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 Programming with Python: Analyzing Patient Data

Analyzing Patient Data

Overview

Teaching: 30 min
Exercises: 0 min
Questions
• How can I process tabular data files in Python?

Objectives
• Explain what a library is, and what libraries are used for.

• Import a Python library and use the functions it contains.

• Read tabular data from a file into a program.

• Assign values to variables.

• Select individual values and subsections from data.

• Perform operations on arrays of data.

• Plot simple graphs from data.

In this lesson we will learn how to manipulate the inflammation dataset with Python. But before we discuss how to deal with many data points, we will show how to store a single value on the computer.

The line below assigns the value 55 to a variable weight_kg:

weight_kg = 55

A variable is just a name for a value, such as x_val, current_temperature, or subject_id. Python’s variables must begin with a letter and are case sensitive. We can create a new variable by assigning a value to it using =. When we are finished typing and press Shift+Enter, the notebook runs our command.

Once a variable has a value, we can print it to the screen:

print(weight_kg)
55

and do arithmetic with it:

print('weight in pounds:', 2.2 * weight_kg)
weight in pounds: 121.0

As the example above shows, we can print several things at once by separating them with commas.

We can also change a variable’s value by assigning it a new one:

weight_kg = 57.5
print('weight in kilograms is now:', weight_kg)
weight in kilograms is now: 57.5

If we imagine the variable as a sticky note with a name written on it, assignment is like putting the sticky note on a particular value:

This means that assigning a value to one variable does not change the values of other variables. For example, let’s store the subject’s weight in pounds in a variable:

weight_lb = 2.2 * weight_kg
print('weight in kilograms:', weight_kg, 'and in pounds:', weight_lb)
weight in kilograms: 57.5 and in pounds: 126.5

and then change weight_kg:

weight_kg = 100.0
print('weight in kilograms is now:', weight_kg, 'and weight in pounds is still:', weight_lb)
weight in kilograms is now: 100.0 and weight in pounds is still: 126.5

Since weight_lb doesn’t “remember” where its value came from, it isn’t automatically updated when weight_kg changes. This is different from the way spreadsheets work.

Who’s Who in Memory

You can use the %whos command at any time to see what variables you have created and what modules you have loaded into the computer’s memory. As this is an IPython command, it will only work if you are in an IPython terminal or the Jupyter Notebook.

%whos
Variable    Type       Data/Info
--------------------------------
numpy       module     <module 'numpy' from '/Us<...>kages/numpy/__init__.py'>
weight_kg   float      100.0
weight_lb   float      126.5

Words are useful, but what’s more useful are the sentences and stories we build with them. Similarly, while a lot of powerful, general tools are built into languages like Python, specialized tools built up from these basic units live in libraries that can be called upon when needed.

In order to load our inflammation data, we need to access (import in Python terminology) a library called NumPy. In general you should use this library if you want to do fancy things with numbers, especially if you have matrices or arrays. We can import NumPy using:

import numpy

Importing a library is like getting a piece of lab equipment out of a storage locker and setting it up on the bench. Libraries provide additional functionality to the basic Python package, much like a new piece of equipment adds functionality to a lab space. Just like in the lab, importing too many libraries can sometimes complicate and slow down your programs - so we only import what we need for each program. Once we’ve imported the library, we can ask the library to read our data file for us:

array([[ 0.,  0.,  1., ...,  3.,  0.,  0.],
[ 0.,  1.,  2., ...,  1.,  0.,  1.],
[ 0.,  1.,  1., ...,  2.,  1.,  1.],
...,
[ 0.,  1.,  1., ...,  1.,  1.,  1.],
[ 0.,  0.,  0., ...,  0.,  2.,  0.],
[ 0.,  0.,  1., ...,  1.,  1.,  0.]])

The expression numpy.loadtxt(...) is a function call that asks Python to run the function loadtxt which belongs to the numpy library. This dotted notation is used everywhere in Python to refer to the parts of things as thing.component.

numpy.loadtxt has two parameters: the name of the file we want to read, and the delimiter that separates values on a line. These both need to be character strings (or strings for short), so we put them in quotes.

Since we haven’t told it to do anything else with the function’s output, the notebook displays it. In this case, that output is the data we just loaded. By default, only a few rows and columns are shown (with ... to omit elements when displaying big arrays). To save space, Python displays numbers as 1. instead of 1.0 when there’s nothing interesting after the decimal point.

Our call to numpy.loadtxt read our file, but didn’t save the data in memory. To do that, we need to assign the array to a variable. Just as we can assign a single value to a variable, we can also assign an array of values to a variable using the same syntax. Let’s re-run numpy.loadtxt and save its result:

This statement doesn’t produce any output because assignment doesn’t display anything. If we want to check that our data has been loaded, we can print the variable’s value:

print(data)
[[ 0.  0.  1. ...,  3.  0.  0.]
[ 0.  1.  2. ...,  1.  0.  1.]
[ 0.  1.  1. ...,  2.  1.  1.]
...,
[ 0.  1.  1. ...,  1.  1.  1.]
[ 0.  0.  0. ...,  0.  2.  0.]
[ 0.  0.  1. ...,  1.  1.  0.]]

Now that our data is in memory, we can start doing things with it. First, let’s ask what type of thing data refers to:

print(type(data))
<class 'numpy.ndarray'>

The output tells us that data currently refers to an N-dimensional array created by the NumPy library. These data correspond to arthritis patients’ inflammation. The rows are the individual patients and the columns are their daily inflammation measurements.

