SMHS MethodsHeterogeneity MetaAnalysis - Revision history

Pineaumi: /* Nonparametric Regression Methods */

2016-05-23T18:55:03Z

‎Nonparametric Regression Methods

Pineaumi: /* Nonparametric Regression Methods */

2016-05-23T18:53:40Z

‎Nonparametric Regression Methods

Pineaumi: /* Quantile Treatment Effect (QTE) */

2016-05-23T18:52:37Z

‎Quantile Treatment Effect (QTE)

Pineaumi: /* Footnotes */

2016-05-23T18:52:00Z

‎Footnotes

Pineaumi: /* Quantile Treatment Effect (QTE) */

2016-05-23T18:51:35Z

‎Quantile Treatment Effect (QTE)

Pineaumi: /* Footnotes */

2016-05-23T18:48:36Z

‎Footnotes

Pineaumi: /* Footnotes */

2016-05-23T18:48:14Z

‎Footnotes

Pineaumi: /* Series of “N of 1” trials */

2016-05-23T18:47:39Z

‎Series of “N of 1” trials

Pineaumi: /* Example */

2016-05-23T18:47:08Z

‎Example

Pineaumi: /* Simulation Example 1 */

2016-05-23T18:45:31Z

‎Simulation Example 1

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   Residual standard error: 0.5608 on 202 degrees of freedom
-  Multiple R-squared:  0.2308,	Adjusted R-squared:  0.2232
+  Multiple R-squared:  <mark>0.2308</mark>,	Adjusted R-squared:  0.2232
   F-statistic:  30.3 on 2 and 202 DF,  p-value: 3.103e-12

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 Nonparametric regression enables dealing with HTE in RCTs. Different nonparametric methods, such as kernel smoothing methods and series methods, can be used to generate test statistics for examining the presence of HTE. A kernel method is a weighting scheme based on a kernel function (e.g. uniform, Gaussian). When evaluating the treatment effect of a patient in RCTs, the kernel method assigns larger weights to those observations with similar covariates. This is done because it is assumed that patients with similar covariates provide more relevant data on predicted treatment response. Examining participants that have different backgrounds (e.g., demographic, clinical), kernel smoothing methods utilize information from highly divergent participants when estimating a particular subject’s treatment effect. Lower weights are assigned to very different subjects and the kernel methods require choosing a set of smoothing parameters to group patients according to their relative degree of similarities. A drawback is that the corresponding proposed test statistics may be sensitive to the chosen bandwidths, which inhibits the interpretation of the results. Series methods use approximating functions (splines or power series of the explanatory variables) to construct test statistics. Compared to kernel smoothing methods, series methods normally have the advantage of computational convenience; however, the precision of test statistics depends on the number of terms selected in the series.
-Canadian Wage Data Example: Nonparametric regression extends the classical parametric regression (e.g., lm, lmer) involving one continuous dependent variable, y, and (1 or more) continuous explanatory variable(s), x. Let’s start with a popular parametric model of a wage equation that we can extend to a fully nonparametric regression model. First, we will compare and contrast the parametric and nonparametric approach towards univariate regression and then proceed to multivariate regression.
+<b>Canadian Wage Data Example:</b> Nonparametric regression extends the classical parametric regression (e.g., lm, lmer) involving one continuous dependent variable, y, and (1 or more) continuous explanatory variable(s), x. Let’s start with a popular parametric model of a wage equation that we can extend to a fully nonparametric regression model. First, we will compare and contrast the parametric and nonparametric approach towards univariate regression and then proceed to multivariate regression.
 Let’s use the Canadian cross-section wage data (<b>cps71</b>) consisting of a random sample taken from the 1971 Canadian Census for male individuals having common education (High-School). N=205 observations, 2 variables, the logarithm of the individual’s wage (logwage) and their age (age). The classical wage equation model includes a quadratic term of age.

