Cox Proportional-Hazards Model - Easy Guides - Wiki - STHDA

I have 10 PCA features with values between -93 and 42 and I want to use them in Cox regression with my dummy variables that are from another dataset. I'd like the hazard ratios (coefficents) to have easily interpretable values, (particularly for the PCA features) since right now I get values that are too small (1.1, 1.01, etc).
Was wondering if I could simply just do minimax scaler https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.MinMaxScaler.html for each of the PCA features to get them on the same order as the dummies.

I have applied a cox proportional model on discontinuation data. There are two groups and OD and OW and I want to know which one patient group has better likelihood of staying on treatment.
If the hazard ratio from cox proportional model is such-
​

Class	Hazard ratio	Parameter estimate	prob chi sq
OD	1.234	0.21002	<0.0001

Then do can we interpret it as OW are 23.4%more likely to stay on treatment as compared to OD? Or do we say OD are 23.4% more likely to discontinue as compared to OD? Or do they mean the same?
Is more likely to stay and more likely to discontinue the same?

Ok so I have this dataset where I’m comparing Monotherapy vs combination therapy in terms of overall survival (OS) and hazard ratio for a specific disease. Now I ran a log rank test on the OS, and it turned out statistically significant that there is a difference between the both survival curves (mono vs combo). So my questions are as follows:
1)Should I proceed to univariate cox regression? Like let’s say there was no statistical significance in OS using log rank test, should I still do univariate cox regression?
2)The covariate in case of univariate cox regression would be whether the patient received monotherapy or combination therapy, right?
3)Let’s say I had 5 variables and 2 of them are not statistically significant, should I still include them in my multivariate cox regression?
4)If my univariate result was statistically significant but not statistically significant in multivariate regression, what should I exactly report/interpret?
I’m fairly new to this and I can’t really find a good resource, so if anyone could direct me towards a great resource to understand cox regression specifically I would be forever thankful.

Hi!
I'm struggling to find information on how to interpret time-covariate interaction and the main effect of the covariate when both the main effect and interaction are statistically significant. Can I interpret the hazard ratio of the covariate as in usual cox regression? Thanks!

https://www.ncbi.nlm.nih.gov/pubmed/30201613

Abstract
Background: Patients are at increased risk of cardiovascular complications while recovering from sepsis. We aimed to study the temporal change and susceptible periods for cardiovascular complications in patients recovering from sepsis by using a national database.
Methods: In this retrospective population-based cohort study, patients with sepsis were identified from the National Health Insurance Research Database in Taiwan. We estimated the risk of myocardial infarction (MI) and stroke following sepsis by comparing a sepsis cohort to a matched population and hospital control cohort. The primary outcome was first occurrence of MI or stroke requiring admission to hospital during the 180-day period following discharge from hospital after sepsis. To delineate the risk profile over time, we plotted the weekly risk of MI and stroke against time using the Cox proportional hazards model. We determined the susceptible period by fitting the 2 phases of time-dependent risk curves with free-knot splines, which highlights the turning point of the risk of MI and stroke after discharge from the hospital.
Results: We included 42 316 patients with sepsis; stroke developed in 831 of these patients and MI developed in 184 within 180 days of discharge from hospital. Compared with population controls, patients recovering from sepsis had the highest risk for MI or stroke in the first week after discharge (hazard ratio [HR] 4.78, 95% confidence interval [CI] 3.19 to 7.17; risk difference 0.0028, 95% CI 0.0021 to 0.0034), with the risk decreasing rapidly until the 28th day (HR 2.38, 95% CI 1.94 to 2.92; risk difference 0.0045, 95% CI 0.0035 to 0.0056) when the risk stabilized. In a repeated analysis comparing the sepsis cohort with the nonsepsis hospital control cohort, we found an attenuated but still marked elevated risk before day 36 after discharge (HR 1.32, 95% CI 1.15 to 1.52; risk difference 0.0026, 95% CI 0.0013 to 0.0039). The risk of MI or stroke was found to interact with age, with younger patients being associated with a higher risk than older patients (interaction p = 0.0004).
Interpretation: Compared with the general population with similar characteristics, patients recovering from sepsis had a markedly elevated risk of MI or stroke in the first 4 weeks after discharge from hospital. More close monitoring and pharmacologic prevention may be required for these patients at the specified time.

