1. Statistical Issues in the Analysis of Patient Outcomes April 11, 2003 Elizabeth Garrett Oncology Biostatistics Acknowledgement: Thanks to Ron Brookmeyer for providing lecture notes from previous years, which I have adapted into powerpoint.

2. Factors of Interest in Outcomes Research How do we measure…. –Treatment effects? –Access to care? –Quality of care? –Continuity of care? Other variables of interest –Demographic/baseline patient characteristics –Type of provider –Etc……

3. Critical Statistical Issues in Patient Outcome Data NOT RANDOMIZED LONGITUDINAL

4. Properties of Randomized Trials Random assignment (Double) blind Defined treatment protocol Patient Eligibility RANDOMIZE AB

5. BIAS Randomization controls bias Potential Biases in non-randomized studies –Physician selects treatment –Patient self-selects treatment –Those in A are probably not ‘like’ those in B –Example: prostate cancer study of men after prostatectomy Patients who received hormonal therapy were more likely to relapse than those who didn’t Why? Study was a retrospective study of patient records. Patients at high risk of relapse were more likely to be given hormonal therapy CONFOUNDING Generalizability of results in non-randomized trial?

6. Randomized versus Other Controls Historical Controls Matched/Selected Controls Example: Pooled Estimates of overall survival in clinical trials of medical versus surgical treatment of coronary artery disease “Adjusted”: adjusted to have same proportion with one-, two- and three- vessel disease as the randomized trials. Number of Studies Number of Patients 1 year survival rate Randomized trials 618861 Surgical92.4 Medical93.4 Historical Trials99290 Surgical93.0 Medical83.8 Surgical Adjusted 93.7 Medical Adjusted 88.2

7. Statistical Adjustment Will not always work! You need to –Know what to adjust for –Have available the adjustment variables –Know the functional form for the adjustment

8. Statistical Analysis and Adjustment Goal: Control for imbalance Outcome data: –Binary (proportions): e.g., cure rate, relapse, death –Continuous: e.g. quality of life, length of stay, cost –Survival time: e.g. time to death, time to discharge –Longitudinal data: e.g.change in quality of life –Multiple outcomes: Competing risks: e.g. procedure puts you at risk of death, but if successful, procedure cures disease. Multivariate outcome: e.g. latent variable which is measured by several variables, such as quality of life, functional status, etc.

9. Adjustment for Binary Outcomes Unadjusted analysis: Compare proportions that improve in groups A and B Fisher’s exact test Confounding? –Maybe all those in A had a better prognosis to begin with….. AB Yes2515 No1525 40 Treatment Improve 63% improvement on A 38% improvement on B Pvalue = 0.04

10. Prenatal Care and Fetal Mortality Low CareHigh Care Died46 (11%)20 (6%) Survived373316 419336 Low CareHigh Care Died12 (6.4%)16 (5.5%) Survived176293 188309 Mortality rates: 11% in low care 6% in high care pvalue = 0.02 Low CareHigh Care Died34 (17.3%)4 (17.4%) Survived19423 419336 Provider 1Provider 2 pvalue = 0.56 pvalue = 1.00

11. Prenatal Care and Fetal Mortality Prenatal care is not associated with mortality Provider is a confounder –Mortality rates are lower in provider 1 than in provider 2. –Distribution of care is different in providers 1 and 2 (62% high care in provider 1 and only 10% in provider 2) Low CareHigh Care Died12 (6.4%)16 (5.5%) Survived176293 188309 Low CareHigh Care Died34 (17.3%)4 (17.4%) Survived19423 23127 Provider 1Provider 2 pvalue = 0.56 pvalue = 1.00

12. Confounding review care mortality ? provider

13. How to adjust We can’t always stratify –Sparseness –What about continuous variables? Solution: regression methods

14. Logistic regression For binary outcomes Outcome: p i = probability of death of infant i Covariates: x 1i = 1 if infant i is in high care, 0 if low care x 2 = 1 if infant i is in high care provider 2, 0 if provider 1 Example:  1 = 0.15, std error = 0.33 e  1 = 1.16 Z = 0.15/0.33 = 0.45 pvalue > 0.5 After controlling for provider, level of care is not associated with mortality

15. Linear Regression Example: Work days missed among patients with asthma Outcome: y i = number of days missed by patient i Covariates: –x 1i = 1 if patient i uses steroid inhaler, 0 if not –x 2i = asthma severity of patient i Results:  1 = 3.0, std error = 0.60 Those with inhalers lose, on average, 3 more days of work, controlling for severity.

