From 0d37155a497399ed91b940c655efe602da4cd98b Mon Sep 17 00:00:00 2001 From: Sangyu Xu Date: Wed, 8 Mar 2023 00:26:56 +0800 Subject: [PATCH] Delta-Delta Tests and Docs 1. added doc string to class DeltaDelta and corrected typos 2. changed delta-delta tests and utils.py to mutant-drug configuration 3. generated test images for delta-delta tests 4. added tutorial page deltadelta.rst to include calculations and example plots 5. modified index.rst to include deltadelta 6. modified api.rst to include deltadelta 7. updated tutorial images for deltadelta --- dabest/_classes.py | 64 ++- ...cummings_unpaired_delta_delta_meandiff.png | Bin 47907 -> 53309 bytes ...mmings_sequential_delta_delta_meandiff.png | Bin 51317 -> 57523 bytes ...cummings_baseline_delta_delta_meandiff.png | Bin 51317 -> 57523 bytes .../test_50_delta_plot_ylabel.png | Bin 53903 -> 60752 bytes .../test_51_delta_plot_change_palette_a.png | Bin 51196 -> 57416 bytes .../test_52_delta_specified.png | Bin 0 -> 51814 bytes .../test_53_delta_change_ylims.png | Bin 55237 -> 59422 bytes .../test_54_delta_invert_ylim.png | Bin 52937 -> 59302 bytes .../test_55_delta_median_diff.png | Bin 41964 -> 49080 bytes .../test_56_delta_cohens_d.png | Bin 33449 -> 42663 bytes .../test_57_delta_show_delta2.png | Bin 35853 -> 45068 bytes .../test_58_delta_axes_invert_ylim.png | Bin 47669 -> 55485 bytes ...ta_axes_invert_ylim_not_showing_delta2.png | Bin 35853 -> 45068 bytes dabest/tests/test_07_delta-delta_plots.py | 26 +- dabest/tests/utils.py | 47 +- docs/source/_images/tutorial_106_0.png | Bin 38950 -> 40592 bytes docs/source/_images/tutorial_107_0.png | Bin 38630 -> 42948 bytes docs/source/_images/tutorial_108_0.png | Bin 56034 -> 51832 bytes docs/source/_images/tutorial_109_0.png | Bin 57948 -> 36767 bytes docs/source/_images/tutorial_110_0.png | Bin 54800 -> 35519 bytes docs/source/api.rst | 2 + docs/source/deltadelta.rst | 432 ++++++++++++++++++ docs/source/index.rst | 1 + 24 files changed, 536 insertions(+), 36 deletions(-) create mode 100644 dabest/tests/baseline_images/test_52_delta_specified.png create mode 100644 docs/source/deltadelta.rst diff --git a/dabest/_classes.py b/dabest/_classes.py index 6fd8a359..06bd77b0 100644 --- a/dabest/_classes.py +++ b/dabest/_classes.py @@ -857,7 +857,65 @@ def _all_plot_groups(self): class DeltaDelta(object): """ - A class to compute and store the delta-delta statistics. + A class to compute and store the delta-delta statistics. In a 2-by-2 arrangement where two independent variables, A and B, each have two categorical values, two primary deltas are first calculated with one independent variable and a delta-delta effect size is calculated as a difference between the two primary deltas. + + .. math:: + + \\hat{\\theta}_{B1} = \\overline{X}_{A2, B1} - \\overline{X}_{A1, B1} + + \\hat{\\theta}_{B2} = \\overline{X}_{A2, B2} - \\overline{X}_{A1, B2} + + .. math:: + + \\hat{\\theta}_{\\theta} = \\hat{\\theta}_{B2} - \\hat{\\theta}_{B1} + + and: + + .. math:: + + s_{\\theta} = \\frac{(n_{A2, B1}-1)s_{A2, B1}^2+(n_{A1, B1}-1)s_{A1, B1}^2+(n_{A2, B2}-1)s_{A2, B2}^2+(n_{A1, B2}-1)s_{A1, B2}^2}{(n_{A2, B1} - 1) + (n_{A1, B1} - 1) + (n_{A2, B2} - 1) + (n_{A1, B2} - 1)} + + Example + ------- + >>> import numpy as np + >>> import pandas as pd + >>> from scipy.stats import norm # Used in generation of populations. + >>> np.random.seed(9999) # Fix the seed so the results are replicable. + >>> from scipy.stats import norm # Used in generation of populations. + >>> N = 20 + >>> # Create samples + >>> y = norm.rvs(loc=3, scale=0.4, size=N*4) + >>> y[N:2*N] = y[N:2*N]+1 + >>> y[2*N:3*N] = y[2*N:3*N]-0.5 + >>> # Add drug column + >>> t1 = np.repeat('Placebo', N*2).tolist() + >>> t2 = np.repeat('Drug', N*2).tolist() + >>> treatment = t1 + t2 + >>> # Add a `rep` column as the first variable for the 2 replicates of experiments done + >>> rep = [] + >>> for i in range(N*2): + >>> rep.append('Rep1') + >>> rep.append('Rep2') + >>> # Add a `genotype` column as the second variable + >>> wt = np.repeat('W', N).tolist() + >>> mt = np.repeat('M', N).tolist() + >>> wt2 = np.repeat('W', N).tolist() + >>> mt2 = np.repeat('M', N).tolist() + >>> genotype = wt + mt + wt2 + mt2 + >>> # Add an `id` column for paired data plotting. + >>> id = list(range(0, N*2)) + >>> id_col = id + id + >>> # Combine all columns into a DataFrame. + >>> df_delta2 = pd.DataFrame({'ID' : id_col, + >>> 'Rep' : rep, + >>> 'Genotype' : genotype, + >>> 'Drug': treatment, + >>> 'Y' : y + >>> }) + + + + """ def __init__(self, effectsizedataframe, permutation_count, @@ -1014,8 +1072,8 @@ def __repr__(self, header=True, sigfig=3): bs2 = "the confidence interval is bias-corrected and accelerated." bs = bs1 + bs2 - pval_def1 = "Any p-value reported is the probability of observing the" + \ - "effect size (or greater),\nassuming the null hypothesis of" + \ + pval_def1 = "Any p-value reported is the probability of observing the " + \ + "effect size (or greater),\nassuming the null hypothesis of " + \ "zero difference is true." pval_def2 = "\nFor each p-value, 5000 reshuffles of the " + \ "control and test labels were performed." diff --git a/dabest/tests/baseline_images/test_47_cummings_unpaired_delta_delta_meandiff.png b/dabest/tests/baseline_images/test_47_cummings_unpaired_delta_delta_meandiff.png index 7424c7cf386cdfd6be3d8afb4856bfc346da9205..f85f1d3d4d3d428195640f89dc0e03c7563e8bc2 100644 GIT binary patch literal 53309 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"Genotype"], y = "Y", delta2 = True, + experiment = "Treatment") -baseline = load(data = df, x = ["Light", "Genotype"], y = "Y", delta2 = True, - experiment = "Experiment", +unpaired_specified = load(data = df, x = ["Genotype", "Genotype"], y = "Y", + delta2 = True, experiment = "Treatment", + experiment_label = ["Drug", "Placebo"], + x1_level = ["M", "W"]) + +baseline = load(data = df, x = ["Treatment", "Rep"], y = "Y", delta2 = True, + experiment = "Genotype", paired="baseline", id_col="ID") -sequential = load(data = df, x = ["Light", "Genotype"], y = "Y", delta2 = True, - experiment = "Experiment", +sequential = load(data = df, x = ["Treatment", "Rep"], y = "Y", delta2 = True, + experiment = "Genotype", paired="sequential", id_col="ID") @pytest.mark.mpl_image_compare(tolerance=10) def test_47_cummings_unpaired_delta_delta_meandiff(): - return unpaired.mean_diff.plot(fig_size=(12, 8), raw_marker_size=4); + return unpaired.mean_diff.plot(); @pytest.mark.mpl_image_compare(tolerance=10) @@ -62,14 +67,13 @@ def test_51_delta_plot_change_palette_a(): @pytest.mark.mpl_image_compare(tolerance=10) -def test_52_delta_dot_sizes(): - return sequential.mean_diff.plot(show_pairs=False,raw_marker_size=3, - es_marker_size=12); +def test_52_delta_specified(): + return unpaired_specified.mean_diff.plot(); @pytest.mark.mpl_image_compare(tolerance=10) def test_53_delta_change_ylims(): - return sequential.mean_diff.plot(swarm_ylim=(0, 5), + return sequential.mean_diff.plot(swarm_ylim=(0, 9), contrast_ylim=(-2, 2), fig_size=(15,6)); diff --git a/dabest/tests/utils.py b/dabest/tests/utils.py index 88649cf2..6feb39d2 100644 --- a/dabest/tests/utils.py +++ b/dabest/tests/utils.py @@ -98,39 +98,42 @@ def create_demo_dataset_delta(seed=9999, N=20): from scipy.stats import norm # Used in generation of populations. # Create samples - y = norm.rvs(loc=3, scale=0.4, size=N*2) + y = norm.rvs(loc=3, scale=0.4, size=N*4) + y[N:2*N] = y[N:2*N]+1 + y[2*N:3*N] = y[2*N:3*N]-0.5 - # Add experiment column - e1 = np.repeat('Control', N).tolist() - e2 = np.repeat('Test', N).tolist() - experiment = e1 + e2 + # Add drug column + t1 = np.repeat('Placebo', N*2).tolist() + t2 = np.repeat('Drug', N*2).tolist() + treatment = t1 + t2 - # Add a `Light` column as the first variable - light = [] - for i in range(N): - light.append('L1') - light.append('L2') + # Add a `rep` column as the first variable for the 2 replicates of experiments done + rep = [] + for i in range(N*2): + rep.append('Rep1') + rep.append('Rep2') # Add a `genotype` column as the second variable - g1 = np.repeat('G1', N/2).tolist() - g2 = np.repeat('G2', N/2).tolist() - g3 = np.repeat('G3', N).tolist() - genotype = g1 + g2 + g3 + wt = np.repeat('W', N).tolist() + mt = np.repeat('M', N).tolist() + wt2 = np.repeat('W', N).tolist() + mt2 = np.repeat('M', N).tolist() + + + genotype = wt + mt + wt2 + mt2 # Add an `id` column for paired data plotting. - id_col = [] - for i in range(N): - id_col.append(i) - id_col.append(i) + id = 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    WildtypeMutant