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I dont know how to interpret “stratified Hazard Ratio”
When a stratified Hazard ratio is reported eg. “The stratified HR was 0.6 (CI 0.4 to 0.8). The Hazard ratio and its CI were estimated using cox proportional hazards model stratified using the stratification factors as per IRT. This indicates that HR were also stratified by age and previous lines of therapy. Could you help me with the interpretation of this stratified HR

https://www.nytimes.com/2017/09/08/well/new-study-favors-fat-over-carbs.html
Summary from The Lancet:
Summary Background The relationship between macronutrients and cardiovascular disease and mortality is controversial. Most available data are from European and North American populations where nutrition excess is more likely, so their applicability to other populations is unclear.
Methods The Prospective Urban Rural Epidemiology (PURE) study is a large, epidemiological cohort study of individuals aged 35–70 years (enrolled between Jan 1, 2003, and March 31, 2013) in 18 countries with a median follow-up of 7·4 years (IQR 5·3–9·3). Dietary intake of 135 335 individuals was recorded using validated food frequency questionnaires. The primary outcomes were total mortality and major cardiovascular events (fatal cardiovascular disease, non-fatal myocardial infarction, stroke, and heart failure). Secondary outcomes were all myocardial infarctions, stroke, cardiovascular disease mortality, and non-cardiovascular disease mortality. Participants were categorised into quintiles of nutrient intake (carbohydrate, fats, and protein) based on percentage of energy provided by nutrients. We assessed the associations between consumption of carbohydrate, total fat, and each type of fat with cardiovascular disease and total mortality. We calculated hazard ratios (HRs) using a multivariable Cox frailty model with random intercepts to account for centre clustering.
Findings During follow-up, we documented 5796 deaths and 4784 major cardiovascular disease events. Higher carbohydrate intake was associated with an increased risk of total mortality (highest [quintile 5] vs lowest quintile [quintile 1] category, HR 1·28 [95% CI 1·12–1·46], ptrend=0·0001) but not with the risk of cardiovascular disease or cardiovascular disease mortality. Intake of total fat and each type of fat was associated with lower risk of total mortality (quintile 5 vs quintile 1, total fat: HR 0·77 [95% CI 0·67–0·87], ptrend<0·0001; saturated fat, HR 0·86 [0·76–0·99], ptrend=0·0088; monounsaturated fat: HR 0·81 [0·71–0·92], ptrend<0·0001; and polyunsaturated fat: HR 0·80 [0·71–0·89], ptrend<0·0001). Higher saturated fat intake was associated with lower risk of stroke (quintile 5 vs quintile 1, HR 0·79 [95% CI 0·64–0·98], ptrend=0·0498). Total fat and saturated and unsaturated fats were not significantly associated with risk of myocardial infarction or cardiovascular disease mortality.
Interpretation High carbohydrate intake was associated with higher risk of total mortality, whereas total fat and individual types of fat were related to lower total mortality. Total fat and types of fat were not associated with cardiovascular disease, myocardial infarction, or cardiovascular disease mortality, whereas saturated fat had an inverse association with stroke. Global dietary guidelines should be reconsidered in light of these findings.
TL:DR -- "Eat carbs if you want to die sooner!"

