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Table 4 Alternative estimator results for log-normal, gamma and weibull distributions for n=100

From: Statistical models for the analysis of skewed healthcare cost data: a simulation study

Data

Estimator

MPE

MPAE

MSE(β)

95% CI

AIC

Prob. H.Lsignif

Lower

upper

Log normal σ2=0.5

OLS for Ln(y)

-0.03144

0.56088

0.06312

0.953

1.049

217.5766

0.0391

Gamma

-0.00007

0.55234

0.05761

0.942

1.052

168.199

0.0361

Weibull

-0.11282

0.58936

0.06098

0.935

1.057

175.260

0.0417

Cox

-1.34295

3.32199

5.63414

-1.423

-1.263

716.154

0.0481

Log normal σ2=1

OLS for Ln(y)

-0.03161

0.77499

0.12623

0.933

1.069

286.891

0.0365

Gamma

-0.00020

0.76419

0.10963

0.907

1.081

192.904

0.0333

Weibull

-0.00812

0.76533

0.12196

0.908

1.080

193.907

0.0330

Cox

-0.94387

3.19872

3.91711

-1.020

-0.868

722.133

0.0479

Log normal σ2=1.5

OLS for Ln(y)

-0.03195

0.93383

0.18935

0.917

1.085

327.438

0.0335

Gamma

-0.00038

0.92175

0.15884

0.873

1.107

189.222

0.0300

Weibull

0.11681

0.86782

0.18295

0.887

1.099

185.001

0.0294

Cox

-0.76851

3.15738

3.26405

-0.844

-0.694

724.207

0.0531

Log normal σ2=2

OLS for Ln(y)

-0.03217

1.05939

0.25247

0.904

1.098

356.206

0.0320

Gamma

-0.00068

1.04672

0.20674

0.840

1.132

172.665

0.0283

Weibull

0.23968

0.92933

0.24393

0.869

1.113

163.925

0.0276

Cox

-0.66436

3.13647

2.90548

-0.738

-0.590

725.262

0.0544

Gamma α=0.5

OLS for Ln(y)

-0.06210

0.98793

0.924

0.842

1.149

444.474

0.1015

Gamma

-0.00071

0.95946

0.382

0.899

1.099

151.970

0.0366

Weibull

0.25749

0.88296

0.456

0.896

1.102

154.259

0.0380

Cox

0.69973

3.18874

2.997

-0.700

-0.626

724.990

0.050

Gamma α =1

OLS for Ln(y)

-0.03843

0.74577

0.307

0.915

1.093

335.557

0.0569

Gamma

-0.00026

0.73384

0.185

0.934

1.072

196.691

0.0391

Weibull

-0.00460

0.73458

0.185

0.934

1.072

196.682

0.0395

Cox

-1.02065

3.27855

4.182

-1.095

-0.947

721.285

0.0518

Gamma α =2

OLS for Ln(y)

-0.03271

0.54277

0.120

0.946

1.057

242.168

0.0504

Gamma

-0.00011

0.53579

0.092

0.950

1.494

171.847

0.0434

Weibull

-0.11069

0.56268

0.087

0.949

1.049

172.908

0.0471

Cox

-1.44678

3.44580

6.080

-1.525

-1.369

714.645

0.0503

Gamma α =4

OLS for Ln(y)

-0.03138

0.39126

0.053

0.966

1.040

160.228

0.0436

Gamma

-0.00001

0.38627

0.046

0.967

1.037

122.262

0.0403

Weibull

-0.13163

0.41676

0.044

0.964

1.038

125.708

0.0515

Cox

-2.05432

3.72857

9.359

-2.138

-1.970

702.730

0.0506

Wiebull α=0.5

OLS for Ln(y)

-0.07169

1.20997

0.82955

0.830

1.186

473.993

0.0833

Gamma

-0.00180

1.16992

0.36191

0.839

1.145

83.622

0.032

Weibull

0.48656

0.96925

0.50264

0.856

1.138

79.302

0.0345

Cox

-0.49779

3.13454

2.38376

-0.668

-0.330

726.558

0.0485

Wiebull α =1

OLS for Ln(y)

-0.03853

0.74709

0.20739

0.915

1.093

335.3635

0.0574

Gamma

-0.00025

0.73522

0.12587

0.928

1.068

196.7417

0.0399

Weibull

-0.00400

0.73582

0.12566

0.928

1.068

196.7316

0.0397

Cox

-1.00326

3.28425

4.16180

-1.176

-0.834

721.3257

0.0505

Wiebull α =5

OLS for Ln(y)

-0.03115

0.18335

0.00829

0.983

1.019

13.476

0.0480

Gamma

-0.00001

0.18277

0.00738

0.984

1.016

-7.0357

0.0437

Weibull

-0.08850

0.19266

0.00503

0.986

1.014

-16.598

0.0639

Cox

-5.04559

6.57363

36.88155

-5.160

-4.932

636.392

0.0472