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Table 2 Parameter estimates and fit statistics of the fitted models for progression rate of ICARS in SCA3 patients

From: The progression rate of spinocerebellar ataxia type 3 varies with disease stage

 

LM1

LM2

LM3

LM4

QM1

PM1

PM2

PM2c

PM3

PM3c

PM4

PM4c

Parameter estimates of fixed effects

 Intercept

2.067 (1.309)

P = 0.115

44.448 (24.183)

P = 0.067

− 16.464 (5.448)

P = 0.003

− 60.517 (38.837)

P = 0.120

10.726 (1.915)

P < 0.001

36.746 (1.955)

P < 0.001

− 59.997 (35.214)

P = 0.089

− 62.620 (31.899)

P = 0.050

35.501 (8.876)

P < 0.001

36.472 (8.274)

P < 0.001

− 217.508 (57.354)

P < 0.001

− 216.416 (49.701)

P < 0.001

 dt

2.744 (0.154)

P < 0.001

− 7.940 (2.670)

P = 0.003

4.050 (0.702)

P < 0.001

− 12.590 (4.346)

P = 0.005

1.199 (0.280)

P < 0.001

–

–

–

–

–

–

–

 dt2

–

–

–

–

0.069 (0.009)

P < 0.001

–

–

–

–

–

–

–

 d1

–

–

–

–

–

2.445 (0.185)

P < 0.001

− 7.264 (3.305)

P = 0.028

− 7.582 (2.771)

P = 0.006

3.671 (0.817)

P < 0.001

3.787 (0.723)

P < 0.001

− 9.944 (5.672)

P = 0.080

− 9.814 (4.606)

P = 0.034

 d2

–

–

–

–

–

3.547

(0.312)

P < 0.001

− 7.516

(5.989)

P = 0.210

− 6.604

(2.785)

P = 0.018

5.323

(1.582)

P < 0.001

4.878

(0.765)

P < 0.001

− 8.414

(9.030)

P = 0.352

− 8.745

(4.618)

P = 0.059

 CAGexp

–

− 0.623

(0.356)

P = 0.084

–

0.562

(0.485)

P = 0.250

–

–

1.429

(0.519)

P = 0.007

− 0.460

(0.328)

P = 0.164

–

–

3.195

(0.716)

P < 0.001

0.970

(0.449)

P = 0.034

 dt*CAGexp

–

0.157

(0.039)

P < 0.001

–

0.205

(0.054)

P < 0.001

–

–

–

0.148

(0.041)

P < 0.001

–

–

–

0.171

(0.058)

P = 0.003

 d1*CAGexp

–

–

–

–

–

–

0.144

(0.049)

P = 0.003

–

–

–

0.171

(0.070)

P = 0.016

–

 d2*CAGexp

–

–

–

–

–

–

0.162

(0.088)

P = 0.067

–

–

–

0.172

(0.113)

P = 0.128

–

 AOga

–

–

0.446

(0.128)

P < 0.001

0.590

(0.184)

P = 0.002

–

–

–

–

0.026

(0.206)

P = 0.898

0.424

(0.112)

P < 0.001

0.895

(0.271)

P = 0.002

0.680

(0.168)

P < 0.001

 dt*AOga

–

–

− 0.032

(0.016)

P = 0.055

0.025

(0.021)

P = 0.232

–

–

–

–

–

− 0.032

(0.017)

P = 0.055

–

0.015

(0.022)

P = 0.513

 d1*AOga

–

–

–

–

–

–

–

–

− 0.030

(0.019)

P = 0.123

–

0.018

(0.027)

P = 0.517

–

 d2*AOga

–

–

–

–

–

–

–

–

− 0.043

(0.037)

P = 0.251

–

0.005

(0.047)

P = 0.917

–

Fit statistics

 AIC

4019.470

4013.763

4021.004

4005.769

3984.778

3945.904

3947.395

3942.736

3952.541

3946.137

3939.014

3928.450

 BIC

4046.163

4049.328

4056.57

4050.194

4015.909

3990.377

4005.148

3996.066

4010.294

3999.467

4010.018

3990.623

 logLik

− 2003.735

− 1998.881

− 2002.502

− 1992.884

− 1985.389

− 1962.952

− 1960.697

− 1959.368

− 1963.270

− 1961.069

− 1953.507

− 1950.225

 Conditional R2

0.970

0.971

0.971

0.972

0.978

0.979

0.979

0.979

0.979

0.979

0.980

0.980

 Marginal R2

0.479

0.540

0.480

0.623

0.488

0.517

0.575

0.575

0.516

0.517

0.641

0.643

 P-value in ANOVA

–

Pa = 0.008

Pa = 0.292

Pa < 0.001

Pa < 0.001

Pb < 0.001

Pa < 0.001

Pa = 0.212

Pb < 0.001

Pb = 0.028

Pc < 0.001

Pb = 0.888

Pc < 0.001

Pb = 0.152

Pc < 0.001

Pb = 0.004

Pc < 0.001

Pb < 0.001

Pc < 0.001

  1. LM1: linear growth model (duration as a variable)
  2. LM2: linear growth model (duration and CAGexp as variables)
  3. LM3: linear growth model (duration and AOga as variables)
  4. LM4: linear growth model (duration, CAGexp and AOga as variables)
  5. QM1: quadratic growth model (duration and duration^2 as variables)
  6. PM1: piece-wise linear growth model (duration as a variable)
  7. PM2: piece-wise linear growth model (duration and CAGexp as variables)
  8. PM2c: piece-wise linear growth model (piece-wise fitting for duration as a variable, linear fitting for CAGexp as a variable)
  9. PM3: piece-wise linear growth model (duration and AOga as variables)
  10. PM3c: piece-wise linear growth model (piece-wise fitting for duration as a variable, linear fitting for AOga as a variable)
  11. PM4: piece-wise linear growth model (duration, CAGexp and AOga as variables)
  12. PM4c: piece-wise linear growth model (piece-wise fitting for duration as a variable, linear fitting for CAGexp and AOga as variables)
  13. Nakagawa R2, usually interpreted as pseudo r-squared, which indicates the amount of heterogeneity accounted for by the fitted model. It includes two types of R2 (marginal and conditional R2). The marginal R2 relates to the variance of the fixed effects, while conditional R2 takes both the fixed and random effects into account. The p-values in ANOVA for model comparison among linear growth model of LM1 null model and other related models were marked by a in each column (i.e., LM1 vs LM2, LM1 vs LM3, LM1 vs LM4, LM1 vs QM1, LM1 vs PM1, respectively). And the ANOVA results for piece-wise growth model of PM1 null model vs quadratic growth model and other piece-wise models were expressed by b (i.e., PM1 vs QM1, PM1 vs PM2, PM1 vs PM2c, PM1 vs PM3, PM1 vs PM3c, PM1 vs PM4, PM1 vs PM4c, respectively), while related linear growth models vs their respective corresponding piece-wise models were denoted by c (i.e., LM1 vs PM1, LM2 vs PM2, LM2 vs PM2c, LM3 vs PM3, LM3 vs PM3c, LM4 vs PM4, and LM4 vs PM4c, respectively). The value of parameter estimates of fixed effects were represented by mean [SE]
  14. ICARS = International Cooperative Ataxia Rating Scale; SE = standard error; dt = entire duration; d1 = early duration; d2 = late duration; CAGexp = expanded CAG repeat; AOga = age at onset of gait ataxia; AIC = Akaike’s information criterion, BIC = Bayesian information criterion (BIC); logLike = Log-Likelihood; R2 = R-squared; ANOVA = analysis of variance