Data Type

A Numpy array contains one or more elements of the same type. type will only tell you that a variable is a NumPy array. We can also find out the type of the data contained in the NumPy array.

print(data.dtype)
dtype('float64')

This tells us that the NumPy array’s elements are floating-point numbers.

With this command we can see the array’s shape:

print(data.shape)
(60, 40)

This tells us that data has 60 rows and 40 columns. When we created the variable data to store our arthritis data, we didn’t just create the array, we also created information about the array, called members or attributes. This extra information describes data in the same way an adjective describes a noun. data.shape is an attribute of data which describes the dimensions of data. We use the same dotted notation for the attributes of variables that we use for the functions in libraries because they have the same part-and-whole relationship.

If we want to get a single number from the array, we must provide an index in square brackets, just as we do in math when referring to an element of a matrix. Our inflammation data has two dimensions, so we will need to use two indices to refer to a value:

print('first value in data:', data[0, 0])
first value in data: 0.0
print('middle value in data:', data[30, 20])
middle value in data: 13.0

The expression data[30, 20] may not surprise you, but data[0, 0] might. Programming languages like Fortran, MATLAB and R start counting at 1, because that’s what human beings have done for thousands of years. Languages in the C family (including C++, Java, Perl, and Python) count from 0 because it represents an offset from the first value in the array (the second value is offset by one index from the first value). This is closer to the way that computers represent arrays (if you are interested in the historical reasons behind counting indices from zero, you can read Mike Hoye’s blog post). As a result, if we have an M×N array in Python, its indices go from 0 to M-1 on the first axis and 0 to N-1 on the second. It takes a bit of getting used to, but one way to remember the rule is that the index is how many steps we have to take from the start to get the item we want.

In the Corner

What may also surprise you is that when Python displays an array, it shows the element with index [0, 0] in the upper left corner rather than the lower left. This is consistent with the way mathematicians draw matrices, but different from the Cartesian coordinates. The indices are (row, column) instead of (column, row) for the same reason, which can be confusing when plotting data.

An index like [30, 20] selects a single element of an array, but we can select whole sections as well. For example, we can select the first ten days (columns) of values for the first four patients (rows) like this:

print(data[0:4, 0:10])
[[ 0.  0.  1.  3.  1.  2.  4.  7.  8.  3.]
[ 0.  1.  2.  1.  2.  1.  3.  2.  2.  6.]
[ 0.  1.  1.  3.  3.  2.  6.  2.  5.  9.]
[ 0.  0.  2.  0.  4.  2.  2.  1.  6.  7.]]

The slice 0:4 means, “Start at index 0 and go up to, but not including, index 4.” Again, the up-to-but-not-including takes a bit of getting used to, but the rule is that the difference between the upper and lower bounds is the number of values in the slice.

We don’t have to start slices at 0:

print(data[5:10, 0:10])
[[ 0.  0.  1.  2.  2.  4.  2.  1.  6.  4.]
[ 0.  0.  2.  2.  4.  2.  2.  5.  5.  8.]
[ 0.  0.  1.  2.  3.  1.  2.  3.  5.  3.]
[ 0.  0.  0.  3.  1.  5.  6.  5.  5.  8.]
[ 0.  1.  1.  2.  1.  3.  5.  3.  5.  8.]]

We also don’t have to include the upper and lower bound on the slice. If we don’t include the lower bound, Python uses 0 by default; if we don’t include the upper, the slice runs to the end of the axis, and if we don’t include either (i.e., if we just use ‘:’ on its own), the slice includes everything:

small = data[:3, 36:]
print('small is:')
print(small)
small is:
[[ 2.  3.  0.  0.]
[ 1.  1.  0.  1.]
[ 2.  2.  1.  1.]]

Arrays also know how to perform common mathematical operations on their values. The simplest operations with data are arithmetic: add, subtract, multiply, and divide. When you do such operations on arrays, the operation is done on each individual element of the array. Thus:

doubledata = data * 2.0

will create a new array doubledata whose elements have the value of two times the value of the corresponding elements in data:

print('original:')
print(data[:3, 36:])
print('doubledata:')
print(doubledata[:3, 36:])
original:
[[ 2.  3.  0.  0.]
[ 1.  1.  0.  1.]
[ 2.  2.  1.  1.]]
doubledata:
[[ 4.  6.  0.  0.]
[ 2.  2.  0.  2.]
[ 4.  4.  2.  2.]]

If, instead of taking an array and doing arithmetic with a single value (as above) you did the arithmetic operation with another array of the same shape, the operation will be done on corresponding elements of the two arrays. Thus:

tripledata = doubledata + data

will give you an array where tripledata[0,0] will equal doubledata[0,0] plus data[0,0], and so on for all other elements of the arrays.

print('tripledata:')
print(tripledata[:3, 36:])
tripledata:
[[ 6.  9.  0.  0.]
[ 3.  3.  0.  3.]
[ 6.  6.  3.  3.]]

Often, we want to do more than add, subtract, multiply, and divide values of data. NumPy knows how to do more complex operations on arrays. If we want to find the average inflammation for all patients on all days, for example, we can ask NumPy to compute data’s mean value:

print(numpy.mean(data))
6.14875

mean is a function that takes an array as an argument. If variables are nouns, functions are verbs: they do things with variables.

Not All Functions Have Input