Distinguishing bacterial and viral meningitis
Motivation
Meningitis is an inflammation of the meninges, the membranes surrounding the brain and spinal cord. It is often caused by infections with viruses or bacteria, and if left untreated, can cause serious harm to the brain and nervous system. Doctors hence treat it as an emergency and seek to immediately start treatment.
However, treating meningitis successfully requires knowing the cause of the infection. Bacterial meningitis, caused by infection with various kinds of bacteria, can be treated with appropriate antibiotics. But viral meningitis, which can be caused by several different kinds of virus, does not respond at all to antibiotics. It’s common to immediately give antibiotics so treatment can start before the cause is definitively known. Doctors then use a lumbar puncture to draw a sample of cerebrospinal fluid (CSF), the fluid surrounding the brain and spine, to test for signs of bacteria. There are several diagnostic signs:
- Gram staining: The sample is stained using crystal violet, which binds to the walls of some kinds of bacteria. They hence show up in bright violet under a microscope, demonstrating the presence of gram-positive bacteria. However, other kinds of bacteria (gram-negative bacteria) do not show up with this test, and it may be negative if the patient already received antibiotics.
- White blood cell count: White blood cells are the body’s immune cells. A high count indicates response to an infection. There are several kinds of white blood cell: Leukocytes suggest a viral infection, while neutrophil suggests a bacterial infection.
- Glucose level: The cerebrospinal fluid usually has a lower glucose level than the blood. In bacterial meningitis it drops even lower.
- Protein levels: Protein levels are typically higher in bacterial infections than viral.
These measurements are fairly fast and easy to get from a CSF sample, but are not definitive. To definitively show a bacterium is present, it must be cultured over several days, or antigens detected in a counterimmunoelectrophoresis test. To definitively prove viral meningitis, the virus must be isolated from blood, stool, or CSF samples, or all other causes must be ruled out. In either case, a definitive ruling takes much more time and effort, while a bacterial infection must be treated straight away. So can we accurately decide whether a patient has bacterial meningitis using just the fast and easy-to-obtain test results?
Data
The data comes from a retrospective observational study at Duke University Medical Center, using records for all patients with acute meningitis between January 1969 and July 1980. The researchers used laboratory records to determine which patients had bacterial or viral meningitis, and extracted initial test results from the patients’ charts. Patients had both blood tests and cerebrospinal fluid (CSF) tests. Most patients had tests conducted immediately upon admission, and some had a second set of tests later in their stay.
Many values are missing, as not every patient had every test conducted. Some variables are present in the data but not documented; these are marked “Unknown”. These undocumented variables were not used in the original published analysis of the data.
Data preview
meningitis.csv
Variable descriptions
| Variable | Description |
|---|---|
| casenum | Case number |
| year | Year of the case (two digits, such as 78 for 1978) |
| month | Month number |
| age | Age of the patient, years |
| race | Race of the patient (Black or White) |
| sex | Sex of the patient (male or female) |
| dx | Unknown |
| priordx | Unknown |
| priorrx | Whether patient received antibiotics prior to admission to the hospital (0 = no, 1 = yes) |
| wbc | White blood cell count per 1,000, in a blood sample |
| pmn | % polymorphonuclear leukocytes (PMNs) in blood |
| bands | Percentage of blood PMNs that are immature “band” forms |
| compns | Unknown |
| daysrx | Unknown |
| offrx | Unknown |
| lptodc | Unknown |
| lpgap | Hours between the first lumbar puncture and the second, if a second was conducted |
| morelabs | Unknown |
| bloodgl | Blood glucose level (mg/dL) |
| gl | CSF glucose level (mg/dL) |
| pr | CSF protein level (mg/dL) |
| reds | CSF red blood cell count (count per mm3) |
| whites | Total leukocytes (white blood cells) in CSF (count per mm3) |
| polys | % polymorphonuclear leukocytes (PMNs) in CSF |
| lymphs | Cerebrospinal fluid lymphocyte count (units not given) |
| monos | Unknown; possibly CSF monocyte percentage |
| others | Unknown; possibly percentage of other white blood cell types in CSF |
| gram | Gram smear result (0 = Gram-negative, positive values mean Gram-positive) |
| culture | Unknown |
| cie | Unknown; possibly the result of counterimmunoelectrophoresis (CIE) tests for presence of specific bacterial antigens, but coding is not clear |
| bloodclt | Unknown |
| bloodgl2 | Unknown; possibly blood glucose level at the time of the second lumbar puncture |
| gl2 | CSF glucose level in the second lumbar puncture |
| pr2 | CSF protein level in the second lumbar puncture |
| reds2 | CSF red blood cell count in the second lumbar puncture |
| whites2 | CSV white blood cell count in the second lumbar puncture |
| polys2 | % PMNs in the second lumbar puncture |
| lymphs2 | CSF lymphocyte count in the second lumbar puncture |
| monos2 | Unknown; possibly CSF monocyte percentage in the second lumbar puncture |
| others2 | Unknown; possibly percentage of other white blood cell types in the second lumbar puncture |
| sumbands | Unknown |
| subset | The original researchers divided the data into a training set and a test set; this gives the assignment of each case |
| abm | Whether the patient has acute bacterial meningitis (1) or viral meningitis (0), as ultimately determined by cultures and antigen tests |
Questions
The original researchers derived several features from the measurements given. Calculate these and add them to your data frame:
- The ratio of CSF to blood glucose levels. It is thought that the ratio is a better predictor than the CSF glucose level alone.
- Number of months from August. (For example, September and July are both 1 month from August.) Bacterial meningitis is most common in the winter and viral meningitis most common in the summer.
Conduct an exploratory data analysis. First, examine the amount of missingness of the key variables. Then construct plots to examine how each key variable, including the new ones you calculated, may be related to the response (whether the patient has bacterial meningitis). The researchers believe age may affect the diagnostic relationships, so compare relationships for patients under 21 and over 21.
As binary outcomes are hard to plot, it may help to divide the range of each predictor into bins, and plot the value against the fraction of cases in the bin that were bacterial. Comment on whether any predictors should be transformed, and the shape of the relationships between predictor and response.
Fit a logistic regression to predict whether the patient has bacterial meningitis, using blood and CSF test results plus the features you derived in step 1. Include age and determine whether the other relationships vary with age. Ensure you hold out a test set before conducting your analysis. Make any necessary transformations and use diagnostics to check the relationships. Try to reduce your model: Are the calculated features more important than the raw test results? What is the simplest model you can construct that is an accurate predictor?
Evaluate your model on the test set and report its performance. Show a confusion matrix.
References
Spanos, Harrell, and Durack (1989). “Differential Diagnosis of Acute Meningitis: An Analysis of the Predictive Value of Initial Observations.” JAMA 262 (19), 2700-2707. https://doi.org/10.1001/jama.1989.03430190084036
Data obtained from https://hbiostat.org/data/ courtesy of the Vanderbilt University Department of Biostatistics.