Cox (Proportional Hazards) Regression
Menu location: Analysis_Survival_Cox Regression.
This function fits Cox's proportional hazards model for survival-time (time-to-event) outcomes on one or more predictors.
Cox regression (or proportional hazards regression) is method for investigating the effect of several variables upon the time a specified event takes to happen. In the context of an outcome such as death this is known as Cox regression for survival analysis. The method does not assume any particular "survival model" but it is not truly nonparametric because it does assume that the effects of the predictor variables upon survival are constant over time and are additive in one scale. You should not use Cox regression without the guidance of a Statistician.
Provided that the assumptions of Cox regression are met, this function will provide better estimates of survival probabilities and cumulative hazard than those provided by the Kaplan-Meier function.
Hazard and hazard-ratios
Cumulative hazard at a time t is the risk of dying between time 0 and time t, and the survivor function at time t is the probability of surviving to time t (see also Kaplan-Meier estimates).
The coefficients in a Cox regression relate to hazard; a positive coefficient indicates a worse prognosis and a negative coefficient indicates a protective effect of the variable with which it is associated.
The hazards ratio associated with a predictor variable is given by the exponent of its coefficient; this is given with a confidence interval under the "coefficient details" option in StatsDirect. The hazards ratio may also be thought of as the relative death rate, see Armitage and Berry (1994). The interpretation of the hazards ratio depends upon the measurement scale of the predictor variable in question, see Sahai and Kurshid (1996) for further information on relative risk of hazards.
Time-dependent and fixed covariates
In prospective studies, when individuals are followed over time, the values of covariates may change with time. Covariates can thus be divided into fixed and time-dependent. A covariate is time dependent if the difference between its values for two different subjects changes with time; e.g. serum cholesterol. A covariate is fixed if its values can not change with time, e.g. sex or race. Lifestyle factors and physiological measurements such as blood pressure are usually time-dependent. Cumulative exposures such as smoking are also time-dependent but are often forced into an imprecise dichotomy, i.e. "exposed" vs. "not-exposed" instead of the more meaningful "time of exposure". There are no hard and fast rules about the handling of time dependent covariates. If you are considering using Cox regression you should seek the help of a Statistician, preferably at the design stage of the investigation.
Model analysis and deviance
A test of the overall statistical significance of the model is given under the "model analysis" option. Here the likelihood chi-square statistic is calculated by comparing the deviance (- 2 * log likelihood) of your model, with all of the covariates you have specified, against the model with all covariates dropped. The individual contribution of covariates to the model can be assessed from the significance test given with each coefficient in the main output; this assumes a reasonably large sample size.
Deviance is minus twice the log of the likelihood ratio for models fitted by maximum likelihood (Hosmer and Lemeshow, 1989 and 1999; Cox and Snell, 1989; Pregibon, 1981). The value of adding a parameter to a Cox model is tested by subtracting the deviance of the model with the new parameter from the deviance of the model without the new parameter, the difference is then tested against a chi-square distribution with degrees of freedom equal to the difference between the degrees of freedom of the old and new models. The model analysis option tests the model you specify against a model with only one parameter, the intercept; this tests the combined value of the specified predictors/covariates in the model.
Some statistical packages offer stepwise Cox regression that performs systematic tests for different combinations of predictors/covariates. Automatic model building procedures such as these can be misleading as they do not consider the real-world importance of each predictor, for this reason StatsDirect does not include stepwise selection.
Survival and cumulative hazard rates
The survival/survivorship function and the cumulative hazard function (as discussed under Kaplan-Meier) are calculated relative to the baseline (lowest value of covariates) at each time point. Cox regression provides a better estimate of these functions than the Kaplan-Meier method when the assumptions of the Cox model are met and the fit of the model is strong.
You are given the option to 'centre continuous covariates' – this makes survival and hazard functions relative to the mean of continuous variables rather than relative to the minimum, which is usually the most meaningful comparison.
If you have binary/dichotomous predictors in your model you are given the option to calculate survival and cumulative hazards for each variable separately.

http://www.thelancet.com/journals/lancet/article/PIIS0140-6736(17)32252-3/fulltext?elsca1=tlxpr
Background
The relationship between macronutrients and cardiovascular disease and mortality is controversial. Most available data are from European and North American populations where nutrition excess is more likely, so their applicability to other populations is unclear.
Methods
The Prospective Urban Rural Epidemiology (PURE) study is a large, epidemiological cohort study of individuals aged 35–70 years (enrolled between Jan 1, 2003, and March 31, 2013) in 18 countries with a median follow-up of 7·4 years (IQR 5·3–9·3). Dietary intake of 135 335 individuals was recorded using validated food frequency questionnaires. The primary outcomes were total mortality and major cardiovascular events (fatal cardiovascular disease, non-fatal myocardial infarction, stroke, and heart failure). Secondary outcomes were all myocardial infarctions, stroke, cardiovascular disease mortality, and non-cardiovascular disease mortality. Participants were categorised into quintiles of nutrient intake (carbohydrate, fats, and protein) based on percentage of energy provided by nutrients. We assessed the associations between consumption of carbohydrate, total fat, and each type of fat with cardiovascular disease and total mortality. We calculated hazard ratios (HRs) using a multivariable Cox frailty model with random intercepts to account for centre clustering.
Findings
During follow-up, we documented 5796 deaths and 4784 major cardiovascular disease events. Higher carbohydrate intake was associated with an increased risk of total mortality (highest [quintile 5] vs lowest quintile [quintile 1] category, HR 1·28 [95% CI 1·12–1·46], ptrend=0·0001) but not with the risk of cardiovascular disease or cardiovascular disease mortality. Intake of total fat and each type of fat was associated with lower risk of total mortality (quintile 5 vs quintile 1, total fat: HR 0·77 [95% CI 0·67–0·87], ptrend<0·0001; saturated fat, HR 0·86 [0·76–0·99], ptrend=0·0088; monounsaturated fat: HR 0·81 [0·71–0·92], ptrend<0·0001; and polyunsaturated fat: HR 0·80 [0·71–0·89], ptrend<0·0001). Higher saturated fat intake was associated with lower risk of stroke (quintile 5 vs quintile 1, HR 0·79 [95% CI 0·64–0·98], ptrend=0·0498). Total fat and saturated and unsaturated fats were not significantly associated with risk of myocardial infarction or cardiovascular disease mortality.
Interpretation
High carbohydrate intake was associated with higher risk of total mortality, whereas total fat and individual types of fat were related to lower total mortality. Total fat and types of fat were not associated with cardiovascular disease, myocardial infarction, or cardiovascular disease mortality, whereas saturated fat had an inverse association with stroke. Global dietary guidelines should be reconsidered in light of these findings.

