Add an example comparing mega- and meta-analysis

examples/02_meta-analysis/plot_compare_mega_and_meta-analysis.py

@@ -0,0 +1,166 @@
+# emacs: -*- mode: python-mode; py-indent-offset: 4; tab-width: 4; indent-tabs-mode: nil -*-
+# ex: set sts=4 ts=4 sw=4 et:
+"""
+.. _meta3:
+
+================================================
+ Run mega- and meta-analysis
+================================================
+
+Steps:
+
+1.  Make a toy dataset
+2.  Run mega-analysis (linear mixed effects model with random intercepts for study)
+3.  Group dataset by study and run OLS on each study separately to construct meta-analysis dataset
+4.  Run meta-analysis with DerSimonian-Laird between-study variance estimator
+"""
+from pprint import pprint
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+import seaborn as sns
+import statsmodels.api as sm
+
+from pymare import Dataset
+from pymare.estimators import DerSimonianLaird
+
+sns.set_theme(style="ticks")
+
+###############################################################################
+# Wrangle some example data
+# -----------------------------------------------------------------------------
+# For this example, we will use the "American National Election Survey 1996"
+# dataset from statsmodels.
+# This dataset includes several elements we care about, including:
+#
+# 1. A large number of observations (944).
+# 2. A variable that can be used as a substitute for "study".
+#    In this case, we will pretend that all observations with similar
+#    populations come from the same cities, which we will in turn pretend
+#    reflect different studies of the same phenomenon by different research
+#    groups.
+data = sm.datasets.anes96.load_pandas().data
+data.head(10)
+
+###############################################################################
+# Convert the populations to "studies" by binning similar populations and
+# assigning them to the same "study" values.
+
+# I selected the first study with a first author starting with each letter from Neurosynth.
+# I figured it would give the dataset some verisimilitude.
+study_names = [
+    "Aarts & Roelofs (2011)",
+    "Baas et al. (2008)",
+    "Cabanis et al. (2013)",
+    "D'Agata et al. (2011)",
+    "Eack et al. (2008)",
+    "Fabbri, Caramazza, & Lingnau (2012)",
+    "Gaab, Gabrieli, & Glover (2007)",
+    "Haag et al. (2014)",
+]
+
+data = data.sort_values(by="popul")
+group_assignments = []
+split_assignments = np.array_split(np.arange(data.shape[0], dtype=int), 8)
+for i_split, split in enumerate(split_assignments):
+    group_assignments += [study_names[i_split]] * len(split)
+
+data["study"] = group_assignments
+data.head(10)
+
+###############################################################################
+fig, ax = plt.subplots(figsize=(16, 8))
+sns.stripplot(data=data, x="logpopul", y="study", ax=ax)
+fig.tight_layout()
+fig.show()
+
+###############################################################################
+# The variables of interest
+# -----------------------------------------------------------------------------
+# First, let's talk about the variables of interest in this analysis.
+# The variables are:
+#
+# 1. TVnews: The number of times, per week, that the respondent watches the news on TV.
+# 2. age: The age of the respondent, in years.
+# 3. educ: The education of the respondent, binned into the following groups:
+#    (1) Grade 1-8, (2) Some high school, (3) High school graduate, (4) Some college,
+#    (5) College graduate, (6) Master's degree, and (7) PhD.
+#    We will evaluate linear relationships with this coded variable, which isn't
+#    optimal, but this is just an example, so... ¯\\_(ツ)_/¯
+#
+# If we visualize the distributions of the different variables, we'll see that
+# they're not exactly normally distributed...
+sns.pairplot(data[["study", "TVnews", "age", "educ"]], hue="study")
+
+###############################################################################
+# The mega-analysis
+# -----------------------------------------------------------------------------
+# Random intercepts model using study.
+# In this model, we test the question, "to what extent do age and education
+# predict TV news watching?"
+#
+# We assume that data from the same study may have different baseline news-watching levels
+# (i.e., random intercepts).
+#
+# Do age and education predict TV news watching?
+model = sm.MixedLM.from_formula("TVnews ~ age + educ", data, groups=data["study"])
+fitted_model = model.fit()
+print(fitted_model.summary())
+
+###############################################################################
+# Create the meta-analysis dataset
+# -----------------------------------
+# We assume that each study performed their own analyses testing the same hypothesis.
+# The hypothesis, in this case, is "to what extent do age and education predict TV news watching"?
+#
+# The model used will, for our example, be exactly the same across studies.
+# This model is just a GLM with age, education, and an intercept predicting the number of hours.
+# Individual studies would then report the parameter estimate and variance for each term in the
+# model.
+data["intercept"] = 1
+target_vars = ["educ", "age", "intercept"]
+
+# calculate coefficient and variance for each variable of interest
+meta_df = []
+for study_name, study_df in data.groupby("study"):
+    model = sm.OLS(study_df["TVnews"], study_df[target_vars])
+    fitted_model = model.fit()
+
+    # extract parameter estimates and errors as Series
+    coefficients = fitted_model.params
+    std_errors = fitted_model.bse
+
+    # convert standard error to sampling variance
+    sampling_variances = std_errors ** 2
+    names = [n + "_var" for n in sampling_variances.index.tolist()]
+    sampling_variances.index = names
+
+    # combine Series and convert to DataFrame
+    coefficients = coefficients.append(sampling_variances)
+    coefficients["study"] = study_name
+    coefficients["sample_size"] = study_df.shape[0]
+    temp_df = pd.DataFrame(coefficients).T
+    meta_df.append(temp_df)
+
+# Combine across studies and convert objects to floats
+meta_df = pd.concat(meta_df).reset_index(drop=True)
+meta_df = meta_df.convert_dtypes()
+meta_df
+
+###############################################################################
+# The meta-analysis
+# --------------------------------------------
+# Are age and education significant predictors of TV news watching across the literature?
+metamodel = DerSimonianLaird()
+dset = Dataset(
+    y=meta_df[["age", "educ"]].values.astype(float),
+    v=meta_df[["age_var", "educ_var"]].values.astype(float),
+    add_intercept=True,
+)
+metamodel.fit_dataset(dset)
+
+###############################################################################
+summary = metamodel.summary()
+results = summary.get_fe_stats()
+pprint(results)

setup.cfg

@@ -60,6 +60,7 @@ doc =
     sphinx_gallery==0.10.1
     sphinx_rtd_theme
     sphinxcontrib-bibtex
+    statsmodels
 tests =
     codecov
     coverage