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 One caveat of applying QRE in clinical trials for examining HTE is that the QTE doesn’t demonstrate the treatment effect for a given patient. Instead, it focuses on the treatment effect among subjects within the qth quantile, such as those who are exactly at the top 10th percent in terms of blood pressure or a depression score for some covariate of interest, for example, comorbidity score. It is not uncommon for the qth quantiles to be two different sets of patients before and after the treatment. For this reason, we have to assume that these two groups of patients are homogeneous if they were in the same quantiles.
-Income-Food Expenditure Example: Let’s examine the Engel data (N=235) on the relationship between food expenditure (foodexp) and household income (income)<sup>11</sup>. We can plot the data and then explore the superposition of the six fitted quantile regression lines.
+<b>Income-Food Expenditure Example:</b> Let’s examine the Engel data (N=235) on the relationship between food expenditure (foodexp) and household income (income)<sup>11</sup>. We can plot the data and then explore the superposition of the six fitted quantile regression lines.
   install.packages("quantreg")

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 *<sup>8</sup> http://onlinelibrary.wiley.com/enhanced/doi/10.1002/jrsm.54
 *<sup>9</sup> http://effectivehealthcare.ahrq.gov/search-for-guides-reviews-and-reports/?pageaction=displayproduct&productID=1857
-*<sup>10</sup>  http://jpepsy.oxfordjournals.org/content/39/2/138.full#sec-14
+*<sup>10</sup> http://jpepsy.oxfordjournals.org/content/39/2/138.full#sec-14
 ==[[SMHS_MethodsHeterogeneity_CER|Next see: Comparative Effectiveness Research (CER)]]==

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 One caveat of applying QRE in clinical trials for examining HTE is that the QTE doesn’t demonstrate the treatment effect for a given patient. Instead, it focuses on the treatment effect among subjects within the qth quantile, such as those who are exactly at the top 10th percent in terms of blood pressure or a depression score for some covariate of interest, for example, comorbidity score. It is not uncommon for the qth quantiles to be two different sets of patients before and after the treatment. For this reason, we have to assume that these two groups of patients are homogeneous if they were in the same quantiles.
-Income-Food Expenditure Example: Let’s examine the Engel data (N=235) on the relationship between food expenditure (foodexp) and household income (income). We can plot the data and then explore the superposition of the six fitted quantile regression lines.
+Income-Food Expenditure Example: Let’s examine the Engel data (N=235) on the relationship between food expenditure (foodexp) and household income (income)<sup>11</sup>. We can plot the data and then explore the superposition of the six fitted quantile regression lines.
   install.packages("quantreg")

← Older revision		Revision as of 18:48, 23 May 2016
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	<sup>8</sup> http://onlinelibrary.wiley.com/enhanced/doi/10.1002/jrsm.54		<sup>8</sup> http://onlinelibrary.wiley.com/enhanced/doi/10.1002/jrsm.54
		+	<sup>9</sup> http://effectivehealthcare.ahrq.gov/search-for-guides-reviews-and-reports/?pageaction=displayproduct&productID=1857
		+	<sup>10</sup> http://jpepsy.oxfordjournals.org/content/39/2/138.full#sec-14

	==[[SMHS_MethodsHeterogeneity_CER\|Next see: Comparative Effectiveness Research (CER)]]==		==[[SMHS_MethodsHeterogeneity_CER\|Next see: Comparative Effectiveness Research (CER)]]==

