Frequentist logistic regression model analysis for binary data adjusting for periods

This function performs logistic regression taking into account all trial data until the arm under study leaves the trial and adjusting for periods as factors.

Usage

fixmodel_bin(data, arm, alpha = 0.025, ncc = TRUE, check = TRUE, ...)

Arguments

data: Data frame with trial data, e.g. result from the datasim_bin() function. Must contain columns named 'treatment', 'response' and 'period'.
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.
ncc: Logical. Indicates whether to include non-concurrent data into the analysis. Default=TRUE.
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 log-odds ratio
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)
model - fitted model

Details

The model-based analysis adjusts for the time effect by including the factor period (defined as a time interval bounded by any treatment arm entering or leaving the platform). The time is then modelled as a step-function with jumps at the beginning of each period. Denoting by $y_j$ the response probability for patient $j$, by $k_j$ the arm patient $j$ was allocated to, and by $M$ the treatment arm under evaluation, the regression model is given by:

$$g(E(y_j)) = \eta_0 + \sum_{k \in \mathcal{K}_M} \theta_k \cdot I(k_j=k) + \sum_{s=2}^{S_M} \tau_s \cdot I(t_j \in T_{S_s})$$

where $g(\cdot)$ denotes the logit link function and $\eta_0$ is the log odds in the control arm in the first period; $\theta_k$ represents the log odds ratio of treatment $k$ and control for $k\in\mathcal{K}_M$, where $\mathcal{K}_M$ is the set of treatments that were active in the trial during periods prior or up to the time when the investigated treatment arm left the trial; $\tau_s$ indicates the stepwise period effect in terms of the log odds ratio between periods 1 and $s$ ($s = 2, \ldots, S_M$), where $S_M$ denotes the period, in which the investigated treatment arm left the trial.

If the data consists of only one period (e.g. in case of a multi-arm trial), the period in not used as covariate.

References

On model-based time trend adjustments in platform trials with non-concurrent controls. Bofill Roig, M., Krotka, P., et al. BMC Medical Research Methodology 22.1 (2022): 1-16.

Author

Pavla Krotka

Examples


trial_data <- datasim_bin(num_arms = 3, n_arm = 100, d = c(0, 100, 250),
p0 = 0.7, OR = rep(1.8, 3), lambda = rep(0.15, 4), trend="stepwise")

fixmodel_bin(data = trial_data, arm = 3)
#> $p_val
#> [1] 0.2436484
#> 
#> $treat_effect
#> [1] 0.2355592
#> 
#> $lower_ci
#> [1] -0.424127
#> 
#> $upper_ci
#> [1] 0.9111935
#> 
#> $reject_h0
#> [1] FALSE
#> 
#> $model
#> 
#> Call:  glm(formula = response ~ as.factor(treatment) + as.factor(period), 
#>     family = binomial, data = data_new)
#> 
#> Coefficients:
#>           (Intercept)  as.factor(treatment)1  as.factor(treatment)2  
#>               1.06960               -0.04699                0.45312  
#> as.factor(treatment)3     as.factor(period)2     as.factor(period)3  
#>               0.23556                0.15502               -0.02392  
#>    as.factor(period)4  
#>               0.33341  
#> 
#> Degrees of Freedom: 499 Total (i.e. Null);  493 Residual
#> Null Deviance:	    521.8 
#> Residual Deviance: 517.6 	AIC: 531.6
#>