    DrugXD, WXD, M
    PlaceboXP, WXP, M
    + + + + +There are 2 ``Treatment`` conditions, ``Placebo`` (control group) and ``Drug`` (test group). There are 2 ``Genotype`` s: ``W`` (wildtype population) and ``M`` (mutant population). In addition, each experiment was done twice (``Rep1`` and ``Rep2``). We shall do a few analyses to visualise these differences in a simulated dataset. + +Simulate a dataset +------------------ + +.. code-block:: python3 + :linenos: + + + import numpy as np + import pandas as pd + from scipy.stats import norm # Used in generation of populations. + + np.random.seed(seed) # Fix the seed so the results are replicable. + # pop_size = 10000 # Size of each population. + + from scipy.stats import norm # Used in generation of populations. + + # Create samples + y = norm.rvs(loc=3, scale=0.4, size=N*4) + y[N:2*N] = y[N:2*N]+1 + y[2*N:3*N] = y[2*N:3*N]-0.5 + + # Add drug column + t1 = np.repeat('Placebo', N*2).tolist() + t2 = np.repeat('Drug', N*2).tolist() + treatment = t1 + t2 + + # Add a `rep` column as the first variable for the 2 replicates of experiments done + rep = [] + for i in range(N*2): + rep.append('Rep1') + rep.append('Rep2') + + # Add a `genotype` column as the second variable + wt = np.repeat('W', N).tolist() + mt = np.repeat('M', N).tolist() + wt2 = np.repeat('W', N).tolist() + mt2 = np.repeat('M', N).tolist() + + + genotype = wt + mt + wt2 + mt2 + + # Add an `id` column for paired data plotting. + id = list(range(0, N*2)) + id_col = id + id + + + # Combine all columns into a DataFrame. + df_delta2 = pd.DataFrame({'ID' : id_col, + 'Rep' : rep, + 'Genotype' : genotype, + 'Drug': treatment, + 'Y' : y + }) + +.. code-block:: python3 + :linenos: + + df_delta2.head() + +.. raw:: html + +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    IDRepGenotypeTreatmentY
    00Rep1WPlacebo2.793984
    11Rep2WPlacebo3.236759
    22Rep1WPlacebo3.019149
    33Rep2WPlacebo2.804638
    44Rep1WPlacebo2.858019
    +
    + +Unpaired Data +-------------- + +To make a delta-delta plot, you need to simply set ``delta2 = True`` in the +``dabest.load()`` function. However, here ``x`` needs to be declared as a list +consisting of 2 elements rather than 1 in most of the cases. The first element +in ``x`` will be the variable plotted along the horizontal axis, and the second +one will determine the colour of dots for scattered plots or the colour of lines +for slopegraphs. We use the ``experiment`` input to specify grouping of the data. + +.. code-block:: python3 + :linenos: + + unpaired_delta2 = dabest.load(data = df_delta2, x = ["Genotype", "Genotype"], y = "Y", delta2 = True, + experiment = "Drug") + +The above function creates the following object: + +.. code-block:: python3 + :linenos: + + unpaired_delta2 + +.. parsed-literal:: + + DABEST v2023.02.14 + ================ + + Good afternoon! + The current time is Mon Mar 6 16:18:39 2023. + + Effect size(s) with 95% confidence intervals will be computed for: + 1. M Placebo minus W Placebo + 2. M Drug minus W Drug + 3. Drug minus Placebo (only for mean difference) + + 5000 resamples will be used to generate the effect size bootstraps. + + +We can quickly check out the effect sizes: + +.. code-block:: python3 + :linenos: + + unpaired_delta2.mean_diff + +.. parsed-literal:: + + DABEST v2023.02.14 + ================ + + Good afternoon! + The current time is Mon Mar 6 16:18:22 2023. + + The unpaired mean difference between W Placebo and M Placebo is 1.23 [95%CI 0.948, 1.52]. + The p-value of the two-sided permutation t-test is 0.0, calculated for legacy purposes only. + + The unpaired mean