# From early RCT: robust inference of Remdesivir effect on time to clinical improvement

Now consider the previous example of Remdesivir but instead we are interested in the continuous outcome variable of time to clinical improvement. Figure 1. Time to clinical improvement in the Remdesivir example. Data from Table 3, Wang et al (2020).

We can interpret the robustness of inference regarding Remdesivir’s effect on time to clinical improvement in following ways.

## Percent bias necessary to invalidate the inference

To invalidate an inference, $$70.544\%$$ of the estimate would have to be due to bias. This is based on a threshold of $$0.362$$ for statistical significance ($$\alpha = 0.05$$). To invalidate an inference, $$186$$ of the observations would have to be replaced with cases for which the effect is $$0$$.

## Impact threshold for a confounding variable

The minimum impact to invalidate an inference for a null hypothesis of $$0$$ effect is based on a correlation of $$0.546$$ with the outcome and at $$0.546$$ with the predictor of interest (conditioning on observed covariates) based on a threshold of $$0.121$$ for statistical significance ($$\alpha = 0.05$$). Correspondingly the impact of an omitted variable (as defined in Frank 2000) must be $$0.546 \times 0.546 = 0.298$$ to invalidate an inference for a null hypothesis of $$0$$ effect.

## Using KonFound-it to reproduce the results

Since the outcome is a continuous variable, we use pkonfound.

konfound::pkonfound(est_eff = 1.23,
std_err = .184,
n_obs = 263,
n_covariates = 0)
## Percent Bias Necessary to Invalidate the Inference:
## To invalidate an inference, 70.544% of the estimate would have to be due to bias. This is based on a threshold of 0.362 for statistical significance (alpha = 0.05).
## To invalidate an inference, 186 observations would have to be replaced with cases for which the effect is 0.
## See Frank et al. (2013) for a description of the method
## Citation: Frank, K.A., Maroulis, S., Duong, M., and Kelcey, B. 2013. What would it take to change an inference? Using Rubin's causal model to interpret the robustness of causal inferences. Education, Evaluation and Policy Analysis, 35 437-460.
## Impact Threshold for a Confounding Variable:
## The minimum impact to invalidate an inference for a null hypothesis of 0 effect is based on a correlation of 0.546 with the outcome and at 0.546 with the predictor of interest (conditioning on observed covariates) based on a threshold of 0.121 for statistical significance (alpha = 0.05).
## Correspondingly the impact of an omitted variable (as defined in Frank 2000) must be 0.546 X 0.546 = 0.298 to invalidate an inference for a null hypothesis of 0 effect.
## See Frank (2000) for a description of the method
## Citation: Frank, K. 2000. Impact of a confounding variable on the inference of a regression coefficient. Sociological Methods and Research, 29 (2), 147-194
## For other forms of output, change to_return to table, raw_output, thres_plot, or corr_plot.
## For models fit in R, consider use of konfound().