R Tutorial : Basic statistical analysis

Key Takeaways

here we will go through some basic statistical analyses for these endpoints when a trial is conducted there is a target population typically patients with a disease we cannot include all those patients so a sample is taken to test the study hypotheses and make inferences back to the target population consider a placebo controlled trial evaluating the effects of a drug on bone mineral density our endpoint is the change from baseline at one year we would state for our null hypothesis that the mean changes in the drug and perceiver groups are equal no treatment difference the alternative hypothesis could be that the group means are not equal in this case we allow for the possibility that the mean change in active drug group to be higher or lower than in the perceiver group a two-sided test in a one-sided test our alternative hypothesis could be that the increase in the drug group is greater than in the placebo we then conduct an appropriate statistical tests on the sample data to provide evidence against the null hypothesis we estimate the treatment effect and its confidence interval that is the range of values for this estimate that has a specified probability of containing the true population treatment effect a test statistic is compared to a distribution in order to determine the p-value that is the probability of observing our data or something more extreme if the null hypothesis is true if this p-value is less than a pre-specified significance level then we reject the null hypothesis commonly this is set to naught point naught 5 ie we allow a 5% chance of incorrectly rejecting the null hypothesis when it is in fact true in our example bone mineral density change is a continuous measure if we find that the changes from baseline within the groups are normally distributed we can test whether the means are equal using a two sample t-test for the t-test function we specify the outcome variable treatment group and data set we also use the var dot equal argument to specify whether we are assuming that the two variances or standard deviations are equal here is d that the p-value provides evidence against the null hypothesis of no treatment difference at the 5% level and that the 95% confidence interval excludes 0 so if there really is no treatment difference in the population the probability of observing this sample or something even more favorable towards the active drug is 0.0018 very low if we have a non-normal distribution presenting means is not appropriate as they are affected by skewness here we can use the wilcoxon rank-sum test the null hypothesis is that the distributions of the two populations are the same and the alternative hypothesis is that there is a left or right translation shift finally with binary outcomes we can test the null hypothesis of equal group proportions with the chi-squared test we use the prop test and table functions specifying a treatment group and response its producers a test statistic that is compared to the chi-squared distribution here the p-value is significant at the 5% level and the 95 percent confidence interval for the difference in proportions excludes 0 providing evidence against the null hypothesis note for these tests we assume that the observations in the treatment groups are independent and that the randomization achieved similar patient characteristics also although not covered in this course many trials collects outcomes over several visits or have more than two groups these require different statistical method