PHM102 Basic statistics for public health and policy FORMATIVE ASSIGNMENT Write (preferably type*) answers to BOTH parts of this assignment. Show your working and give reasons for your answers. *See Hint for typing mathematical work at the end of the assignment. Part 1 Do not attempt this part before completing session BS06 of the computer-aided learning (CD) material. This part of the assignment is designed primarily to give you practice in applying some statistical methods using your calculator (as you might have to, for example, in an exam), and to express your interpretation of results in writing. Thus we advise you not to use STATA, or to use it only to check your calculator work. We also encourage you to make reference to the formula sheet at the end of the Workbook. 1. In a study of patients with Hodgkin s or non-hodgkin s Lymphoma, data were collected on T4 cell counts (in cells/mm 3 ). There were 20 patients in each group, and NO PAIRING between the groups. The data for each of the 40 patients are given below: Summary: Hodgkin s Non-Hodgkin s 396 375 568 375 1212 752 171 208 554 151 1104 116 257 736 435 192 295 315 397 1252 288 675 1004 700 431 440 795 771 1621 688 1378 426 902 410 958 979 1283 377 2415 503 Hodgkin s Non-Hodgkin s Mean 823.2 522.1 Median 681.5 433 Standard Deviation 566.4 293.0 1.1 Compute the 95% confidence intervals for the mean level of T4 counts in each of the 2 groups separately. Interpret your results. 1
Number of Patients 0 2 4 6 Number of Patients 0 1 2 3 4 5 1.2 Perform a test of the null hypothesis that there is no difference between mean count in patients with Hodgkins and non-hodgkins Lymphoma, and obtain a 95% confidence interval for the difference in mean T4 counts between the 2 groups. Interpret your results. 1.3 The data for the 2 illness groups are summarised in the histograms below. What can you say about the shapes of the distributions for Hodgkin s and non-hodgkin s patients? How is this related to the medians and means in the table above? Distribution of T4 count (cells/mm3) among 20 patients with Hodgkin's Disease 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 T4 count (cells/mm3) Distribution of T4 count (cells/mm3) among 20 patients with non-hodgkin's disease 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 T4 count (cells/mm3) 1.4 You are concerned that it may be inappropriate after all to apply a significance test to the raw data, because of observations made about the distribution of the data in Q3. What are your concerns specifically? What can be done about this?
1.5 The data were input into STATA as one variable (column) of T4 counts, and one variable indicating which disease the patient had (1=hodgkins, 0=non-hodgkins). A variable logt4 was created using gen logt4=log(t4). The ttest command was then used to carry out a test on the log-transformed data, with output:. ttest logt4, by(disease) Two-sample t test with equal variances ------------------------------------------------------------------------- Group Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+--------------------------------------------------------------- 0 20 6.486932.1583811.7083018 6.155437 6.818427 1 20 6.08864.1412261.6315823 5.79305 6.38423 ---------+--------------------------------------------------------------- combined 40 6.287786.1094787.6924044 6.066344 6.509228 ---------+--------------------------------------------------------------- diff.3982919.2122013 -.0312871.8278709 ------------------------------------------------------------------------- diff = mean(0) - mean(1) t = 1.8770 Ho: diff = 0 degrees of freedom = 38 Ha: diff < 0 Ha: diff!= 0 Ha: diff > 0 Pr(T < t) = 0.9659 Pr( T > t ) = 0.0682 Pr(T > t) = 0.0341 How does the result of this test (the p-value) compare with that from the un-logged data? Part 2 Do not attempt before completing session BS08 of the computer-aided learning (CD) material. This part of the assignment has two sub-parts. In the first sub-part (2.1), you will undertake a significance test and calculate a confidence interval from data on proportions, using your calculator to do the calculations. In the second sub-part (2.2), you will be asked to interpret presentations of statistical data on proportions. 2.1 Peppermint Eases Pain? The following report appeared in a popular magazine: PEPPERMINT EASES PAIN Peppermint oil has for a long time been known to help relieve indigestion. Now, doctors at two Danish hospitals have carried out a joint clinical trial using Peppermint Oil Capsules on patients with irritable bowel syndrome (IBS) - an uncomfortable, often chronic, condition where the bowel goes into spasm, which can cause a combination of pain, wind, constipation and/or diarrhoea. They found that out of 19 sufferers given peppermint oil, 13 found relief compared to only 6 from the other group of 23 patients who were not given the oil. Peppermint oil appears to have a relaxing effect on the bowel spasms which cause the symptoms.
