coxph_bf: Bayes factor for Cox proportional hazards regression

In maxlinde/baymedr: Computation of Bayes Factors for Common Biomedical Designs

Bayes factor for Cox proportional hazards regression

Description

coxph_bf computes a Bayes factor for Cox proportional hazards regression models with one dichotomous independent variable.

Usage

coxph_bf(
  data,
  null_value = 0,
  alternative = "two.sided",
  direction = NULL,
  prior_mean = 0,
  prior_sd = 1
)

Arguments

data	A data.frame or a list resulting from calling coxph_data_sim. In the former case, the first column represents the survival/censoring times, the second column indicates whether an event (e.g., death) has happened (1) or not (0), and the third column represents the dummy-coded independent variable, where the control group is coded with 0 and the experimental group with 1.
null_value	The value of the point null hypothesis for the beta coefficient. The default is a null value of 0.
alternative	A string specifying whether the alternative hypothesis is two-sided ("two.sided"; the default) or one-sided ("one.sided").
direction	A string specifying the direction of the one-sided alternative hypothesis. This is ignored if alternative = "two.sided". Possible options are "low" and "high".
prior_mean	Mean of the Normal prior for the beta parameter. The default is a mean of 0.
prior_sd	Standard deviation of the Normal prior for the beta parameter. The default is a standard deviation of 1.

Details

The Cox proportional hazards model has the following hypotheses: The null hypothesis (i.e., H0) states that the population hazard ratio between the experimental (e.g., a new medication) and the control group (e.g., a placebo or an already existing medication) is equal to 1 (i.e., beta = 0). The alternative hypothesis can be two-sided or one-sided (either negative or positive).

Since the main goal of coxph_bf is to establish that the hazard ratio is not equal to 1, the resulting Bayes factor quantifies evidence in favor of the alternative hypothesis. For a two-sided alternative hypothesis, we have BF10; for a negative one-sided alternative hypothesis, we have BF-0; and for a positive one-sided alternative hypothesis, we have BF+0. Evidence for the null hypothesis can easily be calculated by taking the reciprocal of the original Bayes factor (i.e., BF01 = 1 / BF10). Quantification of evidence in favor of the null hypothesis is logically sound and legitimate within the Bayesian framework (see e.g., van Ravenzwaaij et al., 2019).

For the calculation of the Bayes factor, a Normal prior density is chosen for beta under the alternative hypothesis. The arguments prior_mean and prior_sd specify the mean and standard deviation of the Normal prior, respectively. By adjusting the Normal prior, different ranges of expected effect sizes can be emphasized. The default is a Normal prior with a mean of 0 and a standard deviation of 1.

Note that at the moment the model specifications are limited. That is, it is only possible to have a single dichotomous independent variable. Further, at the moment only a Normal prior is supported. Lastly, only the Efron partial likelihood and not the many other options are supported.

coxph_bf creates an S4 object of class baymedrCoxProportionalHazards, which has multiple slots/entries (e.g., prior, Bayes factor, etc.; see Value). If it is desired to store or extract solely the Bayes factor, the user can do this with get_bf, by setting the S4 object as an argument (see Examples).

Value

An S4 object of class baymedrCoxProportionalHazards is returned. Contained are a description of the model and the resulting Bayes factor:

• test: The type of analysis

• hypotheses: A statement of the hypotheses

  • h0: The null hypothesis

  • h1: The alternative hypothesis

• prior: The parameters of the Normal prior on beta

• bf: The resulting Bayes factor

A summary of the model is shown by printing the object.

References

Harrell, F. R. (2015). Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis (2nd ed.). Springer.

van Ravenzwaaij, D., Monden, R., Tendeiro, J. N., & Ioannidis, J. P. A. (2019). Bayes factors for superiority, non-inferiority, and equivalence designs. BMC Medical Research Methodology, 19, 71.

See Also

coxph_data_sim.

Examples

# Load aml dataset from the survival R package.
data <- survival::aml
data$x <- ifelse(test = data$x == "Maintained",
                 yes = 0,
                 no = 1)
names(data) <- c("time", "event", "group")

# Assign model to variable.
coxph_mod <- coxph_bf(data = data,
                      null_value = 0,
                      alternative = "one.sided",
                      direction = "high",
                      prior_mean = 0,
                      prior_sd = 1)

# Extract Bayes factor from variable.
get_bf(coxph_mod)

maxlinde/baymedr documentation built on Oct. 4, 2022, 6:27 a.m.