Why and What

Key Ingredients

outline: key ingredients and main components

outline: key ingredients and main components


Research Aim

Confirmatory (purpose A)

  • goal:: confirm an expected difference, relation, …
    maybe the aim is to establish a difference or a pre-specified certainty on a parameter estimate
  • focus:: statistical test or accurate parameter estimate
  • requirement::
    • sample size calculation, if not enough information is obtained to make the confirmation the study failed
      • absence of proof is not proof of absence
      • non-significant results can be due to the lack of effect or the lack of power
    • discuss costs and availability of observations in light of the required sample size, note that interim analysis may be interesting but require a more complicated sample size estimation
    • the link between the research design and especially the primary aim is important to specify, which should link up nicely with the statistical analysis plan
  • minimum:: a study would be successful if it is considered interesting by expert peers and if the effect is significant or accurate enough
  • a special note is due on statistical testing, the aim is not always to establish a difference or relation, sometimes it involves
    • superiority, which requires a sample size to show that some set of observations is not worse, with a pre-specified margin
    • non-equivalence, to show similarity, which requires a sample size for two tests, one to show that the effect can not be smaller than the pre-specified lower margin of tolerance and one that it can not be bigger than the upper margin of tolerance

Exploratory (purpose B)

  • goal:: to explore, there is no clear idea on what the effect should be and what the population variance of the measurement would be
  • while not easy to justify, exploratory studies are quite common
    • focus A:: the interest could be merely a data description and/or parameter estimation, where the results would be interesting whatever they are
      • while testing/accuracy is not the primary aim, it could be secondary in a sense that significance/accuracy is not guaranteed in advance
    • focus B:: most qualitative understanding is exploratory
    • focus C:: various statistical procedures are not (yet) developed enough to provide clear aims for, like hierarchical clustering, …, are the ever more popular predictive modeling that is evaluated using cross-validation instead of significance testing
  • requirement::
    • because it is hard or impossible to justify a study based on statistics, the need/importance of extracted information should be made clear on substantive grounds, without reference to statistical tests
    • a sample size -justification- would argue for a balance between information and cost
    • the link between the research design and the most important information of interest is still of interest, but various hypotheses are now typically of interest, all requiring a statistical plan
  • minimum:: the justification for exploratory studies could be many things, as long as you can sufficiently argue its merit, again, without any reference to significance/accuracy.

Preparatory (purpose C)

  • goal:: while very similar to exploratory studies, preparatory studies (my own label) prepare or justify a future study, the results are not by themselves of interest
  • focus: tyically this type of study implies a small scale set-up to show the potential and/or detect issues, again, not set up to establish effects
    • phase I and II clinical designs
      • such designs are required to decide on whether further studies would be of high enough potential while accounting for the costs involved, it requires decision criteria to proceed or not
    • pilot study, which serve to prepare to implement a future study
      • no statistical testing is implied, that is for the actual study
      • not in itself of interest, therefore not intended for publication
      • could be (partially) qualitative, in fact, everything goes if it provides the required information, it could even be simply monitoring (part of) the intended procedures (not a mini-copy)
  • requirement::
    • it should be clear that the required information will be obtained, but also the future study itself should be made clear
    • a minimal cost to get a rough idea should suffice, for example, with animal experiments this typically results in 3 animals per condition which allow for an estimate of variance
  • minimum: at least the information required for the future study should come out, but there are no strict rules otherwise

Techn(olog)ical advancements (purpose D)

  • goal:: to design, engineer, create, … not all studies are set up to extract information from the outside world
  • focus:: when not focused on information, rarely there is any statistics involved
  • requirement:: there are therefore no requirements in terms of methodology or statistics, the justification should be based on the expected contribution to research versus the cost
    • proof of concept: feasibility
    • proof of principle: functionality
    • development application
  • minimum:: the merit should be shown, and at least a particular state of advancement should be expected

Additional distinctions in aim

  • Quantitative versus Qualitative
    • quantitative research focuses on quantifiable empirical aspects, and typically in doing so reduces the complexity in order to make use of visualization and statistics to summarize and generalize, this type of research can be both descriptive and/or inferential
    • qualitative research focuses on understanding, especially with focus on reasons, opinions, motivations, … trying to embrace the complexity involved, but in doing so limiting the study to descriptive research that is at most hypothesis generating

  • Descriptive versus Inferential
    • inferential research is about the population, based on a sample, which implies generalization and therefore (ideally) representative samples for which it uses uncertainty
    • descriptive research is about the sample and does not go beyond the observed data, which is why data are presented as is without reference to uncertainty nor p-values

