Lab Module 8 Inference about a Relative Risk B_Nguyen

PH 167 Biostatistics Lab Manual San José State University

Lab Module 8: Inference about a Relative Risk Before beginning this lab, attend the relevant lectures 1. New Data File. Until now, we have been working with a subset of data from the investigation by Jolson and coworkers (1992). Download the full data set and save it to your home directory or to a USB drive. Open the data file in SPSS and review the variable names in Variable View. We now ask whether the incidence of toxicity differs in individuals who received the generic version and innovator version of the chemotherapeutic agent in question. a. Explanatory variable. In addressing whether the generic drug is associated with toxicity, what is the name of the explanatory variable? Is this variable categorical or quantitative? How is it coded? Generic. Categorical. Coded as 1 or 2. Note: The explanatory variable is often called the “exposure” in epidemiologic investigations. Note that this exposure is binary. b. Response variable. What is the name of the response variable for the current research question? Is this variable categorical or continuous? Response variable: toxicity. Categorical Note: The response variable is often referred to as the “disease” or the “outcome” in an epidemiologic investigation. c. Sample type. In previous labs we addressed single samples, paired samples, and independent samples. In this lab we compare the occurrence of toxicity in exposed and nonexposed individuals. Is this a single sample problem, paired sample problem, or independent sample problem? Explain your response. Independent sample problem because the two groups are independent. The toxicity is based on the generic or innovator taken by the individual. d. 2-by-2 table. Frequencies of toxicity are cross-tabulated to form a 2-by-2 table with tables cells labeled as follows: Disease + Disease − Total Exposed + a 1 b 1 n 1 Exposed − a 2 b 2 n 2 Total m 1 m 2 N

Note: These proportions represent incidence proportions because they are the proportion of individuals who develop a condition over a specified period. The term “average risk” is synonymous with “incidence proportion.” c. Relative risk. Incidence proportions can be compared in the form of a ratio. The ratio of the two proportions is a relative risk (or incidence proportion ratio). The relative risk estimate, ^ RR = ^ p 1 ^ p 2 . . Calculate this statistic: 0.44/0.0882 = 4.989 d. Direction of association. When p 1 = p 2 , RR = 1. RRs greater than 1 indicate a positive association. RRs less than 1 (i.e., between 0 and 0.99) indicate a negative association. The baseline relative risk indicating no association is one. What is the direction of the current association? RR of 4.989 > 1 Positive Association e. Strength of association. The RR is the “risk multiplier” associated exposure. For example, an RR of 1.25 indicates the risk in the exposed group is 1.25 times that of the non-exposed group. An RR estimate of 3.0 indicates that the exposure triples the risk. Interpret the relative risk in this manner. RR of 4.989 indicates the risk of the exposed group is 4.989 times that of the unexposed group. f. Percentage increase/decrease. The baseline RR is 1, indicating no difference in risk in the groups. If we subtract 1 from the RR, we have the increase or decrease in risk in relative terms. For example, a relative risk of 1.25 indicates that the risk in the exposed group is 0.25 or 25% above the risk in the non- exposed group. In contrast, a relative risk of 0.75 indicates

that the risk in the exposed group is 0.25 or 25% below the baseline relative risk of 1. In percentage terms, how much did the generic drug increase the risk of toxicity? 4.989 – 1 = 3.989 An RR of 4.989 is 398.9% above baseline. g. Interval estimation. The point estimate of relative risk “RR-hat” is the point estimate of the RR parameter. To address the precision of this estimate, calculate a confidence interval (CI). The (1-  )100% CI for the RR is given by: RR = e ln ^ RR ±Z 1 − α / 2 × SE ln ^ RR , where SE ln ^ RR = √ 1 a 1 − 1 n 1 + 1 a 2 − 1 n 2 Calculate the 95% CI for the RR. See lecture for the alternative to performing this calculation. Ln 4.989 +- 1.96 * (0.59568) Ln(4.989) = 1.6072 SEln(RR)= √ 1 11 − 1 25 + 1 3 − 1 34 = 0.59568 0.4397, 2.7747 e^(0.4397, 2.7747) = (1.552, 16.034) Note : We work on the natural logarithm (base e ) scale to calculate the CI for the RR. Optional . Calculate the 95% CI for RR with www.OpenEpi.com > Counts > Two by Two table. Click the “New Data” button and enter the data from the 2-by-2 table. Find the CI for the Relative Risk in the output and confirm you hand-calculated confidence limits.

