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Table 1 Comparison of 95% confidence intervals for three location quotients (LQ1, LQ2, LQ3) using three methods (D = delta, F = Fieller, P = Profile-likelihood). Varying incidence rates (p 1, p 2, p 3) were used along with 3 sets of population size configurations (a) n 1 = 50, n 2 = 80, n 3 = 60 (b) n 1 = 500, n 2 = 900, n 3 = 100 (c) n 1 = 2000, n 2 = 2500, n 3 = 1500. A total of 1000 simulated data sets were used to generate "benchmark" limits (designated as "S" under method)

From: Methods for confidence interval estimation of a ratio parameter with application to location quotients

 

p 1

p 2

p 3

Method

(a)

0.25

0.3

0.2

S

0.5903

1.3959

0.8787

1.4844

0.4332

1.1237

    

D

0.5789

1.3905

0.8860

1.4679

0.4380

1.1155

    

F

0.5664

1.4043

0.8815

1.4824

0.4239

1.1234

    

P

0.5715

1.4995

0.8109

1.5950

0.4375

1.2183

 

0.2

0.4

0.7

S

0.2249

0.6926

0.7125

1.0744

1.3548

1.8404

    

D

0.2235

0.6776

0.7168

1.0909

1.3309

1.8413

    

F

0.2156

0.6758

0.7126

1.0918

1.3464

1.8651

    

P

0.2409

0.7287

0.6719

1.1505

1.3096

1.8251

 

0.9

0.1

0.5

S

1.8387

2.3249

0.0956

0.3765

0.9383

1.3492

    

D

1.7335

2.3942

0.0901

0.3640

0.9040

1.3841

    

F

1.7718

2.4478

0.0846

0.3624

0.9044

1.3910

    

P

1.8297

2.2054

0.1088

0.4035

0.8607

1.4280

 

0.02

0.01

0.1

S

0.0000

1.6889

0.0000

1.0037

1.2667

3.1667

    

D

-0.1536

1.1816

-0.0924

0.6015

1.4479

3.3499

    

F

-0.5404

1.5539

-0.3073

0.7883

1.0254

4.2516

    

P

0.3015

1.0973

0.1272

0.6214

1.9683

3.1071

(b)

0.25

0.3

0.2

S

0.7924

1.0245

1.0156

1.1439

0.4483

1.0191

    

D

0.7917

1.0197

1.0167

1.1489

0.4517

1.0012

    

F

0.7911

1.0199

1.0167

1.1493

0.4504

1.0017

    

P

0.7731

1.0476

0.9765

1.1932

0.4736

1.0343

 

0.2

0.4

0.7

S

0.4766

0.6536

1.0807

1.1854

1.7154

2.2426

    

D

0.4789

0.6537

1.0755

1.1865

1.7326

2.2467

    

F

0.4781

0.6533

1.0757

1.1870

1.7370

2.2525

    

P

0.4715

0.6698

1.0411

1.2225

1.7240

2.2265

 

0.9

0.1

0.5

S

2.2140

2.3684

0.2129

0.2938

1.0390

1.5164

    

D

2.1557

2.4273

0.2084

0.2971

1.0277

1.5079

    

F

2.1629

2.4354

0.2078

0.2967

1.0281

1.5093

    

P

2.2196

2.3530

0.2060

0.3053

1.022

1.5138

 

0.02

0.01

0.1

S

0.5071

1.5517

0.2381

0.8333

2.5862

7.9550

    

D

0.5212

1.5436

0.2396

0.7928

2.6717

7.7130

    

F

0.4819

1.5835

0.2174

0.8136

2.5448

7.9803

    

P

0.5205

1.8078

0.2494

0.9322

2.6765

8.8046

(c)

0.25

0.3

0.2

S

0.9113

1.0322

1.1066

1.2119

0.7077

0.8480

    

D

0.9089

1.0296

1.1088

1.2115

0.7043

0.8439

    

F

0.9088

1.0296

1.1089

1.2117

0.7041

0.8438

    

P

0.8970

1.0440

1.0914

1.2305

0.6977

0.8544

 

0.2

0.4

0.7

S

0.4518

0.5288

0.9424

1.0115

1.6636

1.7688

    

D

0.4519

0.5285

0.9427

1.0147

1.6588

1.7717

    

F

0.4518

0.5283

0.9427

1.0147

1.6595

1.7726

    

P

0.4482

0.5341

0.9319

1.026

1.6577

1.7712

 

0.9

0.1

0.5

S

1.8962

1.9663

0.1923

0.2365

1.0271

1.1150

    

D

1.8797

1.9797

0.1903

0.2374

1.0237

1.1176

    

F

1.8808

1.9808

0.1902

0.2373

1.0237

1.1177

    

P

1.9004

1.9567

0.1896

0.2399

1.0165

1.1249

 

0.02

0.01

0.1

S

0.4000

0.7184

0.1798

0.3847

2.5421

3.0220

    

D

0.4020

0.7094

0.1776

0.3813

2.5418

3.0449

    

F

0.4005

0.7106

0.1766

0.3821

2.5428

3.0504

    

P

0.4018

0.7441

0.1844

0.4026

2.3876

3.2374