  • while used here to show distinctions, they can be combined into one study

Research Design

Quantity of Observations

  • observations should provide information on the questions of interest
    • this implies that more observations are more informative
    • but, observations come with a cost, so there is a reason not to make too many
    • costs can exist in terms of time, money, risk, …
  • when confirmatory studies are of interest, sample size -calculation- should be performed and communicated
    • specify the statistical test in focus, this should reflect the minimal result for the main hypothesis
      do not assume that the test is clear from the context
    • determine the effect size aimed for, and give good enough reasons for it, for both the effect and the uncertainty
      • effect: know what you want to find, ideally specified substantively but otherwise referring to common practice / earlier research (effect size is signal)
      • uncertainty: understand the population variance of your measurement, ideally based on earlier data/research or pilot
      • use rules of thumb when all reasoning fails, only
    • operational characteristics (type I error \(\alpha\) and type II error \(\beta\)), typically with power ranging between .8 and .9, note that the two types of errors are related, decreasing one would increase the other keeping the sample size constant
      note that with \(\alpha\) .05 and power .8, the type I error \(\alpha\) is considered 4 times more severe than the type II error \(\beta\)
    • there are two issues worth mentioning:
      • sample size calculation is relevant for the primary research questions, if there are multiple that are related the highest value is usually considered
      • only use sample size calculation, or power analysis, for future studies, never to justify data can be analyzed already (not retrospective)

Quality of Observations

  • the quality of observations depends on conditions under which they were observed and the method used for making the observation
  • general idea is to isolate the effect, either by avoiding or by measuring the unwanted influences on the observations
  • a general principle is to try and
    • control confounding variables (influence not in the model)
    • maximize systematic variability (explained variance)
    • minimize non-systematic variability (unexplained variance)

  • exercising that principle often implies control, at least to some extent
    • an experimental study exerts control, by definition, therefore it typically offers more quality in terms of observations
      • necessary condition for causal conclusions
    • observational study does not exert control, therefore often the quantity has to be increased rather than the quality
      • naturalistic, survey, … most retrospective

Quality of Observations — Confounders

  • control on confounding variables, to avoid differential influence on the observations from unknown sources
    • randomization (large enough sample size), the most often used method to balance out different sources of confounding
    • repeated measures, to keep various sources stable and measure their variance
    • blocking, to keep various sources stable and measure their variance
    • matching, to keep groups comparable
    • cross-over designs, to create within unit comparisons and allow estimation of order effects
    • (double-) blinding, to avoid unwanted influence from knowing the goal of the study
    • and more …
  • typically, upgrading the design makes it more interesting, but it does also complicate the statistical analysis
    • the correlational structure implied by the design has to be accounted for, this would often require mixed models

Quality of Observations — (Non-) Systematic Variability

  • to maximize systematic variability can be considered from two perspectives
    • use proper explanatory variables, in other words make sure the relevant explaining variables are registered properly
    • use maximally differentiating conditions, in other words make sure that the conditions within explaining variables are selected to maximize the informational potential
      • beware: if focusing on the extremes, there is a threat of introducing artifacts
      • beware: if the evolution in between also is important, some conditions should be set up to make observations there as well

  • minimize non-systematic variability, avoid everything you know nothing about as good as possible
    • maximize systematic variability, in other words, try to explain as much as possible
    • use proper measurement tools
      • your measurement should be of high reliability / precision, if not this would increase the non-systematic variability
      • to get sense on the reliability, different measurement tools can be combined and analysed
    • use categories when necessary only, continuous if possible, to allow an analysis on the finest grid possible and/or valid

Generalizability

  • generalization (inference) is dependent on successful sampling, in theory you can only draw conclusions on the population you have observed by sample
    • the method of sampling thus plays an important rule
      • probabilistic (sampling: random, stratified, multi-stage, ….), necessary for conclusive, unbiased, objective inferences
      • non-probabilistic (sampling: diversity, expert, ….), potentially biasing, more subjective, and best used only explorative
    • missing data can have an effect on the generalizability depending on the mechanism of missingness
      • missing (completely) at random would result in efficiency loss primarily, missing not at random is a problem because bias is introduced
        • avoid missing data, explain how
        • remediate, explain how

Small Example

The aim is to show that the proposed treatment is an improvement over the current standard method.

Participants are randomized into two groups, treatment and control. The control group is given a dummy treatment. A post experiment survey addresses whether participants were aware about dummy treatment. Each participant is measured once, immediately after the (dummy) treatment was administered which results in one score per patient, continuous on a 0-10 scale. A t-test for independent means is used to evaluate whether the scores in the treatment group are higher than those in the control group.

A sample size was derived for the t-test to detect a minimal difference of 2 in favor of the treatment, which was decided upon by our expert panel. In literature, the standard method is indicated to have a population standard deviation of about 4. Because no information is available on the new treatment it is assumed that the same population standard deviation applies. This leads to a sample size of 51 patients in each of both groups, required for a one-sided test, type I error of .05 and power of .8. Earlier experiments showed a drop-out of about 10%, so 51/9*10 < 57 patients are included per group.

Statistics

Practical Suggestions

example for specifying conditions

example for specifying conditions

Conclusion



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