I've run a cox regression analysis and inverted hazard ratios <1 using the (1/HR) formula, for interpretability. However, I want to report the 95% confidence intervals as well - does anyone know how I would go about inverting the 95% CI similarly?
Thanks!

Hoping for some help in interpreting the coxph output in R using the survival package. I am very new to R, but have successfully made my way to aggregating my data set and using the tmerge function to add in my cumulative time-dependent covariate for a sample size of customers.
Here is the code as it stands now:

fit <- coxph( Surv(tstart, tstop, had_event) ~ review_event, data = newdatatestcum) summary(fit) 

The output:

n= 35695, number of events= 54 coef exp(coef) se(coef) z Pr(>|z|) review_event -0.006707 0.993316 0.001771 -3.786 0.000153 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 exp(coef) exp(-coef) lower .95 upper .95 review_event 0.9933 1.007 0.9899 0.9968 Concordance= 0.693 (se = 0.041 ) Rsquare= 0.001 (max possible= 0.014 ) Likelihood ratio test= 24.1 on 1 df, p=9.123e-07 Wald test = 14.34 on 1 df, p=0.0001529 Score (logrank) test = 11.58 on 1 df, p=0.0006658 

Along with this I have used the cox.zph function to test the proportional hazard and from my study so far I do not believe to have violated.

cox.zph(fit) 

The ouput:

 rho chisq p review_event -0.0699 0.332 0.564 

The plot:

plot(cox.zph(fit,transform = "log")) 

(http://i.imgur.com/nf8vwIi.jpg)
Any feedback is very much appreciated as I have come so far only to be unable to interpret anything meaningful after hours of study. Thank you!!

Summary generated by cruyff8's autosummarizer of http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0016885:

