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CM6.1-6 | Biostatistics for Community Medicine — PBL Case

CLINICAL SETTING

Dr. Priya Menon has just completed her Community Medicine posting at the Community Health Centre in Bagalkot, Karnataka, and is preparing her field report. Her supervisor, Dr. Ramesh, gives her a summary sheet from the Block Medical Officer's desk — a comparison of malaria incidence rates between two adjoining blocks (Block A and Block B) for the past year. The report states: 'Block A has more malaria cases (480 cases) than Block B (310 cases); therefore Block A receives priority vector control funding this year.' Dr. Priya is puzzled. She remembers from her SDL that raw case counts alone don't tell the whole story. She decides to dig deeper before submitting her report.

Trigger 1: The Denominator Problem

Dr. Priya finds the population denominators: Block A has 96,000 residents; Block B has 31,000 residents. She calculates the malaria incidence rates. Block A rate = 480/96,000 × 1,000 = 5 per 1,000. Block B rate = 310/31,000 × 1,000 = 10 per 1,000. The incidence rate in Block B is actually DOUBLE that of Block A — yet Block B was ranked lower priority based on raw counts.

DISCUSSION POINTS

  • Why do raw case counts mislead when comparing two populations of different sizes? What is the correct measure to use, and why?
  • Define 'incidence rate' and 'incidence proportion' (attack rate). In which situations would each be used in community medicine practice?
  • The BMO argues that Block A 'has more cases to treat' and therefore deserves more resources. Construct a counter-argument using the incidence rate data. Who do you think is right, and why?
  • What type of data is 'number of malaria cases'? What type is 'malaria incidence rate'? Does this distinction matter for further statistical analysis?
Click to reveal Trigger 2: Testing the Difference (discuss previous trigger first!)

Trigger 2: Testing the Difference

Dr. Priya wants to know whether the difference in malaria incidence between blocks is statistically significant or could have occurred by chance. She constructs a 2×2 table from 200 randomly sampled individuals from each block (simple random sample, confirmed): Block A: Malaria positive 10, Malaria negative 190. Block B: Malaria positive 20, Malaria negative 180. She plans to apply the chi-square test. Her senior colleague Dr. Arun suggests she should also check whether any expected cell frequencies are below 5 before proceeding.

DISCUSSION POINTS

  • State the null and alternative hypotheses for comparing malaria incidence proportions between the two blocks.
  • Calculate the expected frequencies for each cell in the 2×2 table (row total × column total / grand total). Are the conditions for chi-square met?
  • The chi-square test gives χ² = 3.88, p = 0.049. What do you conclude? Is the result statistically significant? Is it clinically significant?
  • Dr. Arun notices one expected frequency is exactly 4.8 (just below 5). Should Fisher's exact test be used instead? What is the threshold, and how does Fisher's exact test differ from chi-square?
Click to reveal Trigger 3: Making Sense for the Policymaker (discuss previous trigger first!)

Trigger 3: Making Sense for the Policymaker

Dr. Priya must now present findings to the District Health Society. She has the following: Block A incidence rate = 5/1,000; Block B incidence rate = 10/1,000; chi-square p = 0.049; 95% CI for the rate difference: (0.02, 9.98) per 1,000. She also has Block C incidence data (rate = 7/1,000, sample n = 200) and the BMO now wants to compare all three blocks simultaneously. Her supervisor reminds her: 'A p-value alone is never enough for a health policy decision.'

DISCUSSION POINTS

  • Interpret the 95% CI (0.02 to 9.98 per 1,000) for the Block A–B rate difference. Does it exclude zero? What does the width of this CI tell you about the precision of the estimate?
  • The BMO suggests three separate chi-square tests to compare Block A vs B, A vs C, and B vs C. Explain the statistical problem with this approach (Type I error inflation) and recommend the correct approach.
  • Write a two-sentence plain-language summary of the findings for inclusion in the District Health Society minutes. This summary must be understood by a non-statistician administrator.
  • Beyond statistical significance, what contextual factors (e.g., local rainfall, vector density, healthcare access) would you consider before recommending resource reallocation from Block A to Block B?

Group Task Assignments

Group 1: Research Question Formulation and Data Types

  • Draft a SMART research question for Dr. Priya's comparison study using the PICO framework (Population, Intervention/Exposure, Comparison, Outcome).
  • Classify all variables in the scenario (number of cases, incidence rate, block type, immunisation status) by scale of measurement and justify each classification.

Competencies: CM6.1, CM6.2

Group 2: Rates, Ratios and Measures of Disease Frequency

  • Calculate and compare malaria incidence rates for both blocks. Explain to the group why rates are more informative than raw counts for inter-population comparison.
  • Define incidence rate, prevalence rate, and attack rate. Give one example of each from community medicine practice.

Competencies: CM6.2, CM6.4

Group 3: Statistical Test Selection and Chi-Square Analysis

  • Apply the test-selection decision algorithm to the Block A vs Block B comparison: data type → number of groups → independent or paired → parametric or non-parametric.
  • Set up the 2×2 table, calculate expected frequencies, and verify chi-square assumptions. Determine whether Fisher's exact test is warranted and justify the decision.

Competencies: CM6.3

Group 4: p-value, CI, and Statistical Software Output

  • Interpret the chi-square output (p = 0.049) and the 95% CI (0.02, 9.98 per 1,000). Explain the distinction between statistical significance and clinical/public health significance.
  • Demonstrate how SPSS or any statistical software would present the chi-square output for this 2×2 table (describe the output table, not the computation).

Competencies: CM6.3, CM6.5

Group 5: Descriptive Statistics and Policy Communication

  • Prepare a descriptive summary table for the District Health Society: present incidence rates with 95% CIs for all three blocks, labelled clearly.
  • Draft the plain-language policy recommendation. Discuss what additional non-statistical information the health society should consider before reallocating funds.

Competencies: CM6.6, CM6.5

Learning Issues

Research these questions and bring your findings to the discussion.

  1. [CM6.1] How is a research question formulated using the PICO framework? What makes a research question SMART?
  2. [CM6.2] What is the difference between a rate, a ratio, and a proportion? When is each measure of disease frequency used in community medicine?
  3. [CM6.3] What is the step-by-step decision algorithm for selecting the correct statistical test? When is Fisher's exact test used instead of chi-square?
  4. [CM6.4] What are the assumptions underlying chi-square? How do you calculate expected frequencies in a 2×2 contingency table?
  5. [CM6.5] How do you read and interpret a chi-square output from statistical software (SPSS)? What does each column in the output mean?
  6. [CM6.6] How is a 95% CI for a rate difference interpreted? What does a wide CI imply about precision? When is statistical significance insufficient for a policy decision?