Creating Objects of Hierarchical Log Win-Ratio Statistic

winratio_ creates an object to be passed into jointCovariance or pated through its ... argument. The object defines a hierarchical win-ratio statistic across a list of endpoints, each declared by nb_tte(), nb_continuous(), or nb_binary().

Usage

winratio_(formula, endpoints, data_index = 1)

Arguments

formula

a two-sided R formula <label> ~ arm. The LHS is used purely as a row label in pated() output; the RHS must contain exactly one variable, the column in data holding treatment-arm assignment.

endpoints

a non-empty list of endpoint specs built by nb_tte(), nb_continuous(), or nb_binary(). The order of the list encodes the hierarchical priority: endpoint 1 is checked first; if it ties, the pair falls through to endpoint 2; and so on.

data_index

integer. Index of the data frame in the data argument of jointCovariance to be used.

Value

An object of class c("jc_spec_winratio", "jc_spec").

Details

The fitted coefficient is on the log scale: $$\widehat\theta = \log(\widehat{WR}) = \log(\widehat\pi_W / \widehat\pi_L)$$ where \(\widehat\pi_W\) and \(\widehat\pi_L\) are the proportions of all control-treatment pairs where the treatment subject wins or loses, respectively. Tied pairs remain in the denominator of both proportions but do not contribute to either numerator.

The raw win ratio can be recovered by exponentiating the coefficient. The log scale is used because it gives the standard large-sample Wald representation and maps the null win ratio of 1 to 0.

The arm reference level is inferred from the arm column the same way model.matrix(~ arm) would: levels(arm)[1] for factor, the smaller value for numeric or logical, and the alphabetically first value for character. To override, convert the column to a factor with the desired level order before calling winratio_().

See also

nb_tte(), nb_continuous(), nb_binary(), jointCovariance(), pated().