Open Access Peer-reviewed Research Article Affiliation: Department of Clinical Neuroscience, Division of Psychiatry, Karolinska Institutet, Stockholm, Sweden Affiliation: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden Affiliation: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden Affiliation: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden Affiliations: Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden, Centre for Violence Prevention, Karolinska Institutet, Stockholm, Sweden * E-mail: [email protected] Affiliations: Department of Clinical Neuroscience, Division of Psychiatry, Karolinska Institutet, Stockholm, Sweden, Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden, Institute of Neuroscience and Physiology, The Sahlgrenska Academy at Gothenburg University, Gothenburg, Sweden The treatment for transsexualism is sex reassignment, including hormonal treatment and surgery aimed at making the person's body as congruent with the opposite sex as possible. Hazard ratios (HR) with 95% confidence intervals (CI) for mortality and psychiatric morbidity were obtained with Cox regression models, which were adjusted for immigrant status and psychiatric morbidity prior to sex reassignment (adjusted HR [aHR]).Our findings suggest that sex reassignment, although alleviating gender dysphoria, may not suffice as treatment for transsexualism, and should inspire improved psychiatric and somatic care after sex reassignment for this patient group.Funding: Financial support was provided through the regional agreement on medical training and clinical research (ALF) between Stockholm County Council and the Karolinska Institutet, and through grants from the Swedish Medical Research Council (K2008-62x-14647-06-3) and the Royal Swedish Academy of Sciences (Torsten Amundson's Foundation).The treatment for transsexualism includes removal of body hair, vocal training, and cross-sex hormonal treatment aimed at making the person's body as congruent with the opposite sex as possible to alleviate the gender dysphoria.With respect to suicide and deaths from other causes after sex reassignment, an early Swedish study followed 24 transsexual persons for an average of six years and reported one suicide.[9] A large Dutch single-centre study (N = 1,109), focusing on adverse events following hormonal treatment, compared the outcome after cross-sex hormone treatment with national Dutch standardized mortality and morbidity rates and found no increased mortality, with the exception of death from suicide and AIDS in male-to-females 25–39 years of age.[9] , [18] A recent systematic review and meta-analysis concluded that approximately 80% reported subjective improvement in terms of gender dysphoria, quality of life, and psychological symptoms, but also that there are studies reporting high psychiatric morbidity and suicide rates after sex reassignment.[6] , [9] , [12] , [21] , [24] , [28] , [29] , [30] Forth, several follow-up studies are hampered by limited follow-up periods. Here, we assessed mortality, psychiatric morbidity, and psychosocial integration expressed in criminal behaviour after sex reassignment in transsexual persons, in a total population cohort study with long-term follow-up information obtained from Swedish registers.National censuses based on mandatory self-report questionnaires completed by all adult citizens in 1960, 1970, 1980, and 1990 provided information on individuals, households, and dwellings, including gender, living area, and highest educational level.In Sweden, a person presenting with gender dysphoria is referred to one of six specialised gender teams that evaluate and treat patients principally according to international consensus guidelines: Standards of Care.A person was defined as exposed to sex reassignment surgery if two criteria were met: (i) at least one inpatient diagnosis of gender identity disorder diagnosis without concomitant psychiatric diagnoses in the Hospital Discharge Register, and (ii) at least one discrepancy between gender variables in the Medical Birth Register (from 1973 and onwards) or the National Censuses from 1960, 1970, 1980, or 1990 and the latest gender designation in the Total Population Register. The date of sex reassignment (start of follow-up) was defined as the first occurrence of a gender identity disorder diagnosis, without any other concomitant psychiatric disorder, in the Hospital Discharge Register after the patient changed sex status (any discordance in sex designation across the Censuses, Medical Birth, and Total Population registers). Using these criteria, a total of 804 patients with gender identity disorder were identified, whereof 324 displayed a shift in the gender variable during the period 1973–2003.Gender identity disorder was coded according to ICD-8: 302.3 (transsexualism) and 302.9 (sexual deviation NOS); ICD-9: 302 (overall code for sexual deviations and disorders, more specific codes were not available in ICD-9); and ICD-10: F64.0 (transsexualism), F64.1 (dual-role transvestism), F64.8 (other gender identity disorder), and F64.9 (gender identity disorder NOS).To study possible gender-specific effects on outcomes of interest, we used two different control groups: one with the same sex as the case individual at birth (birth sex matching) and the other with the sex that the case individual had been reassigned to (final sex matching).Causes of death (Cause of Death Registry from 1952 and onwards) were defined according to ICD as suicide (ICD-8 and ICD-9 codes E950-E959 and E980-E989, ICD-10 codes X60-X84 and Y10-Y34); cardiovascular disease (ICD-8 codes 390-458, ICD-9 codes 390-459, ICD-10 codes I00-I99); neoplasms (ICD-8 and ICD-9 codes 140-239, ICD-10 codes C00-D48), any psychiatric disorder (gender identity disorders excluded); (ICD-8 codes 290-301 and 303-315, ICD-9 codes 290-301 and 303-319, ICD-10 codes F00-F63 and F65-F99); alcohol/drug abuse and dependence (ICD-8 codes 303-304, ICD-9 codes 303-305 (tobacco use disorder excluded), ICD-10 codes F10-F16 and F18-F19 (x5 excluded); and accidents (ICD-8 and ICD-9 codes E800-E929, ICD-10 codes V01-X59). Any criminal conviction during follow-up was counted; specifically, violent crime was defined as homicide and attempted homicide, aggravated assault and assault, robbery, threatening behaviour, harassment, arson, or any sexual offense. [32] Severe psychiatric morbidity was defined as inpatient care according to ICD-8 codes 291, 295-301, 303-304, and 307; ICD-9 codes 291-292, 295-298, 300-301, 303-305 (tobacco use disorder excluded), 307.1, 307.5, 308-309, and 311; ICD-10 codes F10-F16, F18-F25, F28-F45, F48, F50, and F60-F62.Gender-separated analyses were performed and a Kaplan-Meier survival plot graphically illustrates the survival of the sex reassigned cohort and matched controls (all-cause mortality) over time.Immigrant status was twice as common among transsexual individuals compared to controls, living in an urban area somewhat more common, and higher education about equally prevalent.Even though the overall mortality was increased across both time periods, it did not reach statistical significance for the period 1989–2003.Mortality due to cardiovascular disease was moderately increased among the sex-reassigned, whereas the numerically increased risk for malignancies was borderline statistically significant.Transsexual individuals were at increased risk of being convicted for any crime or violent crime after sex reassignment ( Table 2 ); this was, however, only significant in the group who underwent sex reassignment before 1989.By contrast, female-to-males had significantly increased risk of suicide attempts only compared to male controls (aHR 6.8; 95% CI 2.1–21.6) but not compared to female controls (aHR 1.9; 95% CI 0.7–4.8).Second, regarding any crime, male-to-females had a significantly increased risk for crime compared to female controls (aHR 6.6; 95% CI 4.1–10.8) but not compared to males (aHR 0.8; 95% CI 0.5–1.2).The most striking result was the high mortality rate in both male-to-females and female-to males, compared to the general population.[7] , [9] , [10] , [11] Previous clinical studies might have been biased since people who regard their sex reassignment as a failure are more likely to be lost to follow-up. [35] Mortality due to cardiovascular disease was significantly increased among sex reassigned individuals, albeit these results should be interpreted with caution due to the low number of events. [6] , [8] , [10] , [11] suggest that transsexualism is a strong risk factor for suicide, also after sex reassignment, and our long-term findings support the need for continued psychiatric follow-up for persons at risk to prevent this.A previous study of all applications for sex reassignment in Sweden up to 1992 found that 9.7% of male-to-female and 6.1% of female-to-male applicants had been prosecuted for a crime.Many previous studies suffer from low outcome ascertainment, [6] , [9] , [21] , [29] whereas this study has captured almost the entire population of sex-reassigned transsexual individuals in Sweden from 1973–2003.For the purpose of evaluating whether sex reassignment is an effective treatment for gender dysphoria, it is reasonable to compare reported gender dysphoria pre and post treatment. [7] , [12] or retrospectively, [5] , [6] , [9] , [22] , [25] , [26] , [29] , [38] and suggest that sex reassignment of transsexual persons improves quality of life and gender dysphoria.It is therefore important to note that the current study is only informative with respect to transsexuals persons health after sex reassignment; no inferences can be drawn as to the effectiveness of sex reassignment as a treatment for transsexualism.Finally, to estimate start of follow-up, we prioritized using the date of a gender identity disorder diagnosis after changed sex status over before changed sex status, in order to avoid overestimating person-years at risk after sex-reassignment.This study found substantially higher rates of overall mortality, death from cardiovascular disease and suicide, suicide attempts, and psychiatric hospitalisations in sex-reassigned transsexual individuals compared to a healthy control population.

