J Clin Med Res

Journal of Clinical Medicine Research, ISSN 1918-3003 print, 1918-3011 online, Open Access

Article copyright, the authors; Journal compilation copyright, J Clin Med Res and Elmer Press Inc

Journal website http://www.jocmr.org

Original Article

Volume 10, Number 5, May 2018, pages 376-383

The Impact of the Underlying Risk in Control Group and Effect Measures in Non-Inferiority Trials With Time-to-Event Data: A Simulation Study

Figure 2. Upper limit of 95%CI of hazard ratio versus the underlying risk in active control group (true hazard ratio = 1). We randomly selected 1,000 out of 10,000 simulated trials, but the fitted line used the entire data. The horizontal line was an empirical non-inferiority margin, hazard ratio of 1.35.

Figure 3. The upper limit of difference in two Kaplan-Meier estimators versus follow up time (true hazard ratio = 1). We randomly selected 1,000 out of 10,000 simulated trials in this plot, but the fitted line used the entire data. The horizontal line was an empirical non-inferiority margin, representing the difference in two Kaplan-Meier estimators of 10%.

**Table 1.** The Probability of Rejecting the Null Hypothesis Using Hazard Ratio
Non-inferiority margin	Underlying risk in control group
The probability of rejecting the null hypothesis is the same as the statistical power in our simulations.
True hazard ratio = 1
HR = 1.2	0.067	0.152	0.323	0.513
HR = 1.35	0.131	0.323	0.684	0.903
HR = 1.5	0.224	0.527	0.890	0.993
True hazard ratio = 0.95
HR = 1.2	0.094	0.200	0.482	0.716
HR = 1.35	0.194	0.413	0.790	0.968
HR = 1.5	0.286	0.607	0.935	0.999
True hazard ratio = 1.05
HR = 1.2	0.056	0.112	0.198	0.305
HR = 1.35	0.104	0.252	0.544	0.771
HR = 1.5	0.171	0.425	0.821	0.970

Table 1. The Probability of Rejecting the Null Hypothesis Using Hazard Ratio

Non-inferiority margin

Underlying risk in control group

< 10%

10-25%

25-75%

> 75%

The probability of rejecting the null hypothesis is the same as the statistical power in our simulations.

True hazard ratio = 1

HR = 1.2

0.067

0.152

0.323

0.513

HR = 1.35

0.131

0.323

0.684

0.903

HR = 1.5

0.224

0.527

0.890

0.993

True hazard ratio = 0.95

HR = 1.2

0.094

0.200

0.482

0.716

HR = 1.35

0.194

0.413

0.790

0.968

HR = 1.5

0.286

0.607

0.935

0.999

True hazard ratio = 1.05

HR = 1.2

0.056

0.112

0.198

0.305

HR = 1.35

0.104

0.252

0.544

0.771

HR = 1.5

0.171

0.425

0.821

0.970

**Table 2.** The Probability of Rejecting The Null Hypothesis Using the Difference in Two Kaplan-Meier Estimators
Non-inferiority margin	Underlying risk in control group
DTKME: difference in two Kaplan-Meier estimators at follow-up of 5 years. The probability of rejecting the null hypothesis is the same as the statistical power in our simulations.
True hazard ratio = 1
DTKME = 2.5%	0.221	0.117	0.077	0.123
DTKME = 5%	0.656	0.334	0.199	0.352
DTKME = 10%	0.981	0.831	0.607	0.842
DTKME = 15%	1.000	0.990	0.922	0.984
True hazard ratio = 0.95
DTKME = 2.5%	0.275	0.154	0.151	0.229
DTKME = 5%	0.699	0.400	0.319	0.502
DTKME = 10%	0.995	0.885	0.750	0.920
DTKME = 15%	1.000	0.993	0.960	1.000
True hazard ratio = 1.05
DTKME = 2.5%	0.190	0.086	0.039	0.058
DTKME = 5%	0.551	0.257	0.120	0.228
DTKME = 10%	0.977	0.750	0.468	0.735
DTKME = 15%	1.000	0.977	0.858	0.972

Table 2. The Probability of Rejecting The Null Hypothesis Using the Difference in Two Kaplan-Meier Estimators

Non-inferiority margin

Underlying risk in control group

< 10%

10-25%

25-75%

> 75%

DTKME: difference in two Kaplan-Meier estimators at follow-up of 5 years. The probability of rejecting the null hypothesis is the same as the statistical power in our simulations.

True hazard ratio = 1

DTKME = 2.5%

0.221

0.117

0.077

0.123

DTKME = 5%

0.656

0.334

0.199

0.352

DTKME = 10%

0.981

0.831

0.607

0.842

DTKME = 15%

1.000

0.990

0.922

0.984

True hazard ratio = 0.95

DTKME = 2.5%

0.275

0.154

0.151

0.229

DTKME = 5%

0.699

0.400

0.319

0.502

DTKME = 10%

0.995

0.885

0.750

0.920

DTKME = 15%

1.000

0.993

0.960

1.000

True hazard ratio = 1.05

DTKME = 2.5%

0.190

0.086

0.039

0.058

DTKME = 5%

0.551

0.257

0.120

0.228

DTKME = 10%

0.977

0.750

0.468

0.735

DTKME = 15%

1.000

0.977

0.858

0.972