# The point estimate you choose depends on the nature of the outcome of interest odds ratio hazard ratio

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1 Point Estimation Definition: A point estimate is a onenumber summary of data. If you had just one number to summarize the inference from your study.. Examples: Dose finding trials: MTD (maximum tolerable dose) Safety and Efficacy Trials: response rate, median survival Comparative Trials: Odds ratio, hazard ratio

2 Types of Variables The point estimate you choose depends on the nature of the outcome of interest Continuous Variables Examples: change in tumor volume or tumor diameter Commonly used point estimates: mean, median Binary Variables Examples: response, progression, > 50% reduction in tumor size Commonly used point estimate: proportion, relative risk, odds ratio Time-to-Event (Survival) Variables Examples: time to progression, time to death, time to relapse Commonly used point estimates: median survival, k-year survival, hazard ratio Other types of variables: nominal categorical, ordinal categorical

3 Today Point Estimates commonly seen (and misunderstood) in clinical oncology odds ratio risk difference hazard ratio/risk ratio

4 Point Estimates: Odds Ratios Age, Sex, and Racial Differences in the Use of Standard Adjuvant Therapy for Colorectal Cancer, Potosky, Harlan, Kaplan, Johnson, Lynch. JCO, vol. 20 (5), March 2002, p Example: Is gender associated with use of standard adjuvant therapy (SAT) for patients with newly diagnosed stage III colon or stage II/III rectal cancer? 53% of men received SAT* 62% of women received SAT* How do we quantify the difference? * adjusted for other variables

5 Odds and Odds Ratios Odds = p/(1-p) The odds of a man receiving SAT is 0.53/(1-0.53) = The odds of a woman receiving SAT is 0.62/(1-0.62) = Odds Ratio = 1.63/1.13 = 1.44 Interpretation: A woman is 1.44 times more likely to receive SAT than a man.

6 Odds Ratio Odds Ratio for comparing two proportions p1 /( 1 p1) OR = p2 /( 1 p2) p1( 1 p2) = p ( 1 p ) 2 1 OR > 1: increased risk of group 1 compared to 2 OR = 1: no difference in risk of group 1 compared to 2 OR < 1: lower risk ( protective ) in risk of group 1 compared to 2 In our example, p 1 = proportion of women receiving SAT p 2 = proportion of men receiving SAT

7 Odds Ratio from a 2x2 table SAT No SAT Women a = 298 b = Men c = 202 d = OR = p p ( 1 p ) 1 2 ( 1 p ) 2 1 = ad bc

8 More on the Odds Ratio Ranges from 0 to infinity Tends to be skewed (i.e. not symmetric) protective odds ratios range from 0 to 1 increased risk odds ratios range from 1 to Example: Women are at 1.44 times the risk/chance of men Men are at 0.69 times the risk/chance of women

9 More on the Odds Ratio Sometimes, we see the log odds ratio instead of the odds ratio Odds Ratio Log Odds Ratio The log OR comparing women to men is log(1.44) = 0.36 The log OR comparing men to women is log(0.69) = log OR > 0: increased risk log OR = 0: no difference in risk log OR < 0: decreased risk

10 Related Measures of Risk Relative Risk: RR = p 1 /p 2 RR = 0.62/0.53 = Different way of describing a similar idea of risk. Generally, interpretation in words is the similar: Women are at 1.17 times as likely as men to receive SAT RR is appropriate in trials often. But, RR is not appropriate in many settings (e.g. casecontrol studies) Need to be clear about RR versus OR: p 1 = 0.50, p 2 = RR = 0.5/0.25 = 2 OR = (0.5/0.5)/(0.25/0.75) = 3 Same results, but OR and RR give quite different magnitude

11 Related Measures of Risk Risk Difference: p 1 -p 2 Instead of comparing risk via a ratio, we compare risks via a difference. In many CT s, the goal is to increase response rate by a fixed percentage. Example: the current success/response rate to a particular treatment is The goal for new therapy is a response rate of If this goal is reached, then the risk difference will be 0.20.

12 Why do we so often see OR and not others? (1) Logistic regression: Allows us to look at association between two variables, adjusted for other variables. Output is a log odds ratio. Example: In the gender ~ SAT example, the odds ratios were evaluated using logistic regression. In reality, the gender ~ SAT odds ratio is adjusted for age, race, year of dx, region, marital status,.. (2) Can be more globally applied. Design of study does not restrict usage.

13 Point Estimates: Hazard Ratios Randomized Controlled Trial of Single-Agent Paclitaxel Versus Cyclophosphamide, Doxorubicin, and Cisplatin in Patients with Recurrent Ovarian Cancer Who Responded to First-line Platinum-Based Regimens, Cantu, Parma, Rossi, Floriani, Bonazzi, Dell Anna, Torri, Colombo. JCO, vol. 20 (5), March 2002, p What is the effect of CAP on overall survival as compared to paclitaxel? Median survival in CAP group was 34.7 months. Median survival in paclitaxel group was 25.8 months. But, median survival doesn t tell the whole story..

14 Hazard Ratio Compares risk of event in two populations or samples Ratio of risk in group 1 to risk in group 2 First things first.. Kaplan-Meier Curves (productlimit estimate) Makes a picture of survival

15 Hazard Ratios Assumption: Proportional hazards The risk does not depend on time. That is, risk is constant over time But that is still vague.. Example: Assume hazard ratio is 0.7. Patients in temsirolimus group are at 0.7 times the risk of death as those in the interferon-alpha arm, at any given point in time. Hazard function= probably of dying at time t given you survived to time t

16 Survival (S(t)) vs. Hazard (h(t)) Not the same thing. Hard to envision the difference technically, it is the the negative of the slope of the log of the survival curve d dt h( t) = ( log( S( t)) Yikes.don t worry though the statisticians deal with this stuff just remember: the hazard ratio is not the ratio of the survival curves it is a ratio of some function of the survival curves

17 Hazard Ratios Hazard Ratio = hazard function for T hazard function for IA Makes the assumption that this ratio is constant over time. Hazard function Time (months)

18 Hazard Ratios Hazard Ratio = hazard function for T hazard function for IA Makes the assumption that this ratio is constant over time. Hazard function HR= Time (months)

19 Hazard Ratios Hazard Ratio = hazard function for T hazard function for IA Makes the assumption that this ratio is constant over time. Hazard function HR=0.7 HR=0.7 HR= Time (months)

20 Interpretation Again For any fixed point in time, individuals in the T therapy group are at 0.7 times the risk of death as the IA group. Hazard function HR=0.7 HR=0.7 HR= Time (months)

21 Hazard ratio is not always valid. Kaplan-Meier survival estimates, by group Nelson-Aalen cumulative hazard estimates, by group group group group analysis time 0.00 group analysis time Hazard Ratio =.71

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