Table B: Cumulative probabilities for a Standard Normal Z variable; traditional z table. z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 –3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002 –3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 –3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005 –3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 –3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 –2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 –2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019 –2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 –2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036 –2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 –2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 –2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 –2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 –2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 –2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 –1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 –1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294 –1.7 .0446 .0436 .0427 .0418 .0409 .0401 .0392 .0384 .0375 .0367 –1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455 –1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 –1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681 –1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823 –1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985 –1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170 –1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379 –0.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611 –0.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867 –0.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148 –0.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451 –0.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776 –0.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121 –0.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 –0.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859 –0.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247 –0.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641 0.0 .5000 .5040 .5080 .5120 .5160 .5199 .5239 .5279 .5319 .5359 0.1 .5398 .5438 .5478 .5517 .5557 .5596 .5636 .5675 .5714 .5753 0.2 .5793 .5832 .5871 .5910 .5948 .5987 .6026 .6064 .6103 .6141 0.3 .6179 .6217 .6255 .6293 .6331 .6368 .6406 .6443 .6480 .6517 0.4 .6554 .6591 .6628 .6664 .6700 .6736 .6772 .6808 .6844 .6879 0.5 .6915 .6950 .6985 .7019 .7054 .7088 .7123 .7157 .7190 .7224 0.6 .7257 .7291 .7324 .7357 .7389 .7422 .7454 .7486 .7517 .7549 0.7 .7580 .7611 .7642 .7673 .7704 .7734 .7764 .7794 .7823 .7852 0.8 .7881 .7910 .7939 .7967 .7995 .8023 .8051 .8078 .8106 .8133 0.9 .8159 .8186 .8212 .8238 .8264 .8289 .8315 .8340 .8365 .8389 1.0 .8413 .8438 .8461 .8485 .8508 .8531 .8554 .8577 .8599 .8621 1.1 .8643 .8665 .8686 .8708 .8729 .8749 .8770 .8790 .8810 .8830 1.2 .8849 .8869 .8888 .8907 .8925 .8944 .8962 .8980 .8997 .9015 1.3 .9032 .9049 .9066 .9082 .9099 .9115 .9131 .9147 .9162 .9177 1.4 .9192 .9207 .9222 .9236 .9251 .9265 .9279 .9292 .9306 .9319 1.5 .9332 .9345 .9357 .9370 .9382 .9394 .9406 .9418 .9429 .9441 1.6 .9452 .9463 .9474 .9484 .9495 .9505 .9515 .9525 .9535 .9545 1.7 .9554 .9564 .9573 .9582 .9591 .9599 .9608 .9616 .9625 .9633 1.8 .9641 .9649 .9656 .9664 .9671 .9678 .9686 .9693 .9699 .9706 1.9 .9713 .9719 .9726 .9732 .9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772 .9778 .9783 .9788 .9793 .9798 .9803 .9808 .9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838 .9842 .9846 .9850 .9854 .9857 2.2 .9861 .9864 .9868 .9871 .9875 .9878 .9881 .9884 .9887 .9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906 .9909 .9911 .9913 .9916 2.4 .9918 .9920 .9922 .9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5 .9938 .9940 .9941 .9943 .9945 .9946 .9948 .9949 .9951 .9952 2.6 .9953 .9955 .9956 .9957 .9959 .9960 .9961 .9962 .9963 .9964 2.7 .9965 .9966 .9967 .9968 .9969 .9970 .9971 .9972 .9973 .9974 2.8 .9974 .9975 .9976 .9977 .9977 .9978 .9979 .9979 .9980 .9981 2.9 .9981 .9982 .9982 .9983 .9984 .9984 .9985 .9985 .9986 .9986 3.0 .9987 .9987 .9987 .9988 .9988 .9989 .9989 .9989 .9990 .9990 3.1 .9990 .9991 .9991 .9991 .9992 .9992 .9992 .9992 .9993 .9993 3.2 .9993 .9993 .9994 .9994 .9994 .9994 .9994 .9995 .9995 .9995 7

3.3 .9995 .9995 .9995 .9996 .9996 .9996 .9996 .9996 .9996 .9997 3.4 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9997 .9998 8