Journal List > Transl Clin Pharmacol > v.24(4) > 1082635

Chae and Park: An imputation-based method to reduce bias in model parameter estimates due to non-random censoring in oncology trials

Abstract

In oncology trials, patients are withdrawn from study at the time when progressive disease (PD) is diagnosed, which is defined as 20% increase of tumor size from the minimum. Such informative censoring can lead to biased parameter estimates when nonlinear mixed effects models are fitted using NONMEM. In this work, we investigated how empirical Bayes estimates (EBE) could be exploited to impute missing tumor size observations and partially correct biases in the parameter estimates. 50 simulated datasets, each consisting of 100 patients, were generated based on the published model. From the simulated dataset, censoring due to PD diagnosis has been implemented. Using the post-hoc EBEs acquired from fitting the censored datasets using NONMEM, imputed values were generated from the tumor size model. Model fitting was carried out using censored and imputed datasets. Parameter estimates using both datasets were compared with true values. Tumor growth rate and cell kill rate were approximately 28% and 16% underestimated when fitted using the censored dataset, respectively. With the imputed datasets, relative biases of tumor growth rate and cell kill rate decreased to about 6% and 0%, respectively. Our work demonstrates that using EBEs acquired from fitting the model to the censored dataset and imputing the unknown tumor size observations with individual predictions beyond the PD time point is a viable option to solve the bias associated with structural parameter estimates. This approach, however, would not be helpful in getting better estimates of variance parameters.

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Figure 1.
Comparison plots of tumor size observations of original (LEFT), censored (CENTER), and imputed (RIGHT) datasets.
tcp-24-189f1.tif
Table 1.
Estimate (%RSE) of tumor growth model parameters reporte in the original publication
Parameter Estimate (%RSE)
Structural parameters  
 Tumor growth rate, KL /week 0.015 (25.4)
 Cell kill rate, KD /g week 0.058 (17.0)
 Resistance appearance, λ/week 0.042 (28.7)
Variance parameters  
 IIV (variance) of KL 0.556 (27.8)
 IIV (variance) of KD 0.540 (43.7)
 IIV (variance) of λ 0.450 (55.5)
 Sigma, mm 14.9
Table 2.
Estimate (%RSE) and relative bias (%RSE) of tumor growth model parameters obtained from fitting the model to the original, censored and imputed datasets
Parameter Original Dataset Censored Dataset Imputed Dataset
Structural parameters
 Tumor growth rate, KL /week      
  Estimate (%RSE) 0.015 (17.43) 0.011 (35.79) 0.014 (41.21)
  Relative Bias (%RSE) - 28.17 (21.73) 6.06 (35.07)
 Cell kill rate, KD /g week      
  Estimate (%RSE) 0.056 (8.85) 0.047 (13.58) 0.056 (16.47)
  Relative Bias (%RSE) - 15.71 (8.62) 0.098 (14.00)
 Resistance appearance, λ/week      
  Estimate (%RSE) 0.042 (13.86) 0.041 (15.90) 0.044 (17.77)
  Relative Bias (%RSE) - 3.12 (9.27) -3.38 (14.99)
Variance parameters
 IIV (variance) of KL      
  Estimate (%RSE) 0.52 (35.54) 0.26 (187.3) 0.77 (185.05)
  Relative Bias (%RSE) - 58.17 (49.27) -29.77 (124.68)
 IIV (variance) of KD      
  Estimate (%RSE) 0.62 (17.14) 0.85 (27.82) 0.69 (32.72)
  Relative Bias (%RSE) - -37.81 (27.72) -11.66 (28.47)
 IIV (variance) of λ      
  Estimate (%RSE) 0.40 (27.91) 0.41 (28.96) 0.54 (35.44)
  Relative Bias (%RSE) - -1.75 (13.12) -37.99 (47.22)
 Sigma (variance)      
  Estimate (%RSE) 0.0096 (5.83) 0.01 (8.51) 0.012 (11.76)
  Relative Bias (%RSE) - -3.61 (3.67) -19.55 (12.78)
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