This function performs separate analysis (only taking into account concurrent controls) using a logistic model.
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.
- 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 ratiolower_ci- lower limit of the (1-2*alpha)*100% confidence intervalupper_ci- upper limit of the (1-2*alpha)*100% confidence intervalreject_h0- indicator of whether the null hypothesis was rejected or not (p_val<alpha)model- fitted model
Details
The separate analysis takes into account only the data from the evaluated experimental treatment arm and its concurrent controls and uses a logistic regression model to evaluate the given treatment arm. 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:
$$g(E(y_j)) = \eta_0 + \theta_M \cdot I(k_j=M)$$
where \(g(\cdot)\) denotes the logit link function and \(\eta_0\) is the log odds in the concurrent controls; \(\theta_M\) represents the log odds ratio of treatment \(M\) and control.
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")
sepmodel_bin(data = trial_data, arm = 3)
#> $p_val
#> [1] 0.08700646
#>
#> $treat_effect
#> [1] 0.4703789
#>
#> $lower_ci
#> [1] -0.2022231
#>
#> $upper_ci
#> [1] 1.160792
#>
#> $reject_h0
#> [1] FALSE
#>
#> $model
#>
#> Call: glm(formula = response ~ as.factor(treatment), family = binomial,
#> data = data_new)
#>
#> Coefficients:
#> (Intercept) as.factor(treatment)3
#> 1.0460 0.4704
#>
#> Degrees of Freedom: 199 Total (i.e. Null); 198 Residual
#> Null Deviance: 210.8
#> Residual Deviance: 208.9 AIC: 212.9
#>