Spline regression analysis for continuous data with knots placed according to calendar time units

This function performs linear regression taking into account all trial data until the arm under study leaves the trial and adjusting for time using regression splines with knots placed according to calendar time units.

Usage

splines_cal_cont(
  data,
  arm,
  alpha = 0.025,
  unit_size = 25,
  ncc = TRUE,
  bs_degree = 3,
  check = TRUE,
  ...
)

Arguments

data: Data frame with trial data, e.g. result from the datasim_cont() function. Must contain columns named 'treatment', 'response' and 'j'.
arm: Integer. Index of the treatment arm under study to perform inference on (vector of length 1). This arm is compared to the control group.
alpha: Double. Significance level (one-sided). Default=0.025.
unit_size: Integer. Number of patients per calendar time unit. Default=25.
ncc: Logical. Indicates whether to include non-concurrent data into the analysis. Default=TRUE.
bs_degree: Integer. Degree of the polynomial spline. Default=3 for cubic spline.
check: Logical. Indicates whether the input parameters should be checked by the function. Default=TRUE, unless the function is called by a simulation function, where the default is FALSE.
...: Further arguments passed by wrapper functions when running simulations.

Value

List containing the following elements regarding the results of comparing arm to control:

p-val - p-value (one-sided)
treat_effect - estimated treatment effect in terms of the difference in means
lower_ci - lower limit of the (1-2*alpha)*100% confidence interval
upper_ci - upper limit of the (1-2*alpha)*100% confidence interval
reject_h0 - indicator of whether the null hypothesis was rejected or not (p_val < alpha)
knots - positions of the knots in terms of patient index
model - fitted model

Author

Pavla Krotka

Examples


trial_data <- datasim_cont(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
theta = rep(0.25, 3), lambda = rep(0.15, 4), sigma = 1, trend = "linear")

splines_cal_cont(data = trial_data, arm = 3)
#> $p_val
#> [1] 1.956967e-05
#> 
#> $treat_effect
#> [1] 0.5488463
#> 
#> $lower_ci
#> [1] 0.2890825
#> 
#> $upper_ci
#> [1] 0.8086101
#> 
#> $reject_h0
#> [1] TRUE
#> 
#> $knots
#>  [1]  25  50  75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450
#> 
#> $model
#> 
#> Call:
#> lm(formula = response ~ as.factor(treatment) + bs(j, knots = bs_knots, 
#>     degree = bs_degree), data = data_new)
#> 
#> Coefficients:
#>                                   (Intercept)  
#>                                       0.20723  
#>                         as.factor(treatment)1  
#>                                       0.23294  
#>                         as.factor(treatment)2  
#>                                       0.13747  
#>                         as.factor(treatment)3  
#>                                       0.54885  
#>  bs(j, knots = bs_knots, degree = bs_degree)1  
#>                                      -0.44304  
#>  bs(j, knots = bs_knots, degree = bs_degree)2  
#>                                       0.22151  
#>  bs(j, knots = bs_knots, degree = bs_degree)3  
#>                                      -0.60998  
#>  bs(j, knots = bs_knots, degree = bs_degree)4  
#>                                       1.10625  
#>  bs(j, knots = bs_knots, degree = bs_degree)5  
#>                                      -1.15322  
#>  bs(j, knots = bs_knots, degree = bs_degree)6  
#>                                       0.79721  
#>  bs(j, knots = bs_knots, degree = bs_degree)7  
#>                                      -0.18413  
#>  bs(j, knots = bs_knots, degree = bs_degree)8  
#>                                      -0.33418  
#>  bs(j, knots = bs_knots, degree = bs_degree)9  
#>                                      -0.88051  
#> bs(j, knots = bs_knots, degree = bs_degree)10  
#>                                       0.81786  
#> bs(j, knots = bs_knots, degree = bs_degree)11  
#>                                      -1.03584  
#> bs(j, knots = bs_knots, degree = bs_degree)12  
#>                                       0.53960  
#> bs(j, knots = bs_knots, degree = bs_degree)13  
#>                                      -0.75128  
#> bs(j, knots = bs_knots, degree = bs_degree)14  
#>                                       0.08619  
#> bs(j, knots = bs_knots, degree = bs_degree)15  
#>                                      -0.83784  
#> bs(j, knots = bs_knots, degree = bs_degree)16  
#>                                       0.32746  
#> bs(j, knots = bs_knots, degree = bs_degree)17  
#>                                      -0.82535  
#> bs(j, knots = bs_knots, degree = bs_degree)18  
#>                                      -0.42178  
#> bs(j, knots = bs_knots, degree = bs_degree)19  
#>                                       0.40940  
#> bs(j, knots = bs_knots, degree = bs_degree)20  
#>                                      -0.56506  
#> bs(j, knots = bs_knots, degree = bs_degree)21  
#>                                      -0.49957  
#> 
#>