Why nursing students should understand statistics. Objectives of lecture. Why Statistics? Not to put students off statistics!

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1 Why nursing students should understand statistics Objectives of lecture Not to put students off statistics! Review methods of displaying and summarizing data. Review basic statistical concepts used in analyzing data Why Statistics? Medicine is a quantitative science but not exact Statistics is about handling and quantifying variation and uncertainty

2 Variation Humans differ in response to exposure to adverse effects Humans differ in response to treatment Humans differ in disease symptoms Diagnosis and treatment is often probabilistically based Summary statistics All nurses need to be able to summarize results and to interpret summaries All nurses need to be able to display data Nominal Categorical Ordinal Interval Ratio Types of data The type of data available drives the statistics that are available

3 Recent examples from the news Recently a surgeon had a mortality of 60% for a heart operation in children less than one year old. Would you sack him? No! Need to know what rate to expect. Example: rate by other surgeons doing comparable operations Surgeon continued Nationally the mortality rate for this operation in this age group was 16/123 = 13% Would you sack him now? No! He may be unlucky. He may be operating on more severe cases He may only have done a few operations. For example 2/3 is 66%. Surgeon (3) In fact no evidence babies were more ill. The surgeon operated on 15 babies of whom 9 died (60%). The 95% confidence interval for the national rate (13%) is (11%, 36%). Would you now sack him? Yes!

4 Example (Swinscow, 1996) Type of vaccine Got Avoided Total Influenza Influenza I (new vaccine) 43(A) 237 (B) 280 II (Control) 52 (C) 198 (D) 250 Nominal data displayed using a barchart Display percentages Always give sample sizes Avoid pie-charts Avoid 3-d barcharts Barchart showing infection rates for two vaccines 25Infection rate (%) Vaccine I (n=280) Vaccine II (n=250)

5 Risk RISK Number of subjects in a group who have an event divided by total number of subjects in the group. It is the probability of (proportion) having an event in that group (P). It is called incidence when expressed per unit time A/(A+B)= P 1 RELATIVE RISK (RR) Ratio of risk in exposed group to risk in not exposed group (P 1 /P 2 ) Example Type of vaccine Got Avoided Total Influenza Influenza I II (Control) Risk of disease in Vaccine Group I = 43/280=0.154 Risk of disease in Vaccine Group II=52/250=0.208 Relative Risk (Risk Ratio) =0.154/0.208 =0.74 Odds ODDS Probability of developing disease divided by probability of not developing disease. P/ (1-P) Often expressed as number of times something expected not to happen: number of times something expected to happen. ODDS RATIO (OR) Ratio of odds for exposed group divided by odds for not exposed group. {P 1 /(1-P 1 )}/{P 2 /(1-P 2 )} Odds ratios are treated as relative risks, especially when events are rare, and emerge naturally in some types of studies (case-control studies) Logistic Regression (a multivariate type of analysis when the dependent variable is nominal) calculates odds ratios

6 Example Odds of disease in Vaccine Group I = 0.154/( )=0.182 Odds of disease in Vaccine Group II= 0.208/( )=0.263 Odds ratio of getting disease in Group I relative to Group II=0.182/0.263=0.69 (close to relative risk of 0.74) Absolute risk reduction Absolute risk reduction (ARR) Risk in treated group minus risk in control group ARR=p 1 -p 2 Number need to treat=1/arr This is the number you would need to treat under each of two treatments to get one extra person cured under the new treatment Example Absolute risk reduction for vaccine I= =0.054 NNT=1/0.054=18.5 Thus on average one would have to give vaccine I to 19 patients to expect one extra patient is being protected from influenza compared with vaccine II.

7 Contraceptive Pill Scare (October 1995) Committee on Safety of Medicine issued warning of association between 3rd generation contraceptive pill and deep vein thrombosis Relative risk of 2 widely reported Women advised to discuss risks with GP at time of next prescription Story leaked to the press before doctors could be properly informed Contraceptive Pill Scare CSM warning based on the following results: 30 cases DVT per 100,000 users per year 3rd gen. pill 15 cases per 100,000 users per year 2nd gen. pill Thus Relative Risk 3rd gen. to 2nd gen. = 2 However: Absolute risk reduction = 15 per 100,000 Thus Number needed to get one extra DVT on 3rd gen. = 6700 women years. Note also: 5 cases per 100,000 per year non-users 80 cases per 100,000 per year for pregnant women Mortality from DVT ~ 1-2% Contraceptive Pill Scare (October 1995) Advice to consult GP misunderstood Many women stopped taking the pill immediately or did not finish course Increase in unwanted pregnancies Increase in abortion

8 Legal abortions performed per quarter, Number of legal abortions 49,000 47,000 45,000 43,000 41,000 39,000 37,000 35,000 Pill scare Conclusions Due to a misunderstanding of risk, many women came off pill Many subsequently got pregnant and had an abortion Risks due to pregnancy and abortion far exceed those due to 3rd generation contraceptive pill Why should nursing students understand statistics? It will help in other courses Ultimately, patients will benefit

9 Normally Distributed Ordinal or higher level Data Testing for differences between groups Dependent variable is what type of variable? Chi square P-value T-test, ANOVA Level of significance P-value or Confidence Interval Group Statistics Gend N Std. Error Mean d. Deviatio Mean Current S Fema Male 216 6,031.92, $ ,441.78, , Independent Samples Test Levene's Test for quality of Variance t-test for Equality of Means % Confidence Interva Mean Std. Error the Difference F Sig. t df Sig. (2-tailedDifferenceDifference Lower Upper Current SaEqual varian assumed $15,409.86, , Equal varian not assumed $15,409.86, ,

10 Correlation/regression To look for association To predict Scores on Two Tests Test 1 Test 2 Student Student Student Student Student Plot of scores 100 Correlation of Test Scores 90 Test Test 1

11 Relationships Perfect positive relationship is When you know the score of one variable, you will also know the score of the second variable Educational Level (years) Current Salary A correlation matrix Correlations Beginning Salary Beginning Salary Pearson Correlatio Sig. (2-tailed) N Current Salary Pearson Correlatio Sig. (2-tailed) N Educational Level (yea Pearson Correlatio Sig. (2-tailed) N **. Correlation is significant at the 0.01 level (2-tailed). Educational Current Salary Level (years) 1.880**.633** ** 1.661** **.661**

12 Strength of Relationship When r is: little if any low moderate high very high Types of Relationships The graph of the relationship between two variables may result in: No correlation Curvilinear relationship Positive correlation Negative correlation