16. Interactions What if effect of inhaler varies by severity? Assume only two levels of severity for simplicity. x 1 x 2 = interaction between severity and inhaler Interpretation: –  1 is the number of days due to inhaler in patients with low severity –  1 +  3 i s the number of days due to inhaler in patients with high severity

17. Regression for survival outcomes Cox proportional hazards model –Time to event outcome –Allows for ‘censoring’ (i.e. incomplete follow-up) h(t) = hazard or incidence rate Example: mental health –Time to next inpatient visit

18. Time to inpatient visit Looking at patients on treatment A versus treatment B for schizophrenia. Relative risk = rate ratio = 2 Patients on treatment B are at twice the risk of inpatient visit compared to those on A. A B Could it be that those on B already failed on treatment A? That would make them ‘worse prognosis’ patients.

19. Longitudinal Analysis Repeated observations on the same patient over time Example: physical well-being score Random effects model: –Linear regression setting –Each patient has his own intercept –i indexes patients, j indexes time

20. Compare slopes Treatment A: slopes = 1 Treatment B: slopes = 2

21. Longitudinal (continued) In addition to modeling over time, can include adjustments for confounders. SAS proc mixed, Stata (xtreg) Generalized Estimating Equations –Liang and Zeger –Accounts for correlation –Can use for continuous or binary data LDA class offered 3 rd term (Dr. Dominici)

22. Quality of Life Data Often interested in whether or not survival with poor quality of life is better than death without suffering. “QALY”= Quality Adjusted Years of Life Example: –Cancer: many patients would rather not get toxic therapies and have more enjoyable end of life The general idea is to down-weight time spent in periods of poor quality of life. Methodologically challenging: –How to determine the weights? –Different settings might need different weights.

23. Quality Adjusted Survival QTWIST: Quality-Adjusted Time Without Symptoms of disease and Toxicity. Evaluate therapies based on both quantity and quality of life through survival analysis Based on QALYs. –Define QOL health states, including one with good health (minimal symptoms). –Patients progress through health states and never back-track. –Partition the area under the Kaplan-Meier Curve and calculate the average time spent in each clinical health state. –Compare treatment regimens using weighted sums durations, weights are utility based. Example: 5 year survival 3 adjusted years of life Compare the average QTWIST in two treatment groups. Could be that on treatment A, people live longer, but QOL is worse. Quality of Life for Individual

24. Multiple Outcome Measures Multiple instruments or subscales Examples: –Physical functioning –General health –Mental health –Pain –Social functioning “Latent variables” Approaches –“STA”: Summarize then analyze –“ATS”: Analyze then summarize –“SAA”: Summarize and analyze

25. Summarize then Analyze Choose a summary score for your outcome variable –E.g. the total number of depression symptoms –E.g. the average pain score over the previous week –E.g. the sum of the individual physical function items Treat this summary score as “observed” Proceed with analysis (e.g. look for treatment differences) Pros: easy to understand, face validity Con: ignores measurement error, might not be a valid or efficient measure.

26. Analyze then Summarize Analyze each item in the scale separately Example: How is treatment related to –Pain on day 1? –Pain on day 2? –Pain on day 3? –….. Qualitatively summarize the results. Pros: considers that the items are each different (i.e. issue of “exchangeability”) Cons: Summarizing can be difficult especially if associations are in different directions; no “number” at the end of the analysis to quantify the association or its significance.

27. Structural Equation Models “path models” Uses ‘factor analysis’ approach to summarize variables (i.e. measurement model) and create latent variables Uses regression techniques to associate other variables with latent variable

28. Do both in one model. “Structural Equation Models” Summarize and Analyze Simultaneously X   Y1Y1 Y2Y2 YmYm...... 11 mm 22 11 22 mm Assume variable of interest is general health status (  ). The Y variables are indicators of general health. We want to see how treatment is associated with general health status.

29. Summary Main statistical issue is outcomes research: LACK OF RANDOMIZATION –Bias introduced –Needs adjustment Regression methods can be used to adjust –Binary: logistic –Continuous: linear –Survival: Cox proportional hazards –Longitudinal: random effects, GEE Quality of Life –QALYs –QTWiST Multiple measures and latent variables

30. References Longitudinal: Diggle, Liang, and Zeger Survival Analysis: Collett Quality of Life: see handout from Fairclough and Gelber Thanks (again) to R. Brookmeyer for his handouts and examples from previous lectures.