7/27/2019 Why Bootstrap Simulations

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Why Bootstrap (resampling) Methods and Simulations in Statistics?

The continuing revolution in computing is having a dramatic influence in Statistics. Given the copious

amounts of computation to even the small sets of data, the new methods that are applied now were

unthinkable in the past. Thus, the new methods produce confidence intervals and tests of significance

in settings that do not meet the conditions (small sample or skewed distributions or complicated

statistics such as ratio) for reliable application of the usual methods of inference.

The methods which we use to compare two groups, mean or proportion, testing associations, etc,

centres on the use of normal distributions. However, many a times, data is not exactly following

normal distribution. In such situations, we cannot use t confidence intervals and tests, if the data is

immensely skewed, unless the given samples are quite large. Similarly, inference about spread based

on normal distributions is not robust and is therefore of little use in practice. For example, we are

interested in, a ratio of means and ratio of proportions, rates etc, such as the ratio of BP in new

treatment group vs control (reference group) or the ratio of two incidences (ratio of intervention group

vs control group). Particularly, the traditional statistical methods are not stable or reliable, when the

observations are small. There is no simple traditional inference method for dealing with small

numbers, though there is non parametric tests, these tests will provide p values but would not result

95%CI for the effective size of the ratio of two means.

The bootstrap (resampling) confidence intervals and permutation testsif applied, provides power torelax some of the conditions needed or avoid distribution assumptions for traditional inference. The

fundamental reasoning is still based on posing, What would happen if we applied this method a

number of times? Answers to this question are still given by confidence levels and P -values based on

the sampling distributions of statistics. The New methods set us free from the need for normal data or

large samples. They also set us free from formulas. They work the same way (without formulas) for

many different statistics in many different settings. They can, with sufficient computing power, give

results that are more accurate than those from traditional methods. Also, this course trains researchers

in simulating Regression Methods as well.Clinical Trials: Permutation Tests are recommended for Phase II trials and they are invariably based

on small numbers and may have skewed distributions. Permutation test based on simulations would

provide a better estimate than the traditional methods.