a) Carry out a test of statistical significance to examine the strength of evidence for a difference in the proportion getting relief between those given peppermint oil and those not given the oil. (If you find this question difficult to start, there is a hint at the end of this assignment.) b) Calculate and interpret in a sentence a 95% confidence interval for the difference in proportions. c) Do you think that the study provides convincing evidence that peppermint oil gives relief from IBS pain? 2.2 Diabetes in pregnancy A randomized control trial was carried out to compare twice versus four times daily insulin for diabetes in pregnancy (Nachum Z et al., BMJ 1999;319:1223-7). Some of the results are given in Table 1, which is on the next page. Take a few minutes to get a sense of the structure of the table - what the columns and rows represent. Focusing on the patients with gestational diabetes (first three columns), and without doing any calculations, answer the following questions, with reason(s): a) How big was the difference in percentage with adequate glycaemic control between the Insulin twice daily and Insulin four times daily groups? b) How strong is the evidence that this difference in % with glycaemic control is a true difference? Could it have been due to chance? c) Is a difference (in % with glycaemic control) as large as 50% compatible with these data? [If puzzled by the wording of this question, see a hint at the end of this assignment.] d) Is a difference (in % with glycaemic control) as large as 25% compatible with these data? e) Was the difference in percentages with pregnancy induced hypertension statistically significant at p<0.05? (Do not do any calculations.) f) Is a difference (in % with pregnancy-induced hypertension) as large as 25% compatible with these data? g) Is a difference (in % with hypertension) as large as 5% compatible with these data? h) The table shows no confidence interval for the difference in percentages of who had caesarian sections. Would it be possible to calculate such an interval? Now look at Table 2 overleaf. Again, focusing on patients with gestational diabetes and without doing any calculations, answer the following questions: i) How strong is the evidence for a difference in overall neonatal morbidity between treatment groups (could the difference be due to chance)? j) How strong is the evidence for a difference in hypoglycaemia between treatment groups? k) How strong is the evidence for a difference in birth trauma between treatment groups?
Table 1: Variables of glycaemic control and obstetric data of diabetic pregnant women. Values are means (SD) unless stated otherwise. Variable Insulin twice daily Gestational diabetes Insulin four times daily Difference (95% CI) Insulin twice daily Pregestational diabetes Insulin four Difference times daily (95% CI) No of women 136 138 60 58 Gestational week at delivery 38.6 (1.9) 38.9 (1.6) 0.3 (-0.1 to 0.7) 38.3 (2.0) 38.1 (2.8) -0.2 (-1.0 to 0.6) Maternal weight gain (kg) 11.4 (3.5) 10.7 (3.6) -0.7 (-1.5 to 0.1) 12.5 (4.0) 12.0 (4.5) -0.5 (-2.0 to 1.0) Capillary whole blood glucose (mmol/l) 5.60 (0.48) 5.42 (0.54) 0.19 (0.13 to 0.25) 5.9 (0.92) 5.47 (0.78) 0.45 (0.28 to 0.60) Haemoglobin A 10 (%) 5.8 (1.0) 5.5 (1.0) -0.3 (-0.2 to -0.4) 6.7 (1.8) 6.2 (1.3) -0.5 (-0.2 to -0.8) Fructosamine (µmol/l) 229 (43) 188 (27) -41 (-37 to -45) 261 (62) 210 (33) -51 (-45 to -57) Daily insulin at delivery (units/day) 43 (84) 65 (80) 22 (12 to 32) 92 (54) 120 (84) 28 (15 to 41) No (%) with adequate glycaemic control* 101 (74) 126 (91) 17 (8 to 26) 33 (55) 50 (86) 31 (15 to 47) No (%) with severe maternal hypoglycaemia 1 (0.7) 1 (0.7) 0 11 (18) 10 (17) -1 (-15 to 13) No (%) who had caesarian sections 38 (28) 39 (28) 0 19 (32) 13 (22) -10 (-25 to 5) No (%) with pregnancy induced hypertension 12 (9) 11 (8) -1 (-11 to 9) 6 (10) 5 (9) -1 (-11 to 9) * Mean capillary blood glucose concentration <5.8 mmol/l. Requiring help from another person. (Nachum Z et al., BMJ 1999;319:1223-7
