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Table 2 Finite sample properties using Monte Carlo simulation study

From: Estimation of marginal structural models under irregular visits and unmeasured confounder: calibrated inverse probability weights

Estimator

Effect

\(\psi\)

Estimate

Bias

R. Bias(%)

MCEa

rMSEb

\(\alpha\)-level

Scenario 1: No irregular visits, no unmeasured confounder

Naïve

\(A_{j-1}\)

-0.3

-0.274

0.0260

8.67%

0.2966

0.2978

0.939

sIPTW

\(A_{j-1}\)

-0.3

-0.2796

0.0204

6.8%

0.3183

0.3189

0.944

cIPTW

\(A_{j-1}\)

-0.3

-0.2842

0.0158

5.27%

0.3071

0.3075

0.943

Scenario 2: No irregular visits, unmeasured confounder

Naïve

\(A_{j-1}\)

-0.3

-0.2642

0.0358

11.93%

0.3484

0.3502

0.936

sIPTW

\(A_{j-1}\)

-0.3

-0.2839

0.0161

5.37%

0.3181

0.3185

0.928

cIPTW

\(A_{j-1}\)

-0.3

-0.2909

0.0091

3.03%

0.3138

0.3139

0.940

Scenario 3: Irregular visits, no unmeasured confounder

Naïve

\(A_{j-1}\)

-0.3

-0.2678

0.0322

10.73%

0.3421

0.3436

0.927

sIPTW

\(A_{j-1}\)

-0.3

-0.2719

0.0281

9.37%

0.3332

0.3343

0.934

sIPVW

\(A_{j-1}\)

-0.3

-0.2776

0.0224

7.47%

0.3142

0.3150

0.940

sIPTW\(\times\)sIPVW

\(A_{j-1}\)

-0.3

-0.2859

0.0141

4.7%

0.3292

0.3295

0.935

cIPTW\(\times\)cIPVW

\(A_{j-1}\)

-0.3

-0.3029

-0.0029

-0.97%

0.3341

0.3341

0.944

Scenario 4: Irregular visits, unmeasured confounder

Naïve

\(A_{j-1}\)

-0.3

-0.2612

0.0388

12.93%

0.3397

0.3419

0.921

sIPTW

\(A_{j-1}\)

-0.3

-0.2672

0.0328

10.93%

0.3317

0.3333

0.938

sIPVW

\(A_{j-1}\)

-0.3

-0.2692

0.0308

10.27%

0.3162

0.3177

0.932

sIPTW\(\times\)sIPVW

\(A_{j-1}\)

-0.3

-0.2777

0.0223

7.43%

0.3294

0.3301

0.940

cIPTW\(\times\)cIPVW

\(A_{j-1}\)

-0.3

-0.2932

0.0068

2.27%

0.2934

0.2934

0.947

  1. \(\psi =\) marginal causal effect
  2. sIPT(V)W= stabilized inverse probability treatment (visit) weights
  3. cIPT(V)W= calibrated inverse probability treatment (visit) weights
  4. aMCE= Monte Carlo Error (standard deviation of Monte Carlo estimator)
  5. brMSE = root Mean Square Error= \(\sqrt{Bias^2+Var}\)