions. The number of tests is defined with the input GroupSizes, as shall be detailed here after the desciption of Person_timeRatioH0.

An alternative way to inform the threshold is by using Person_timeRatioH0, which is in the scale of the ratio between the person-time in the surveillance period and the overall person-time of the historical period. Using the notation by Silva et al. (2019a) and Silva et al. (2019b), let V denote the total person-time from the historical data, where cc events were observed, and let P_{k(i)} denote the the cummulative person-time from the surveillance data at the i-th test with a cummulative k(i) events. With Person_timeRatioH0, the entries must have increasing numbers, from the first to the last. For example, for a three-group sequential plan with sample sizes of 20, 15, 25, a hypothetical choice is Person_timeRatioH0=c(0.1, 0.5, 1). This way, H0 is rejected if: P_20/V <= 0.1 in the first test, or P_35/V <= 0.5 in the second test, or P_60/V <= 1 in the third test.

Note: only one of the inputs CV.upper or Person_timeRatioH0 is to be used.

With GroupSizes the user informs the sample size of each test in the scale of the number of events in the surveillance period. Therefore, only positive numbers are accepted in GroupSizes. For irregular group sizes, a vector must be informed with each test-specific number of events between two looks at the data, therefore the entries of GroupSizes must sums up K. For regular group sizes, a single number can be informed for the constant sample size of each test. For example, for continuous sequential analysis, GroupSizes=1. For ten-group sequential analysis with K=50, GroupSizes=5.

For RR the user must specify the target relative risks for calculation of statistical performance measures. It can be a vector of positive numbers or a single number.

For details on the calculation of signaling thresholds and alpha spending for Poisson data conditioned to historical data, see the papers by Silva et al. (2019a) and Silva et al. (2019b), respectively.

Value

Performance

A matrix with the following three performance measures for each target RR: statistical power, expected time to signal and expected sample size.

AlphaSpend

The alpha spending associated to the user-specified threshold.

Acknowledgements

Development of the Performance.Threshold.CondPoisson 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.CondPoisson: for calculating performance and signaling threshold for user-specified alpha spending with conditional Poisson data.
CV.CondPoisson: for calculating Wald-type signaling thresholds for continuous sequential analysis with conditional Poisson data based on the CMaxSPRT test statistic.
Analyze.CondPoisson: for performing sequential analysis with group, continuous or unpredictable sequential fashion for condicional Poisson data based on the CMaxSPRT test statistic.

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.

Li L, Kulldorff M. (2010). A conditional maximized sequential probability ratio test for Pharmacovigilance. Statistics in Medicine, 29 (2), 284–295.

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, Li L, Kulldorff M. (2019a), Exact conditional maximized sequential probability ratio test adjusted for covariates. Sequential Analysis, 38(1), 115–133.

Silva IR., Lopes LM., Dias P., Yih WK. (2019b). Alpha Spending for Historical Versus Surveillance Poisson Data With CMaxSPRT. Statistics in Medicine, 38(12), 2126–2138.

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. (2019). Exact Sequential Analysis Using R Sequential. Working Paper.

Examples

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#### Example 1
## Power, expected time to signal, expected sample size and
## alpha spending of three group CMaxSPRT sequential analysis with
#  a maximum sample size of 30 events for upper-tailed
#  testing, i.e. H0:RR<=1, with regular groups of sizes 10
#  and a flat threshold equal to 3.6. 
#  The statistical performance is evaluated for two
#  target RR= 1.5, 2:

# Performance.Threshold.CondPoisson(K=30,cc=10,CV.upper=3.6, Person_timeRatioH0="n",
# GroupSizes=10,RR=c(1.5,2))

#### Example 2
## Power, expected time to signal, expected sample size and
#  alpha spending of three group CMaxSPRT sequential analysis with
#  a maximum sample size of 30 events for upper-tailed
#  testing, i.e. H0:RR<=1, with regular groups of sizes 10
#  and thresholds given in the P_k/V scale:
#  "Person_timeRatioH0=c(0.1, 0.5, 1)". 
#  The statistical performance is evaluated for two
#  target RR= 1.5, 2:

# Performance.Threshold.CondPoisson(K=30,cc=10,CV.upper="n", Person_timeRatioH0=c(0.1, 0.5, 1),
# GroupSizes=10,RR=c(1.5,2))

Sequential documentation built on Feb. 22, 2021, 9:09 a.m.