Table 2: Perinatal and neonatal outcome in diabetic pregnant women. Values are numbers (percentages) unless stated otherwise. Variable Gestational diabetes Insulin twice daily Insulin four times daily Pregestational diabetes Insulin twice daily Insulin four times daily No of women 136 138 60 58 Mean (SD) birth weight (g) 3436 (672) 3437 (587) 3376 (639) 3229 (758) Perinatal mortality 1 (0.7) 0 2 (3.3) 2 (3.4) Major congenital anomalies 2 (1.5) 1 (0.7) 3 (5.0) 3 (5.1) Small for gestational age ( 10 centile) Large for gestational age ( 90 centile) 7 (5.0) 4 (3.0) 3 (5.0) 3 (5.1) 41 (30) 36 (26) 17 (28) 14 (24) Macrosomia ( 4000 g) 26 (19) 22 (16) 8 (18) 5 (9) Apgar score <7 at 5 minutes 2 (1.5) 6 (4.3) 5 (8) 5 (9) Hyaline membrane disease 0 1 (0.7) 4 (6.7) 1 (1.2) Hypoglycaemia 8 (5.9) 1 (0.7)* 12 (20.0) 2 (3.4)** Hypocalcaemia 0 1 (0.7) 5 (8.3) 6 (10.3) Polycythaemia 3 (2.2) 7 (5.1) 5 (8.3) 3 (5.2) Hyperbilirubinaemia 29 (21) 15 (11)* 28 (47) 27 (47) Birth trauma 3 (2.2) 2 (1.4) 1 (1.7) 1 (1.7) Overall neonatal morbidity 40 (29) 24 (17)* 36 (60) 29 (50) * P=0.02; ** P=0.01. Fatal, requiring surgery, or having significant psychological effects on fetus in later life. According to Brenner et al. Plasma glucose concentration <1.9 mmol/l in term infants or <1.4 mmol/l in preterm infants at least on two different occasions during first 48 hours of life. Serum calcium concentration <2.0 mmol/l. Venous haematocrit >65%. Serum bilirubin concentration >205 mmol/l at 34 weeks gestation or >137 mmol/l at <34 weeks gestation. Peripheral nerve injury or bone fracture. (Nachum Z et al., BMJ 1999;319:1223-7
Hints Hint for typing mathematical work It is possible to present most calculations using regular typing symbols, though it may not look very beautiful, and you might need more brackets that way. If you do wish to learn to type maths expressions beautifully, you can use you word processor s equation editor (eg MS equation editor). For example in equation editor you could type: 1 1 1 1 SE( diff ) p(1 p)( ) 0.5(1 0.5)( ) 0.05 n n 200 200 1 2 Or in regular word you could type: SE(diff)=sqrt[(pbar(1-pbar)(1/n1+1/n2)] = sqrt[(0.5(1-0.5)(1/200+1/200)]=0.05 Or in regular word with some symbols and subscripts: SE(diff)= [(p (1-p )(1/n 1 +1/n 1 )] = [(0.5(1-0.5)(1/200+1/200)]=0.05 You will not be marked down for not typing maths beautifully (just so long as it is clear)! Hint for Formative Assignment Part 2, Question 2.1a How to structure a significance test for comparing proportions: We suggest that you: Draw up a table of data; State the null hypothesis; Calculate the difference in proportions; Calculate the standard error of the difference; Calculate the Z value; Find the P-value from the table A1 in the back of your workbook (double for two-sided); Write the result in a sentence. Hint for Formative Assignment Part 2, Question 2.2c Some students find the word compatible hard to interpret in statistical terms. The easiest way to find whether an hypothesized value of a summary is compatible with a sample of data is from a confidence interval for that summary. A CI includes all those values that are compatible with the data. To make this more precise we would have to refer to the level of confidence used (eg 95%, 90%, etc), but for most purposes this detail need not be mentioned if 95% CIs are used, because these are by far the most common. For example the value a study finding a mean 2.2, 95%CI (1.2-3.2) is compatible with an hypothesized mean of 1.5, but not with an hypothesized mean of 1.0.
Presentation guidelines Either type and double space your assignment answer(s) using 12 point font, or (exceptionally for this module) write clearly by hand, scan and send as JPEG image(s). Insert page numbers. You are not required to rely on materials other than the course materials, but are welcome to use other materials if you are able. Assignments must be submitted via the Assignment Management System no later than 31 March. Do not put your name on the assignment but use your student number. There is no word limit for this practical.