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 ==Series of “N of 1” trials==
-This technique combines (a “series of”) n-of-1 trial data to identify HTE. An n-of-1 trial is a repeated crossover trial for a single patient, which randomly assigns the patient to one treatment vs. another for a given time period, after which the patient is re-randomized to treatment for the next time period, usually repeated for 4-6 time periods. Such trials are most feasibly done in chronic conditions, where little or no washout period is needed between treatments and treatment effects are identifiable in the short-term, such as pain or reliable surrogate markers. Combining data from identical n-of-1 trials across a set of patients enables the statistical analysis controlling for patient fixed or random effects, covariates, centers, or sequence effects, see <b>Figure</b> below. These combined trials are often analyzed within a Bayesian context using shrinkage estimators that combine individual and group mean treatment effects to create a “posterior” individual mean treatment effect estimate which is a form of inverse variance-weighted average of the individual and group effects. Such trials are typically more expensive than standard RCTs on a per-patient basis, however, they require much smaller sample sizes, often less than 100 patients (due to the efficient individual-as-own-control design), and create individual treatment effect estimates that are not possible in a non-crossover design  . For the individual patient, the treatment effect can be re-estimated after each time period, and the trial stopped at any point when the more effective treatment is identified with reasonable statistical certainty.
+This technique combines (a “series of”) n-of-1 trial data to identify HTE. An n-of-1 trial is a repeated crossover trial for a single patient, which randomly assigns the patient to one treatment vs. another for a given time period, after which the patient is re-randomized to treatment for the next time period, usually repeated for 4-6 time periods. Such trials are most feasibly done in chronic conditions, where little or no washout period is needed between treatments and treatment effects are identifiable in the short-term, such as pain or reliable surrogate markers. Combining data from identical n-of-1 trials across a set of patients enables the statistical analysis controlling for patient fixed or random effects, covariates, centers, or sequence effects, see <b>Figure</b> below. These combined trials are often analyzed within a Bayesian context using shrinkage estimators that combine individual and group mean treatment effects to create a “posterior” individual mean treatment effect estimate which is a form of inverse variance-weighted average of the individual and group effects. Such trials are typically more expensive than standard RCTs on a per-patient basis, however, they require much smaller sample sizes, often less than 100 patients (due to the efficient individual-as-own-control design), and create individual treatment effect estimates that are not possible in a non-crossover design<sup>9</sup>. For the individual patient, the treatment effect can be re-estimated after each time period, and the trial stopped at any point when the more effective treatment is identified with reasonable statistical certainty.
 ====Example====

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 ====Example====
-A study involving 8 participants collected data across 30 days, in which 15 treatment days and 15 control days are randomly assigned within each participant. The treatment effect is represented as a binary variable (control day=0; treatment day=1). The outcome variable represents the response to the intervention within each of the 8 participants. Study employed a fixed-effects modeling. By creating N − 1 dummy-coded variables representing the N=8 participants, where the last (i=8) participant serves as the reference (i.e., as the model intercept). So, each dummy-coded variable represents the difference between each participant (i) and the 8th participant. Thus, all other patients' values will be relative to the values of the 8th (reference) subject. The overall differences across participants in fixed effects can be evaluated with multiple <b>degree-of-freedom F-tests.</b>
+A study involving 8 participants collected data across 30 days, in which 15 treatment days and 15 control days are randomly assigned within each participant<sup>10</sup>. The treatment effect is represented as a binary variable (control day=0; treatment day=1). The outcome variable represents the response to the intervention within each of the 8 participants. Study employed a fixed-effects modeling. By creating N − 1 dummy-coded variables representing the N=8 participants, where the last (i=8) participant serves as the reference (i.e., as the model intercept). So, each dummy-coded variable represents the difference between each participant (i) and the 8th participant. Thus, all other patients' values will be relative to the values of the 8th (reference) subject. The overall differences across participants in fixed effects can be evaluated with multiple <b>degree-of-freedom F-tests.</b>
 <center>[[Image:SMHS_Methods11.png|500px]] </center>

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 <center>[[Image:SMHS_Methods10.png|500px]] </center>
-The <b>forest plo</b>t shows the I2 test indicates the evidence to reject the null hypothesis (no study heterogeneity and the fixed effects model should be used).
+The <b>forest plo</b>t shows the ''I''<sup>2</sup> test indicates the evidence to reject the null hypothesis (no study heterogeneity and the fixed effects model should be used).
 ==Series of “N of 1” trials==