fac2x2analyze {factorial2x2}

Significance testing for the Proportional Allocation 2, Equal Allocation 3, Equal Allocation 2 procedures

Description

Performs significance testing for the Proportional Allocation 2, Equal Allocation 3, Equal Allocation 2 procedures. Also reports the hazard ratios, 95% confidence intervals, p-values, nominal significance levels, and correlations for the overall and simple test statistics.

Usage

fac2x2analyze(time, event, indA, indB, covmat, alpha, dig = 2, niter = 5)

Arguments

time

follow-up times

event

event indicators (0/1)

indA

treatment A indicators (0/1)

indB

treatment B indicators (0/1)

covmat

covariate matrix, must be non-NULL. Factor variables MUST use 0/1 dummy variables

alpha

two-sided familywise significance level

dig

number of decimal places to which we roundDown the critical value

niter

number of interations passed to crit2x2 function call

Details

For each of the three multiple testing procedures, the critical values for the overall A (respectively, simple A) logrank statistics may be slightly different from the overall B (respectively, simple B) logrank statistics. This is due to their slightly different correlations with each other (i.e., correlation between overall A and simple A, respectively, overall B and simple B, statistics) as well as with the simple AB statistic.

Value

loghrAoverall

overall A log hazard ratio

seAoverall

standard error of the overall A log hazard ratio

ZstatAoverall

Z-statistic for the overall A log hazard ratio

pvalAoverall

two-sided p-value for the overall hazard ratio

hrAoverall

overall A hazard ratio

ciAoverall

95% confidence interval for the overall A hazard ratio

loghrAsimple

simple A log hazard ratio

seAsimple

standard error of the simple A log hazard ratio

ZstatAsimple

Z-statistic for the simple A log hazard ratio

pvalAsimple

two-sided p-value for the simple A hazard ratio

hrAsimple

simple A hazard ratio

ciAsimple

95% confidence interval for the simple A hazard ratio

loghrABsimple

simple AB log hazard ratio

seABsimple

standard error of the simple AB log hazard ratio

ZstatABsimple

Z-statistic for the simple AB log hazard ratio

pvalABsimple

two-sided p-value for the simple AB hazard ratio

hrABsimple

simple AB hazard ratio

ciABsimple

95% confidence interval for the simple AB hazard ratio

critEA3_A

Equal Allocation 3's critical value for the overall A simple A, and simple AB hypotheses

sigEA3_A

Equal Allocation 3's p-value rejection criterion for the overall A, simple A, and simple AB hypotheses

resultEA3_A

Equal Allocation 3's accept/reject decisions for the overall A, simple A, and simple AB hypotheses

critPA2overallA

Proportional Allocation 2's critical value for the overall A statistic

sigPA2overallA

Proportional Allocation 2's p-value rejection criterion for the overall A hypothesis

critPA2simpleAB

Proportional Allocation 2's critical value for the simple AB hypothesis

sigPA2simpleAB

Proportional Allocation 2 procedure's p-value rejection criterion for the simple AB hypothesis

resultPA2_A

Proportional Allocation 2 procedure's accept/reject decisions for the overall A and simple A hypotheses

critEA2_A

Equal Allocation 2 procedure's critical value for the simple A and simple AB hypotheses

sigEA2_A

Equal Allocation 2 procedure's p-value rejection criterion for the simple A and simple AB hypotheses

resultEA2_A

Equal Allocation 2 procedure's accept/reject decisions for the simple A and simple AB hypotheses

corAa

correlation between the overall A and simple A logrank statistics

corAab

correlation between the overall A and simple AB logrank statistics

coraab

correlation between the simple A and simple AB logrank statistics

Author(s)

Eric Leifer, James Troendle

References

Leifer, E.S., Troendle, J.F., Kolecki, A., Follmann, D. Joint testing of overall and simple effect for the two-by-two factorial design. (2020). Submitted.

Lin, D-Y., Gong, J., Gallo, P., et al. Simultaneous inference on treatment effects in survival studies with factorial designs. Biometrics. 2016; 72: 1078-1085.

Slud, E.V. Analysis of factorial survival experiments. Biometrics. 1994; 50: 25-38.

Examples

 # First load the simulated data variables. The "simdataSub" file is
 # a 100-by-9 matrix which is loaded with the factorial2x2 package.
 time <- simdataSub[, "time"]
 event <- simdataSub[, "event"]
 indA <- simdataSub[, "indA"]
 indB <- simdataSub[, "indB"]
 covmat <- simdataSub[, 6:10]
 fac2x2analyze(time, event, indA, indB, covmat, alpha = 0.05, niter = 5)
#  $loghrA
# [1] 0.05613844

# $seA
# [1] 0.4531521

# $ZstatA
# [1] 0.1238843

# $pvalA
# [1] 0.9014069

# $hrA
# [1] 1.057744

# $ciA
# [1] 0.4351608 2.5710556

# $loghra
# [1] 0.1987329

# $sea
# [1] 0.6805458

# $Zstata
# [1] 0.2920198

# $pvala
# [1] 0.7702714

# $hra
# [1] 1.219856

# $cia
# [1] 0.3213781 4.6302116

# $loghrab
# [1] 0.2864932

# $seab
# [1] 0.6762458

# $Zstatab
# [1] 0.4236525

# $pvalab
# [1] 0.6718193

# $hrab
# [1] 1.331749

# $ciab
# [1] 0.3538265 5.0125010

# $critPA2A
# [1] -2.129

# $sigPA2A
# [1] 0.03325426

# $critPA2ab
# [1] -2.299

# $sigPA2ab
# [1] 0.02150494

# $result23
# [1] "accept overall A" "accept simple AB"

# $critEA3
# [1] -2.338

# $sigEA3
# [1] 0.01938725

# $result13
# [1] "accept overall A" "accept simple A"  "accept simple AB"

# $critEA2
# [1] -2.216

# $sigEA2
# [1] 0.0266915

# $result12
# [1] "accept simple A"  "accept simple AB"

# $corAa
# [1] 0.6123399

# $corAab
# [1] 0.5675396

# $coraab
# [1] 0.4642737