difference between W Drug and M Drug is 0.326 [95%CI 0.0934, 0.584]. + The p-value of the two-sided permutation t-test is 0.0122, calculated for legacy purposes only. + + The delta-delta between Placebo and Drug is -0.903 [95%CI -1.26, -0.535]. + The p-value of the two-sided permutation t-test is 0.0, calculated for legacy purposes only. + + 5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated. + Any p-value reported is the probability of observing the effect size (or greater), + assuming the null hypothesis of zero difference is true. + For each p-value, 5000 reshuffles of the control and test labels were performed. + + To get the results of all valid statistical tests, use `.mean_diff.statistical_tests` + +.. code-block:: python3 + :linenos: + + unpaired_delta2.mean_diff.plot() + +.. image:: _images/tutorial_106_0.png + +In the above plot, the horizontal axis represents the ``Genotype`` condition +and the dot colour is also specified by ``Genotype``. The left pair of +scattered plots is based on the ``Placebo`` group while the right pair is based +on the ``Drug`` group. The bottom left axis contains the two primary deltas: the ``Placebo`` delta +and the ``Drug`` delta. We can easily see that when only the placebo was +administered, the mutant phenotype is around 1.23 [95%CI 0.948, 1.52]. This difference was shrunken to around 0.326 [95%CI 0.0934, 0.584] when the drug was administered. This gives us some indication that the drug is effective in amiliorating the disease phenotype. Since the ``Drug`` did not completely eliminate the mutant phenotype, we have to calculate how much net effect the drug had. This is where ``delta-delta`` comes in. We use the ``Placebo`` delta as a reference for how much the mutant phenotype is supposed to be, and we subtract the ``Drug`` delta from it. The bootstrapped mean differences (delta-delta) between the ``Placebo`` +and ``Drug`` group are plotted at the right bottom with a separate y-axis from other bootstrap plots. +This effect size, at about -0.903 [95%CI -1.26, -0.535], is the net effect size of the drug treatment. That is to say that treatment with drug A reduced disease phenotype by 0.903. + +.. math:: + + \hat{\theta}_{P} = \overline{X}_{P, M} - \overline{X}_{P, W} + + \hat{\theta}_{D} = \overline{X}_{D, M} - \overline{X}_{D, W} + +.. math:: + + + \hat{\theta}_{\theta} = \hat{\theta}_{D} - \hat{\theta}_{P} + +and: + +.. math:: + + s_{\theta} = \frac{(n_{P, M}-1)s_{P, M}^2+(n_{P, W}-1)s_{P, W}^2+(n_{D, M}-1)s_{D, M}^2+(n_{D, M}-1)s_{D, M}^2}{(n_{P, M} - 1) + (n_{P, W} - 1) + (n_{D, M} - 1) + (n_{D, M} - 1)} + + + +where :math:`\overline{X}` is the sample mean, :math:`\hat{\theta}` is the mean difference, :math:`s` is the variance and :math:`n` is the sample size. + + +In the example above, we used the convention of "test - control' but you can manipulate the orders of experiment groups as well as the horizontal axis variable by setting ``experiment_label`` and ``x1_level``. + +.. code-block:: python3 + :linenos: + + unpaired_delta2_specified = dabest.load(data = df_delta2, + x = ["Genotype", "Genotype"], y = "Y", + delta2 = True, experiment = "Treatment", + experiment_label = ["Drug", "Placebo"], + x1_level = ["M", "W"]) + + unpaired_delta2_specified.mean_diff.plot() + +.. image:: _images/tutorial_107_0.png + +Paired Data +----------- + +The delta - delta function also supports paired data, which is useful for us to visualise the data in an alternate way. Assuming that the placebo and drug treatment were done on the same subjects, our data is paired between the treatment conditions. We can specify this by using ``Treatment`` as ``x`` and ``Genotype`` as ``experiment``, and we further specify that ``id_col`` is ``ID``, linking data from the same subject with each other. Since we have done two replicates of the experiments, we can also colour the slope lines according to ``Rep``. + +.. code-block:: python3 + :linenos: + + paired_delta2 = dabest.load(data = df_delta2, + paired = "baseline", id_col="ID", + x = ["Treatment", "Rep"], y = "Y", + delta2 = True, experiment = "Genotype") + paired_delta2.mean_diff.plot() + +We produce the following plot: + +.. image:: _images/tutorial_108_0.png + +We see that the drug had a non-specific effect of -0.321 [95%CI -0.498, -0.131] on wildtype subjects even when they were not sick, and it had a bigger effect of -1.22 [95%CI -1.52, -0.906] in mutant subjects. In this visualisation, we can see the delta-delta value of -0.903 [95%CI -1.21, -0.587] as the net effect of the drug accounting for non-specific actions in healthy individuals. + +.. math:: + + \hat{\theta}_{W} = \overline{X}_{D, W} - \overline{X}_{P, W} + + \hat{\theta}_{W} = \overline{X}_{D, M} - \overline{X}_{P, M} + +.. math:: + + \hat{\theta}_{\theta} = \hat{\theta}_{M} - \hat{\theta}_{W} + +and: + +.. math:: + + s_{\theta} = \frac{(n_{D, W}-1)s_{D, W}^2+(n_{P, W}-1)s_{P, W}^2+(n_{D, M}-1)s_{D, M}^2+(n_{P, M}-1)s_{P, M}^2}{(n_{D, W} - 1) + (n_{P, W} - 1) + (n_{D, M} - 1) + (n_{P, M} - 1)} + + + +where :math:`\overline{X}` is the sample mean, :math:`\hat{\theta}` is the mean difference, :math:`s` is the variance and :math:`n` is the sample size. + + + +Connection to ANOVA +------------------- + +The configuration of comparison we performed above is reminiscent of a two-way ANOVA. In fact, the delta - delta is an effect size estimated for the interaction term between ``Treatment`` and ``Genotype``. Main effects of ``Treatment`` and ``Genotype``, on the other hand, can be determined by simpler, univariate contrast plots. + + + +Omitting Delta-delta Plot +------------------------- +If for some reason you don't want to display the delta-delta plot, you can easily do so by + +.. code-block:: python3 + :linenos: + + unpaired_delta2.mean_diff.plot(show_delta2=False) + +.. image:: _images/tutorial_109_0.png + + + +Other Effect Sizes +------------------ + +Since the delta-delta function is only applicable to mean differences, plots +of other effect sizes will not include a delta-delta bootstrap plot. + +.. code-block:: python3 + :linenos: + + unpaired_delta2.cohens_d.plot() + +.. image:: _images/tutorial_110_0.png + + +Statistics +------------------ + +You can find all outputs of the delta - delta calculation by assessing the attribute named ``delta_delta`` of the +effect size object. + +.. code-block:: python3 + :linenos: + + unpaired_delta2.mean_diff.delta_delta + +.. parsed-literal:: + + DABEST v2023.02.14 + ================ + + Good afternoon! + The current time is Mon Mar 6 15:50:44 2023. + + The delta-delta between Placebo and Treatment is -0.903 [95%CI -1.26, -0.535]. + The p-value of the two-sided permutation t-test is 0.0, calculated for legacy purposes only. + + 5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated. + Any p-value reported is the probability of observing the effect size (or greater), + assuming the null hypothesis of zero difference is true. + For each p-value, 5000 reshuffles of the control and test labels were performed. + + +``delta_delta`` has its own attributes, containing various information of delta - delta. + + - ``difference``: the mean bootstrapped differences between the 2 groups of bootstrapped mean differences + - ``bootstraps``: the 2 groups of bootstrapped mean differences + - ``bootstraps_delta_delta``: the bootstrapped differences between the 2 groups of bootstrapped mean differences + - ``permutations``: the mean difference between the two groups of bootstrapped mean differences calculated based on the permutation data + - ``permutations_var``: the pooled group variances of two groups of bootstrapped mean differences calculated based on permutation data + - ``permutations_delta_delta``: the delta-delta calculated based on the permutation data + +``delta_delta.to_dict()`` will return to you all the attributes in a dictionary format. diff --git a/docs/source/index.rst b/docs/source/index.rst index 18d9fc91..574db54f 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -82,6 +82,7 @@ Contents repeatedmeasures proportion-plot minimetadelta + deltadelta plotaesthetics release-notes api