Hi community,
I'm playing around (mostly for the first time) running Cox regression models on a attrition dataset. My models predict teacher attrition from a school district.
The outcome is the duration of employment (in years). My models control for school type (high school; middle school; elem omitted); job position (bunch of dummy variables); age (year of birth, meaning higher numbers are younger people); and school poverty (a school- variable, defined as the % of students on reduced or free lunch [rfl]).
My main IV of interest is school climate, which reflects the degree to which a principal is supportive. Like poverty, school climate is school level variable (same value assigned to all teachers in the same site). It it takes the school average of teachers responses to some survey questions (about principal supportiveness), where responses were measured on a 4 point agree-to-disagree scale).
The school climate variable is called collab_fac in my models. I was hoping to get a direct effect for collab_fac but it hasn't been supported in the data. However, I am finding an interesting and sensible interaction between school climate and poverty. The negative interaction suggests that the positive effect (i.e., higher hazard rate) of poverty on teacher attrition is attenuated by having a supportive principal. Sensible, I think.
I think I understand how to interpret the direct effects in the model. Yet, while I understand the interaction is negative (since the hazard ratio is < 1), I'm struggling to put the interaction coefficient (.09) into more concrete terms -- e.g., "for every 1 point increase in collab_fac (I probably should have standardized it), the effect of poverty on attrition goes down by X%."
I'm hoping someone will graciously provide some insight here. You can see my Stata code and model output (I include descriptive statistics) at the following Google Docs link.
(https://docs.google.com/document/d/13Hda-JJm0i67B8fasyODKtdedkOUqipnQLcVzb-eFlw/edit?usp=sharing)
Thanks, Poobiedog